lindong28 commented on code in PR #253:
URL: https://github.com/apache/flink-ml/pull/253#discussion_r1313857237


##########
flink-ml-lib/src/main/java/org/apache/flink/ml/anomalydetection/isolationforest/IsolationForestParams.java:
##########
@@ -0,0 +1,56 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.flink.ml.anomalydetection.isolationforest;
+
+import org.apache.flink.ml.common.param.HasDistanceMeasure;
+import org.apache.flink.ml.common.param.HasFeaturesCol;
+import org.apache.flink.ml.common.param.HasPredictionCol;
+import org.apache.flink.ml.common.param.HasWindows;
+import org.apache.flink.ml.param.IntParam;
+import org.apache.flink.ml.param.Param;
+
+/**
+ * Params of {@link IsolationForestModel}.
+ *
+ * @param <T> The class of this instance.
+ */
+public interface IsolationForestParams<T>
+        extends HasDistanceMeasure<T>, HasFeaturesCol<T>, HasPredictionCol<T>, 
HasWindows<T> {
+    Param<Integer> TREES_NUMBER =
+            new IntParam("treesNumber", "The max number of trees to create.", 
2);
+
+    Param<Integer> ITERS =

Review Comment:
   Would it be simpler to re-use HasMaxIter?



##########
flink-ml-lib/src/main/java/org/apache/flink/ml/anomalydetection/isolationforest/IsolationForest.java:
##########
@@ -0,0 +1,611 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.flink.ml.anomalydetection.isolationforest;
+
+import org.apache.flink.api.common.functions.FlatMapFunction;
+import org.apache.flink.api.common.functions.MapFunction;
+import org.apache.flink.api.common.functions.MapPartitionFunction;
+import org.apache.flink.api.common.functions.ReduceFunction;
+import org.apache.flink.api.common.state.ListState;
+import org.apache.flink.api.common.state.ListStateDescriptor;
+import org.apache.flink.api.common.typeinfo.TypeInformation;
+import org.apache.flink.api.common.typeinfo.Types;
+import org.apache.flink.iteration.DataStreamList;
+import org.apache.flink.iteration.IterationBody;
+import org.apache.flink.iteration.IterationBodyResult;
+import org.apache.flink.iteration.IterationConfig;
+import org.apache.flink.iteration.IterationListener;
+import org.apache.flink.iteration.Iterations;
+import org.apache.flink.iteration.ReplayableDataStreamList;
+import org.apache.flink.iteration.datacache.nonkeyed.ListStateWithCache;
+import org.apache.flink.iteration.operator.OperatorStateUtils;
+import org.apache.flink.ml.api.Estimator;
+import org.apache.flink.ml.common.datastream.DataStreamUtils;
+import org.apache.flink.ml.common.iteration.ForwardInputsOfLastRound;
+import org.apache.flink.ml.common.iteration.TerminateOnMaxIter;
+import org.apache.flink.ml.linalg.DenseVector;
+import org.apache.flink.ml.linalg.Vector;
+import org.apache.flink.ml.linalg.typeinfo.DenseVectorTypeInfo;
+import org.apache.flink.ml.param.Param;
+import org.apache.flink.ml.util.ParamUtils;
+import org.apache.flink.ml.util.ReadWriteUtils;
+import org.apache.flink.runtime.state.StateInitializationContext;
+import org.apache.flink.runtime.state.StateSnapshotContext;
+import org.apache.flink.streaming.api.datastream.DataStream;
+import org.apache.flink.streaming.api.datastream.SingleOutputStreamOperator;
+import org.apache.flink.streaming.api.operators.AbstractStreamOperator;
+import org.apache.flink.streaming.api.operators.TwoInputStreamOperator;
+import org.apache.flink.streaming.runtime.streamrecord.StreamRecord;
+import org.apache.flink.table.api.Table;
+import org.apache.flink.table.api.bridge.java.StreamTableEnvironment;
+import org.apache.flink.table.api.internal.TableImpl;
+import org.apache.flink.types.Row;
+import org.apache.flink.util.Collector;
+import org.apache.flink.util.OutputTag;
+import org.apache.flink.util.Preconditions;
+
+import java.io.IOException;
+import java.io.Serializable;
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.HashMap;
+import java.util.Iterator;
+import java.util.List;
+import java.util.Map;
+import java.util.Objects;
+import java.util.Random;
+
+/**
+ * An Estimator which implements the Isolation Forest algorithm.
+ *
+ * <p>See https://en.wikipedia.org/wiki/Isolation_forest.
+ */
+public class IsolationForest
+        implements Estimator<IsolationForest, IsolationForestModel>,
+                IsolationForestParams<IsolationForest> {
+    private final Map<Param<?>, Object> paramMap = new HashMap<>();
+
+    public IsolationForest() {
+        ParamUtils.initializeMapWithDefaultValues(paramMap, this);
+    }
+
+    @Override
+    public IsolationForestModel fit(Table... inputs) {
+        Preconditions.checkArgument(inputs.length == 1);
+        Integer treesNumber = getTreesNumber();
+        Integer iters = getIters();
+        Preconditions.checkArgument(
+                treesNumber != null || treesNumber > 0, "Param treesNumber is 
illegal.");
+        Preconditions.checkArgument(iters != null || iters > 0, "Param iters 
is illegal.");
+        IForest iForest = new IForest(treesNumber, iters);
+        StreamTableEnvironment tEnv =
+                (StreamTableEnvironment) ((TableImpl) 
inputs[0]).getTableEnvironment();
+
+        DataStream<DenseVector[]> points =
+                tEnv.toDataStream(inputs[0]).map(new 
FormatDataMapFunction(getFeaturesCol()));
+
+        DataStream<IForest> initModelData =
+                selectRandomSample1(points).map(new 
InitModelData(iForest)).setParallelism(1);
+
+        DataStream<IsolationForestModelData> finalModelData =
+                Iterations.iterateBoundedStreamsUntilTermination(
+                                DataStreamList.of(initModelData),
+                                ReplayableDataStreamList.notReplay(points),
+                                IterationConfig.newBuilder()
+                                        .setOperatorLifeCycle(
+                                                
IterationConfig.OperatorLifeCycle.ALL_ROUND)
+                                        .build(),
+                                new IsolationForestIterationBody(iters))
+                        .get(0);
+
+        Table finalModelDataTable = tEnv.fromDataStream(finalModelData);
+        IsolationForestModel model = new 
IsolationForestModel().setModelData(finalModelDataTable);
+        ParamUtils.updateExistingParams(model, paramMap);
+        return model;
+    }
+
+    @Override
+    public void save(String path) throws IOException {
+        ReadWriteUtils.saveMetadata(this, path);
+    }
+
+    public static IsolationForestModel load(StreamTableEnvironment tEnv, 
String path)
+            throws IOException {
+        return ReadWriteUtils.loadStageParam(path);
+    }
+
+    @Override
+    public Map<Param<?>, Object> getParamMap() {
+        return paramMap;
+    }
+
+    private static class FormatDataMapFunction implements MapFunction<Row, 
DenseVector[]> {
+        private final String featuresCol;
+        private List<DenseVector> list;
+
+        public FormatDataMapFunction(String featuresCol) {
+            this.featuresCol = featuresCol;
+        }
+
+        @Override
+        public DenseVector[] map(Row row) throws Exception {
+            list = new ArrayList<>(256);
+            DenseVector denseVector = ((Vector) 
row.getField(featuresCol)).toDense();
+            list.add(denseVector);
+            return list.toArray(new DenseVector[0]);
+        }
+    }
+
+    private static DataStream<DenseVector[]> selectRandomSample1(
+            DataStream<DenseVector[]> samplesData) {
+        DataStream<DenseVector[]> resultStream =
+                DataStreamUtils.mapPartition(
+                        DataStreamUtils.sample(samplesData, 256, 
System.currentTimeMillis()),
+                        (MapPartitionFunction<DenseVector[], DenseVector[]>)
+                                (iterable, collector) -> {
+                                    Iterator<DenseVector[]> 
samplesDataIterator =
+                                            iterable.iterator();
+                                    List<DenseVector> list = new ArrayList<>();
+                                    while (samplesDataIterator.hasNext()) {
+                                        
list.addAll(Arrays.asList(samplesDataIterator.next()));
+                                    }
+                                    collector.collect(list.toArray(new 
DenseVector[0]));
+                                },
+                        Types.OBJECT_ARRAY(DenseVectorTypeInfo.INSTANCE));
+        resultStream.getTransformation().setParallelism(1);
+        return resultStream;
+    }
+
+    private static class InitModelData implements MapFunction<DenseVector[], 
IForest> {
+        private final IForest iForest;
+
+        private InitModelData(IForest iForest) {
+            this.iForest = iForest;
+        }
+
+        @Override
+        public IForest map(DenseVector[] denseVectors) throws Exception {
+            iForest.createIForest(denseVectors);
+            DenseVector scores = iForest.calculateAnomalyScore(denseVectors);
+            iForest.classifyByCluster(scores);
+            return iForest;
+        }
+    }
+
+    private static class IsolationForestIterationBody implements IterationBody 
{
+        private final Integer iters;
+
+        public IsolationForestIterationBody(Integer iters) {
+            this.iters = iters;
+        }
+
+        @Override
+        public IterationBodyResult process(
+                DataStreamList variableStreams, DataStreamList dataStreams) {
+            DataStream<IForest> centersData = variableStreams.get(0);
+            DataStream<DenseVector[]> samplesData = dataStreams.get(0);
+            final OutputTag<IForest> modelDataOutputTag =
+                    new OutputTag<IForest>("IsolationForest") {};
+
+            SingleOutputStreamOperator terminationCriteria =
+                    centersData.flatMap(new TerminateOnMaxIter(iters));
+
+            DataStream<IForest> centers =
+                    samplesData
+                            .connect(centersData.broadcast())
+                            .transform(
+                                    "CentersUpdateAccumulator",
+                                    TypeInformation.of(IForest.class),
+                                    new 
CentersUpdateAccumulator(modelDataOutputTag));
+
+            DataStream<IsolationForestModelData> newModelData =
+                    centers.countWindowAll(centers.getParallelism())
+                            .reduce(
+                                    new ReduceFunction<IForest>() {
+                                        @Override
+                                        public IForest reduce(IForest 
iForest1, IForest iForest2)
+                                                throws Exception {
+                                            if (iForest2.center0 == null
+                                                    || iForest2.center1 == 
null) {
+                                                return iForest1;
+                                            }
+                                            return iForest2;
+                                        }
+                                    })
+                            .flatMap(
+                                    new FlatMapFunction<IForest, 
IsolationForestModelData>() {
+                                        @Override
+                                        public void flatMap(
+                                                IForest iForest,
+                                                
Collector<IsolationForestModelData> collector)
+                                                throws Exception {
+                                            if (iForest.center0 != null
+                                                    && iForest.center1 != 
null) {
+                                                collector.collect(
+                                                        new 
IsolationForestModelData(iForest));
+                                            }
+                                        }
+                                    });
+
+            DataStream<IForest> newCenters = newModelData.map(x -> 
x.iForest).setParallelism(1);
+
+            DataStream<IsolationForestModelData> finalModelData =
+                    newModelData.flatMap(new ForwardInputsOfLastRound<>());
+
+            return new IterationBodyResult(
+                    DataStreamList.of(newCenters),
+                    DataStreamList.of(finalModelData),
+                    terminationCriteria);
+        }
+    }
+
+    private static class CentersUpdateAccumulator extends 
AbstractStreamOperator<IForest>
+            implements TwoInputStreamOperator<DenseVector[], IForest, IForest>,
+                    IterationListener<IForest> {
+        private final OutputTag<IForest> modelDataOutputTag;
+
+        private ListStateWithCache<DenseVector[]> samplesData;
+
+        private ListState<IForest> samplesDataCenter;
+
+        private ListStateWithCache<DenseVector[]> samplesDataScores;
+
+        public CentersUpdateAccumulator(OutputTag<IForest> modelDataOutputTag) 
{
+            this.modelDataOutputTag = modelDataOutputTag;
+        }
+
+        @Override
+        public void initializeState(StateInitializationContext context) throws 
Exception {
+            super.initializeState(context);
+
+            samplesDataCenter =
+                    context.getOperatorStateStore()
+                            .getListState(
+                                    new ListStateDescriptor<IForest>(
+                                            "centers", 
TypeInformation.of(IForest.class)));
+
+            samplesData =
+                    new ListStateWithCache<>(
+                            Types.OBJECT_ARRAY(DenseVectorTypeInfo.INSTANCE)
+                                    .createSerializer(getExecutionConfig()),
+                            getContainingTask(),
+                            getRuntimeContext(),
+                            context,
+                            config.getOperatorID());
+
+            samplesDataScores =
+                    new ListStateWithCache<>(
+                            Types.OBJECT_ARRAY(DenseVectorTypeInfo.INSTANCE)
+                                    .createSerializer(getExecutionConfig()),
+                            getContainingTask(),
+                            getRuntimeContext(),
+                            context,
+                            config.getOperatorID());
+        }
+
+        @Override
+        public void snapshotState(StateSnapshotContext context) throws 
Exception {
+            super.snapshotState(context);
+            samplesData.snapshotState(context);
+        }
+
+        @Override
+        public void processElement1(StreamRecord<DenseVector[]> streamRecord) 
throws Exception {
+            samplesData.add(streamRecord.getValue());
+        }
+
+        @Override
+        public void processElement2(StreamRecord<IForest> streamRecord) throws 
Exception {
+            
Preconditions.checkState(!samplesDataCenter.get().iterator().hasNext());
+            samplesDataCenter.add(streamRecord.getValue());
+        }
+
+        @Override
+        public void onEpochWatermarkIncremented(
+                int epochWatermark, Context context, Collector<IForest> 
collector)
+                throws Exception {
+            IForest centers =
+                    Objects.requireNonNull(
+                            
OperatorStateUtils.getUniqueElement(samplesDataCenter, "centers")
+                                    .orElse(null));
+            Iterator<DenseVector[]> samplesDataIterator = 
samplesData.get().iterator();
+            List<DenseVector> list = new ArrayList<>();
+            while (samplesDataIterator.hasNext()) {
+                DenseVector[] sampleData = samplesDataIterator.next();
+                list.add(centers.calculateAnomalyScore(sampleData));
+            }
+            DenseVector[] scores = list.toArray(new DenseVector[0]);
+            samplesDataScores.add(scores);
+
+            collector.collect(samplesDataCenter.get().iterator().next());
+            samplesDataCenter.clear();
+        }
+
+        @Override
+        public void onIterationTerminated(Context context, Collector<IForest> 
collector)
+                throws Exception {
+            IForest centers =
+                    Objects.requireNonNull(
+                            
OperatorStateUtils.getUniqueElement(samplesDataCenter, "centers")
+                                    .orElse(null));
+            double centers0Sum1 = 0.0, centers1Sum1 = 0.0, centers0Sum2 = 0.0, 
centers1Sum2 = 0.0;
+            int size1 = 0, size2 = 0;
+            Iterator<DenseVector[]> samplesDataScoresIterator = 
samplesDataScores.get().iterator();
+            while (samplesDataScoresIterator.hasNext()) {
+                for (DenseVector denseVector : 
samplesDataScoresIterator.next()) {
+                    DenseVector denseVector1 = 
centers.classifyByCluster(denseVector);
+                    centers0Sum1 += denseVector1.get(0);
+                    centers1Sum1 += denseVector1.get(1);
+                    size1++;
+                }
+                centers0Sum2 = centers0Sum1 / size1;
+                centers1Sum2 = centers1Sum1 / size1;
+                size2++;
+            }
+
+            centers.center0 = centers0Sum2 / size2;
+            centers.center1 = centers1Sum2 / size2;
+
+            context.output(modelDataOutputTag, centers);
+
+            samplesDataCenter.clear();
+            samplesDataScores.clear();
+            samplesData.clear();
+        }
+    }
+
+    /** Construct isolation forest. */
+    public static class IForest implements Serializable {
+        public int treesNumber;
+        public int iters;
+        public List<ITree> iTreeList;
+        public Double center0;
+        public Double center1;
+        public int subSamplesSize;
+
+        public IForest() {}
+
+        public IForest(int treesNumber, int iters) {
+            this.iters = iters;
+            this.treesNumber = treesNumber;
+            this.iTreeList = new ArrayList<>();
+            this.center0 = null;
+            this.center1 = null;
+        }
+
+        private void createIForest(DenseVector[] samplesData) throws Exception 
{
+            this.subSamplesSize = Math.min(256, samplesData.length);
+
+            // 限制高度(向上取整)
+            int limitHeight = (int) Math.ceil(Math.log(subSamplesSize) / 
Math.log(2));
+
+            int rows = samplesData.length;
+
+            Random random = new Random(System.currentTimeMillis());
+            for (int i = 0; i < this.treesNumber; i++) {
+                DenseVector[] subSamples = new DenseVector[subSamplesSize];
+                for (int j = 0; j < subSamplesSize; j++) {
+                    int r = random.nextInt(rows);
+                    subSamples[j] = samplesData[r];
+                }
+                ITree iTree = ITree.createITree(subSamples, 0, limitHeight);
+                this.iTreeList.add(iTree);
+            }
+        }
+
+        private DenseVector calculateAnomalyScore(DenseVector[] samplesData) 
throws Exception {
+            int n = samplesData.length;
+
+            DenseVector scores = new DenseVector(n);
+            for (int i = 0; i < n; i++) {
+                double pathLengthSum = 0;
+                for (ITree iTree : iTreeList) {
+                    pathLengthSum += calculatePathLength(samplesData[i], 
iTree);
+                }
+
+                double pathLengthAvg = pathLengthSum / iTreeList.size();
+                double cn = calculateCn(subSamplesSize);
+                double index = pathLengthAvg / cn;
+                scores.set(i, Math.pow(2, -index));
+            }
+            return scores;
+        }
+
+        private double calculatePathLength(DenseVector sampleData, ITree 
iTree) throws Exception {
+            double pathLength = -1;
+            ITree tmpITree = iTree;
+            while (tmpITree != null) {
+                pathLength += 1;
+                if (tmpITree.leftTree == null
+                        || tmpITree.rightTree == null
+                        || sampleData.get(tmpITree.attributeIndex)
+                                == tmpITree.splitAttributeValue) {
+                    break;
+                } else if (sampleData.get(tmpITree.attributeIndex) < 
tmpITree.splitAttributeValue) {
+                    tmpITree = tmpITree.leftTree;
+                } else {
+                    tmpITree = tmpITree.rightTree;
+                }
+            }
+
+            return pathLength + calculateCn(tmpITree.leafNodesNum);
+        }
+
+        private double calculateCn(double n) {
+            if (n <= 1) {
+                return 0;
+            }
+            return 2.0 * (Math.log(n - 1.0) + 0.5772156649015329) - 2.0 * (n - 
1.0) / n;
+        }
+
+        private DenseVector classifyByCluster(DenseVector scores) {
+            int scoresSize = scores.size();
+            this.center0 = scores.get(0); // Cluster center of abnormal
+            this.center1 = scores.get(0); // Cluster center of normal
+
+            for (int p = 1; p < scores.size(); p++) {
+                if (scores.get(p) > center0) {
+                    center0 = scores.get(p);
+                }
+
+                if (scores.get(p) < center1) {
+                    center1 = scores.get(p);
+                }
+            }
+
+            int cnt0, cnt1;
+            double diff0, diff1;
+            int[] labels = new int[scoresSize];
+
+            for (int i = 0; i < iters; i++) {
+                cnt0 = 0;
+                cnt1 = 0;
+
+                for (int j = 0; j < scoresSize; j++) {
+                    diff0 = Math.abs(scores.get(j) - center0);
+                    diff1 = Math.abs(scores.get(j) - center1);
+
+                    if (diff0 < diff1) {
+                        labels[j] = 0;
+                        cnt0++;
+                    } else {
+                        labels[j] = 1;
+                        cnt1++;
+                    }
+                }
+
+                diff0 = center0;
+                diff1 = center1;
+
+                center0 = 0.0;
+                center1 = 0.0;
+                for (int k = 0; k < scoresSize; k++) {
+                    if (labels[k] == 0) {
+                        center0 += scores.get(k);
+                    } else {
+                        center1 += scores.get(k);
+                    }
+                }
+
+                center0 /= cnt0;
+                center1 /= cnt1;
+
+                if (center0 - diff0 <= 1e-6 && center1 - diff1 <= 1e-6) {
+                    break;
+                }
+            }
+            return new DenseVector(new double[] {center0, center1});
+        }
+    }
+
+    /** Construct isolation tree. */
+    public static class ITree implements Serializable {
+        public int attributeIndex;

Review Comment:
   Can we mark these variables `final` if possible?
   
   `final` variables are immutable and more readable in general.



##########
flink-ml-lib/src/main/java/org/apache/flink/ml/anomalydetection/isolationforest/IsolationForestModelData.java:
##########
@@ -0,0 +1,111 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.flink.ml.anomalydetection.isolationforest;
+
+import org.apache.flink.api.common.ExecutionConfig;
+import org.apache.flink.api.common.serialization.Encoder;
+import org.apache.flink.api.common.typeinfo.TypeInformation;
+import org.apache.flink.api.common.typeutils.TypeSerializer;
+import org.apache.flink.configuration.Configuration;
+import org.apache.flink.connector.file.src.reader.SimpleStreamFormat;
+import org.apache.flink.core.fs.FSDataInputStream;
+import org.apache.flink.core.memory.DataInputViewStreamWrapper;
+import org.apache.flink.core.memory.DataOutputViewStreamWrapper;
+import 
org.apache.flink.ml.anomalydetection.isolationforest.IsolationForest.IForest;
+import org.apache.flink.streaming.api.datastream.DataStream;
+import org.apache.flink.table.api.Table;
+import org.apache.flink.table.api.bridge.java.StreamTableEnvironment;
+import org.apache.flink.table.api.internal.TableImpl;
+
+import java.io.EOFException;
+import java.io.IOException;
+import java.io.OutputStream;
+
+/**
+ * Model data of {@link IsolationForestModel}.
+ *
+ * <p>This class also provides methods to convert model data from Table to 
Datastream, and classes
+ * to save/load model data.
+ */
+public class IsolationForestModelData {
+
+    public IForest iForest;

Review Comment:
   Can we move the definition of the data structure which represents the model 
data from `IsolationForest.java` to `IsolationForestModelData.java`? This can 
make the code a bit more readable by separating data structure from the 
training/processing logic.
   
   This can also make the code more consistent with the existing code style.



##########
flink-ml-lib/src/main/java/org/apache/flink/ml/anomalydetection/isolationforest/IsolationForestParams.java:
##########
@@ -0,0 +1,56 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.flink.ml.anomalydetection.isolationforest;
+
+import org.apache.flink.ml.common.param.HasDistanceMeasure;
+import org.apache.flink.ml.common.param.HasFeaturesCol;
+import org.apache.flink.ml.common.param.HasPredictionCol;
+import org.apache.flink.ml.common.param.HasWindows;
+import org.apache.flink.ml.param.IntParam;
+import org.apache.flink.ml.param.Param;
+
+/**
+ * Params of {@link IsolationForestModel}.
+ *
+ * @param <T> The class of this instance.
+ */
+public interface IsolationForestParams<T>
+        extends HasDistanceMeasure<T>, HasFeaturesCol<T>, HasPredictionCol<T>, 
HasWindows<T> {
+    Param<Integer> TREES_NUMBER =
+            new IntParam("treesNumber", "The max number of trees to create.", 
2);

Review Comment:
   It seems that `IForest#iTreeList` would contain exactly the given number of 
trees. Would it be more accurate to specify "The number of trees" in the doc?
   
   If yes, it might be better to name this parameter `numTrees` for consistency 
with the `numTrees` parameter used by 
`org.apache.spark.mllib.tree.RandomForest` in Spark ML.



##########
flink-ml-lib/src/main/java/org/apache/flink/ml/anomalydetection/isolationforest/IsolationForest.java:
##########
@@ -0,0 +1,611 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.flink.ml.anomalydetection.isolationforest;
+
+import org.apache.flink.api.common.functions.FlatMapFunction;
+import org.apache.flink.api.common.functions.MapFunction;
+import org.apache.flink.api.common.functions.MapPartitionFunction;
+import org.apache.flink.api.common.functions.ReduceFunction;
+import org.apache.flink.api.common.state.ListState;
+import org.apache.flink.api.common.state.ListStateDescriptor;
+import org.apache.flink.api.common.typeinfo.TypeInformation;
+import org.apache.flink.api.common.typeinfo.Types;
+import org.apache.flink.iteration.DataStreamList;
+import org.apache.flink.iteration.IterationBody;
+import org.apache.flink.iteration.IterationBodyResult;
+import org.apache.flink.iteration.IterationConfig;
+import org.apache.flink.iteration.IterationListener;
+import org.apache.flink.iteration.Iterations;
+import org.apache.flink.iteration.ReplayableDataStreamList;
+import org.apache.flink.iteration.datacache.nonkeyed.ListStateWithCache;
+import org.apache.flink.iteration.operator.OperatorStateUtils;
+import org.apache.flink.ml.api.Estimator;
+import org.apache.flink.ml.common.datastream.DataStreamUtils;
+import org.apache.flink.ml.common.iteration.ForwardInputsOfLastRound;
+import org.apache.flink.ml.common.iteration.TerminateOnMaxIter;
+import org.apache.flink.ml.linalg.DenseVector;
+import org.apache.flink.ml.linalg.Vector;
+import org.apache.flink.ml.linalg.typeinfo.DenseVectorTypeInfo;
+import org.apache.flink.ml.param.Param;
+import org.apache.flink.ml.util.ParamUtils;
+import org.apache.flink.ml.util.ReadWriteUtils;
+import org.apache.flink.runtime.state.StateInitializationContext;
+import org.apache.flink.runtime.state.StateSnapshotContext;
+import org.apache.flink.streaming.api.datastream.DataStream;
+import org.apache.flink.streaming.api.datastream.SingleOutputStreamOperator;
+import org.apache.flink.streaming.api.operators.AbstractStreamOperator;
+import org.apache.flink.streaming.api.operators.TwoInputStreamOperator;
+import org.apache.flink.streaming.runtime.streamrecord.StreamRecord;
+import org.apache.flink.table.api.Table;
+import org.apache.flink.table.api.bridge.java.StreamTableEnvironment;
+import org.apache.flink.table.api.internal.TableImpl;
+import org.apache.flink.types.Row;
+import org.apache.flink.util.Collector;
+import org.apache.flink.util.OutputTag;
+import org.apache.flink.util.Preconditions;
+
+import java.io.IOException;
+import java.io.Serializable;
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.HashMap;
+import java.util.Iterator;
+import java.util.List;
+import java.util.Map;
+import java.util.Objects;
+import java.util.Random;
+
+/**
+ * An Estimator which implements the Isolation Forest algorithm.
+ *
+ * <p>See https://en.wikipedia.org/wiki/Isolation_forest.
+ */
+public class IsolationForest
+        implements Estimator<IsolationForest, IsolationForestModel>,
+                IsolationForestParams<IsolationForest> {
+    private final Map<Param<?>, Object> paramMap = new HashMap<>();
+
+    public IsolationForest() {
+        ParamUtils.initializeMapWithDefaultValues(paramMap, this);
+    }
+
+    @Override
+    public IsolationForestModel fit(Table... inputs) {
+        Preconditions.checkArgument(inputs.length == 1);
+        Integer treesNumber = getTreesNumber();
+        Integer iters = getIters();
+        Preconditions.checkArgument(
+                treesNumber != null || treesNumber > 0, "Param treesNumber is 
illegal.");
+        Preconditions.checkArgument(iters != null || iters > 0, "Param iters 
is illegal.");
+        IForest iForest = new IForest(treesNumber, iters);
+        StreamTableEnvironment tEnv =
+                (StreamTableEnvironment) ((TableImpl) 
inputs[0]).getTableEnvironment();
+
+        DataStream<DenseVector[]> points =
+                tEnv.toDataStream(inputs[0]).map(new 
FormatDataMapFunction(getFeaturesCol()));
+
+        DataStream<IForest> initModelData =
+                selectRandomSample1(points).map(new 
InitModelData(iForest)).setParallelism(1);
+
+        DataStream<IsolationForestModelData> finalModelData =
+                Iterations.iterateBoundedStreamsUntilTermination(
+                                DataStreamList.of(initModelData),
+                                ReplayableDataStreamList.notReplay(points),
+                                IterationConfig.newBuilder()
+                                        .setOperatorLifeCycle(
+                                                
IterationConfig.OperatorLifeCycle.ALL_ROUND)
+                                        .build(),
+                                new IsolationForestIterationBody(iters))
+                        .get(0);
+
+        Table finalModelDataTable = tEnv.fromDataStream(finalModelData);
+        IsolationForestModel model = new 
IsolationForestModel().setModelData(finalModelDataTable);
+        ParamUtils.updateExistingParams(model, paramMap);
+        return model;
+    }
+
+    @Override
+    public void save(String path) throws IOException {
+        ReadWriteUtils.saveMetadata(this, path);
+    }
+
+    public static IsolationForestModel load(StreamTableEnvironment tEnv, 
String path)
+            throws IOException {
+        return ReadWriteUtils.loadStageParam(path);
+    }
+
+    @Override
+    public Map<Param<?>, Object> getParamMap() {
+        return paramMap;
+    }
+
+    private static class FormatDataMapFunction implements MapFunction<Row, 
DenseVector[]> {
+        private final String featuresCol;
+        private List<DenseVector> list;
+
+        public FormatDataMapFunction(String featuresCol) {
+            this.featuresCol = featuresCol;
+        }
+
+        @Override
+        public DenseVector[] map(Row row) throws Exception {
+            list = new ArrayList<>(256);
+            DenseVector denseVector = ((Vector) 
row.getField(featuresCol)).toDense();
+            list.add(denseVector);
+            return list.toArray(new DenseVector[0]);
+        }
+    }
+
+    private static DataStream<DenseVector[]> selectRandomSample1(
+            DataStream<DenseVector[]> samplesData) {
+        DataStream<DenseVector[]> resultStream =
+                DataStreamUtils.mapPartition(
+                        DataStreamUtils.sample(samplesData, 256, 
System.currentTimeMillis()),
+                        (MapPartitionFunction<DenseVector[], DenseVector[]>)
+                                (iterable, collector) -> {
+                                    Iterator<DenseVector[]> 
samplesDataIterator =
+                                            iterable.iterator();
+                                    List<DenseVector> list = new ArrayList<>();
+                                    while (samplesDataIterator.hasNext()) {
+                                        
list.addAll(Arrays.asList(samplesDataIterator.next()));
+                                    }
+                                    collector.collect(list.toArray(new 
DenseVector[0]));
+                                },
+                        Types.OBJECT_ARRAY(DenseVectorTypeInfo.INSTANCE));
+        resultStream.getTransformation().setParallelism(1);
+        return resultStream;
+    }
+
+    private static class InitModelData implements MapFunction<DenseVector[], 
IForest> {
+        private final IForest iForest;
+
+        private InitModelData(IForest iForest) {
+            this.iForest = iForest;
+        }
+
+        @Override
+        public IForest map(DenseVector[] denseVectors) throws Exception {
+            iForest.createIForest(denseVectors);
+            DenseVector scores = iForest.calculateAnomalyScore(denseVectors);
+            iForest.classifyByCluster(scores);
+            return iForest;
+        }
+    }
+
+    private static class IsolationForestIterationBody implements IterationBody 
{
+        private final Integer iters;
+
+        public IsolationForestIterationBody(Integer iters) {
+            this.iters = iters;
+        }
+
+        @Override
+        public IterationBodyResult process(
+                DataStreamList variableStreams, DataStreamList dataStreams) {
+            DataStream<IForest> centersData = variableStreams.get(0);
+            DataStream<DenseVector[]> samplesData = dataStreams.get(0);
+            final OutputTag<IForest> modelDataOutputTag =
+                    new OutputTag<IForest>("IsolationForest") {};
+
+            SingleOutputStreamOperator terminationCriteria =
+                    centersData.flatMap(new TerminateOnMaxIter(iters));
+
+            DataStream<IForest> centers =
+                    samplesData
+                            .connect(centersData.broadcast())
+                            .transform(
+                                    "CentersUpdateAccumulator",
+                                    TypeInformation.of(IForest.class),
+                                    new 
CentersUpdateAccumulator(modelDataOutputTag));
+
+            DataStream<IsolationForestModelData> newModelData =
+                    centers.countWindowAll(centers.getParallelism())
+                            .reduce(
+                                    new ReduceFunction<IForest>() {
+                                        @Override
+                                        public IForest reduce(IForest 
iForest1, IForest iForest2)
+                                                throws Exception {
+                                            if (iForest2.center0 == null
+                                                    || iForest2.center1 == 
null) {
+                                                return iForest1;
+                                            }
+                                            return iForest2;
+                                        }
+                                    })
+                            .flatMap(
+                                    new FlatMapFunction<IForest, 
IsolationForestModelData>() {
+                                        @Override
+                                        public void flatMap(
+                                                IForest iForest,
+                                                
Collector<IsolationForestModelData> collector)
+                                                throws Exception {
+                                            if (iForest.center0 != null
+                                                    && iForest.center1 != 
null) {
+                                                collector.collect(
+                                                        new 
IsolationForestModelData(iForest));
+                                            }
+                                        }
+                                    });
+
+            DataStream<IForest> newCenters = newModelData.map(x -> 
x.iForest).setParallelism(1);
+
+            DataStream<IsolationForestModelData> finalModelData =
+                    newModelData.flatMap(new ForwardInputsOfLastRound<>());
+
+            return new IterationBodyResult(
+                    DataStreamList.of(newCenters),
+                    DataStreamList.of(finalModelData),
+                    terminationCriteria);
+        }
+    }
+
+    private static class CentersUpdateAccumulator extends 
AbstractStreamOperator<IForest>
+            implements TwoInputStreamOperator<DenseVector[], IForest, IForest>,
+                    IterationListener<IForest> {
+        private final OutputTag<IForest> modelDataOutputTag;
+
+        private ListStateWithCache<DenseVector[]> samplesData;
+
+        private ListState<IForest> samplesDataCenter;
+
+        private ListStateWithCache<DenseVector[]> samplesDataScores;
+
+        public CentersUpdateAccumulator(OutputTag<IForest> modelDataOutputTag) 
{
+            this.modelDataOutputTag = modelDataOutputTag;
+        }
+
+        @Override
+        public void initializeState(StateInitializationContext context) throws 
Exception {
+            super.initializeState(context);
+
+            samplesDataCenter =
+                    context.getOperatorStateStore()
+                            .getListState(
+                                    new ListStateDescriptor<IForest>(
+                                            "centers", 
TypeInformation.of(IForest.class)));
+
+            samplesData =
+                    new ListStateWithCache<>(
+                            Types.OBJECT_ARRAY(DenseVectorTypeInfo.INSTANCE)
+                                    .createSerializer(getExecutionConfig()),
+                            getContainingTask(),
+                            getRuntimeContext(),
+                            context,
+                            config.getOperatorID());
+
+            samplesDataScores =
+                    new ListStateWithCache<>(
+                            Types.OBJECT_ARRAY(DenseVectorTypeInfo.INSTANCE)
+                                    .createSerializer(getExecutionConfig()),
+                            getContainingTask(),
+                            getRuntimeContext(),
+                            context,
+                            config.getOperatorID());
+        }
+
+        @Override
+        public void snapshotState(StateSnapshotContext context) throws 
Exception {
+            super.snapshotState(context);
+            samplesData.snapshotState(context);
+        }
+
+        @Override
+        public void processElement1(StreamRecord<DenseVector[]> streamRecord) 
throws Exception {
+            samplesData.add(streamRecord.getValue());
+        }
+
+        @Override
+        public void processElement2(StreamRecord<IForest> streamRecord) throws 
Exception {
+            
Preconditions.checkState(!samplesDataCenter.get().iterator().hasNext());
+            samplesDataCenter.add(streamRecord.getValue());
+        }
+
+        @Override
+        public void onEpochWatermarkIncremented(
+                int epochWatermark, Context context, Collector<IForest> 
collector)
+                throws Exception {
+            IForest centers =
+                    Objects.requireNonNull(
+                            
OperatorStateUtils.getUniqueElement(samplesDataCenter, "centers")
+                                    .orElse(null));
+            Iterator<DenseVector[]> samplesDataIterator = 
samplesData.get().iterator();
+            List<DenseVector> list = new ArrayList<>();
+            while (samplesDataIterator.hasNext()) {
+                DenseVector[] sampleData = samplesDataIterator.next();
+                list.add(centers.calculateAnomalyScore(sampleData));
+            }
+            DenseVector[] scores = list.toArray(new DenseVector[0]);
+            samplesDataScores.add(scores);
+
+            collector.collect(samplesDataCenter.get().iterator().next());
+            samplesDataCenter.clear();
+        }
+
+        @Override
+        public void onIterationTerminated(Context context, Collector<IForest> 
collector)
+                throws Exception {
+            IForest centers =
+                    Objects.requireNonNull(
+                            
OperatorStateUtils.getUniqueElement(samplesDataCenter, "centers")
+                                    .orElse(null));
+            double centers0Sum1 = 0.0, centers1Sum1 = 0.0, centers0Sum2 = 0.0, 
centers1Sum2 = 0.0;
+            int size1 = 0, size2 = 0;
+            Iterator<DenseVector[]> samplesDataScoresIterator = 
samplesDataScores.get().iterator();
+            while (samplesDataScoresIterator.hasNext()) {
+                for (DenseVector denseVector : 
samplesDataScoresIterator.next()) {
+                    DenseVector denseVector1 = 
centers.classifyByCluster(denseVector);
+                    centers0Sum1 += denseVector1.get(0);
+                    centers1Sum1 += denseVector1.get(1);
+                    size1++;
+                }
+                centers0Sum2 = centers0Sum1 / size1;
+                centers1Sum2 = centers1Sum1 / size1;
+                size2++;
+            }
+
+            centers.center0 = centers0Sum2 / size2;
+            centers.center1 = centers1Sum2 / size2;
+
+            context.output(modelDataOutputTag, centers);
+
+            samplesDataCenter.clear();
+            samplesDataScores.clear();
+            samplesData.clear();
+        }
+    }
+
+    /** Construct isolation forest. */
+    public static class IForest implements Serializable {
+        public int treesNumber;
+        public int iters;
+        public List<ITree> iTreeList;
+        public Double center0;
+        public Double center1;
+        public int subSamplesSize;
+
+        public IForest() {}
+
+        public IForest(int treesNumber, int iters) {
+            this.iters = iters;
+            this.treesNumber = treesNumber;
+            this.iTreeList = new ArrayList<>();
+            this.center0 = null;
+            this.center1 = null;
+        }
+
+        private void createIForest(DenseVector[] samplesData) throws Exception 
{
+            this.subSamplesSize = Math.min(256, samplesData.length);
+
+            // 限制高度(向上取整)
+            int limitHeight = (int) Math.ceil(Math.log(subSamplesSize) / 
Math.log(2));
+
+            int rows = samplesData.length;
+
+            Random random = new Random(System.currentTimeMillis());
+            for (int i = 0; i < this.treesNumber; i++) {
+                DenseVector[] subSamples = new DenseVector[subSamplesSize];
+                for (int j = 0; j < subSamplesSize; j++) {
+                    int r = random.nextInt(rows);
+                    subSamples[j] = samplesData[r];
+                }
+                ITree iTree = ITree.createITree(subSamples, 0, limitHeight);
+                this.iTreeList.add(iTree);
+            }
+        }
+
+        private DenseVector calculateAnomalyScore(DenseVector[] samplesData) 
throws Exception {
+            int n = samplesData.length;
+
+            DenseVector scores = new DenseVector(n);
+            for (int i = 0; i < n; i++) {
+                double pathLengthSum = 0;
+                for (ITree iTree : iTreeList) {
+                    pathLengthSum += calculatePathLength(samplesData[i], 
iTree);
+                }
+
+                double pathLengthAvg = pathLengthSum / iTreeList.size();
+                double cn = calculateCn(subSamplesSize);
+                double index = pathLengthAvg / cn;
+                scores.set(i, Math.pow(2, -index));
+            }
+            return scores;
+        }
+
+        private double calculatePathLength(DenseVector sampleData, ITree 
iTree) throws Exception {
+            double pathLength = -1;
+            ITree tmpITree = iTree;
+            while (tmpITree != null) {
+                pathLength += 1;
+                if (tmpITree.leftTree == null
+                        || tmpITree.rightTree == null
+                        || sampleData.get(tmpITree.attributeIndex)
+                                == tmpITree.splitAttributeValue) {
+                    break;
+                } else if (sampleData.get(tmpITree.attributeIndex) < 
tmpITree.splitAttributeValue) {
+                    tmpITree = tmpITree.leftTree;
+                } else {
+                    tmpITree = tmpITree.rightTree;
+                }
+            }
+
+            return pathLength + calculateCn(tmpITree.leafNodesNum);
+        }
+
+        private double calculateCn(double n) {
+            if (n <= 1) {
+                return 0;
+            }
+            return 2.0 * (Math.log(n - 1.0) + 0.5772156649015329) - 2.0 * (n - 
1.0) / n;
+        }
+
+        private DenseVector classifyByCluster(DenseVector scores) {
+            int scoresSize = scores.size();
+            this.center0 = scores.get(0); // Cluster center of abnormal
+            this.center1 = scores.get(0); // Cluster center of normal
+
+            for (int p = 1; p < scores.size(); p++) {
+                if (scores.get(p) > center0) {
+                    center0 = scores.get(p);
+                }
+
+                if (scores.get(p) < center1) {
+                    center1 = scores.get(p);
+                }
+            }
+
+            int cnt0, cnt1;
+            double diff0, diff1;
+            int[] labels = new int[scoresSize];
+
+            for (int i = 0; i < iters; i++) {
+                cnt0 = 0;
+                cnt1 = 0;
+
+                for (int j = 0; j < scoresSize; j++) {
+                    diff0 = Math.abs(scores.get(j) - center0);
+                    diff1 = Math.abs(scores.get(j) - center1);
+
+                    if (diff0 < diff1) {
+                        labels[j] = 0;
+                        cnt0++;
+                    } else {
+                        labels[j] = 1;
+                        cnt1++;
+                    }
+                }
+
+                diff0 = center0;
+                diff1 = center1;
+
+                center0 = 0.0;
+                center1 = 0.0;
+                for (int k = 0; k < scoresSize; k++) {
+                    if (labels[k] == 0) {
+                        center0 += scores.get(k);
+                    } else {
+                        center1 += scores.get(k);
+                    }
+                }
+
+                center0 /= cnt0;
+                center1 /= cnt1;
+
+                if (center0 - diff0 <= 1e-6 && center1 - diff1 <= 1e-6) {
+                    break;
+                }
+            }
+            return new DenseVector(new double[] {center0, center1});
+        }
+    }
+
+    /** Construct isolation tree. */
+    public static class ITree implements Serializable {
+        public int attributeIndex;
+        public double splitAttributeValue;
+        public ITree leftTree, rightTree;

Review Comment:
   Can we declare one variable at a line for consistency with the existing code 
style?



##########
flink-ml-lib/src/main/java/org/apache/flink/ml/anomalydetection/isolationforest/IsolationForestParams.java:
##########
@@ -0,0 +1,56 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.flink.ml.anomalydetection.isolationforest;
+
+import org.apache.flink.ml.common.param.HasDistanceMeasure;
+import org.apache.flink.ml.common.param.HasFeaturesCol;
+import org.apache.flink.ml.common.param.HasPredictionCol;
+import org.apache.flink.ml.common.param.HasWindows;
+import org.apache.flink.ml.param.IntParam;
+import org.apache.flink.ml.param.Param;
+
+/**
+ * Params of {@link IsolationForestModel}.
+ *
+ * @param <T> The class of this instance.
+ */
+public interface IsolationForestParams<T>

Review Comment:
   Would it be better to let `IsolationForestParams` extend 
`IsolationForestModelParams` for consistency with e.g. how 
`LogisticRegressionParams` extends `LogisticRegressionModelParams`?
   
   This change can make it explicit that the estimator parameters covers all 
the corresponding model's parameter.



##########
flink-ml-lib/src/main/java/org/apache/flink/ml/anomalydetection/isolationforest/IsolationForestModel.java:
##########
@@ -0,0 +1,200 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.flink.ml.anomalydetection.isolationforest;
+
+import org.apache.flink.api.common.functions.RichMapFunction;
+import org.apache.flink.api.common.typeinfo.BasicTypeInfo;
+import org.apache.flink.api.java.typeutils.RowTypeInfo;
+import 
org.apache.flink.ml.anomalydetection.isolationforest.IsolationForest.ITree;
+import org.apache.flink.ml.api.Model;
+import org.apache.flink.ml.common.broadcast.BroadcastUtils;
+import org.apache.flink.ml.common.datastream.TableUtils;
+import org.apache.flink.ml.linalg.DenseVector;
+import org.apache.flink.ml.linalg.Vector;
+import org.apache.flink.ml.param.Param;
+import org.apache.flink.ml.util.ParamUtils;
+import org.apache.flink.ml.util.ReadWriteUtils;
+import org.apache.flink.ml.util.RowUtils;
+import org.apache.flink.streaming.api.datastream.DataStream;
+import org.apache.flink.table.api.Table;
+import org.apache.flink.table.api.bridge.java.StreamTableEnvironment;
+import org.apache.flink.table.api.internal.TableImpl;
+import org.apache.flink.types.Row;
+import org.apache.flink.util.Preconditions;
+
+import org.apache.commons.lang3.ArrayUtils;
+
+import java.io.IOException;
+import java.util.Collections;
+import java.util.HashMap;
+import java.util.List;
+import java.util.Map;
+
+/**
+ * A Model which detection anomaly data using the model data computed by 
{@link IsolationForest}.
+ */
+public class IsolationForestModel
+        implements Model<IsolationForestModel>, 
IsolationForestParams<IsolationForestModel> {

Review Comment:
   Would it be better to replace `IsolationForestParams` with 
`IsolationForestModelParams` in this line?



##########
flink-ml-lib/src/main/java/org/apache/flink/ml/anomalydetection/isolationforest/IsolationForest.java:
##########
@@ -0,0 +1,611 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.flink.ml.anomalydetection.isolationforest;
+
+import org.apache.flink.api.common.functions.FlatMapFunction;
+import org.apache.flink.api.common.functions.MapFunction;
+import org.apache.flink.api.common.functions.MapPartitionFunction;
+import org.apache.flink.api.common.functions.ReduceFunction;
+import org.apache.flink.api.common.state.ListState;
+import org.apache.flink.api.common.state.ListStateDescriptor;
+import org.apache.flink.api.common.typeinfo.TypeInformation;
+import org.apache.flink.api.common.typeinfo.Types;
+import org.apache.flink.iteration.DataStreamList;
+import org.apache.flink.iteration.IterationBody;
+import org.apache.flink.iteration.IterationBodyResult;
+import org.apache.flink.iteration.IterationConfig;
+import org.apache.flink.iteration.IterationListener;
+import org.apache.flink.iteration.Iterations;
+import org.apache.flink.iteration.ReplayableDataStreamList;
+import org.apache.flink.iteration.datacache.nonkeyed.ListStateWithCache;
+import org.apache.flink.iteration.operator.OperatorStateUtils;
+import org.apache.flink.ml.api.Estimator;
+import org.apache.flink.ml.common.datastream.DataStreamUtils;
+import org.apache.flink.ml.common.iteration.ForwardInputsOfLastRound;
+import org.apache.flink.ml.common.iteration.TerminateOnMaxIter;
+import org.apache.flink.ml.linalg.DenseVector;
+import org.apache.flink.ml.linalg.Vector;
+import org.apache.flink.ml.linalg.typeinfo.DenseVectorTypeInfo;
+import org.apache.flink.ml.param.Param;
+import org.apache.flink.ml.util.ParamUtils;
+import org.apache.flink.ml.util.ReadWriteUtils;
+import org.apache.flink.runtime.state.StateInitializationContext;
+import org.apache.flink.runtime.state.StateSnapshotContext;
+import org.apache.flink.streaming.api.datastream.DataStream;
+import org.apache.flink.streaming.api.datastream.SingleOutputStreamOperator;
+import org.apache.flink.streaming.api.operators.AbstractStreamOperator;
+import org.apache.flink.streaming.api.operators.TwoInputStreamOperator;
+import org.apache.flink.streaming.runtime.streamrecord.StreamRecord;
+import org.apache.flink.table.api.Table;
+import org.apache.flink.table.api.bridge.java.StreamTableEnvironment;
+import org.apache.flink.table.api.internal.TableImpl;
+import org.apache.flink.types.Row;
+import org.apache.flink.util.Collector;
+import org.apache.flink.util.OutputTag;
+import org.apache.flink.util.Preconditions;
+
+import java.io.IOException;
+import java.io.Serializable;
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.HashMap;
+import java.util.Iterator;
+import java.util.List;
+import java.util.Map;
+import java.util.Objects;
+import java.util.Random;
+
+/**
+ * An Estimator which implements the Isolation Forest algorithm.
+ *
+ * <p>See https://en.wikipedia.org/wiki/Isolation_forest.
+ */
+public class IsolationForest
+        implements Estimator<IsolationForest, IsolationForestModel>,
+                IsolationForestParams<IsolationForest> {
+    private final Map<Param<?>, Object> paramMap = new HashMap<>();
+
+    public IsolationForest() {
+        ParamUtils.initializeMapWithDefaultValues(paramMap, this);
+    }
+
+    @Override
+    public IsolationForestModel fit(Table... inputs) {
+        Preconditions.checkArgument(inputs.length == 1);
+        Integer treesNumber = getTreesNumber();
+        Integer iters = getIters();
+        Preconditions.checkArgument(
+                treesNumber != null || treesNumber > 0, "Param treesNumber is 
illegal.");
+        Preconditions.checkArgument(iters != null || iters > 0, "Param iters 
is illegal.");
+        IForest iForest = new IForest(treesNumber, iters);
+        StreamTableEnvironment tEnv =
+                (StreamTableEnvironment) ((TableImpl) 
inputs[0]).getTableEnvironment();
+
+        DataStream<DenseVector[]> points =
+                tEnv.toDataStream(inputs[0]).map(new 
FormatDataMapFunction(getFeaturesCol()));
+
+        DataStream<IForest> initModelData =
+                selectRandomSample1(points).map(new 
InitModelData(iForest)).setParallelism(1);
+
+        DataStream<IsolationForestModelData> finalModelData =
+                Iterations.iterateBoundedStreamsUntilTermination(
+                                DataStreamList.of(initModelData),
+                                ReplayableDataStreamList.notReplay(points),
+                                IterationConfig.newBuilder()
+                                        .setOperatorLifeCycle(
+                                                
IterationConfig.OperatorLifeCycle.ALL_ROUND)
+                                        .build(),
+                                new IsolationForestIterationBody(iters))
+                        .get(0);
+
+        Table finalModelDataTable = tEnv.fromDataStream(finalModelData);
+        IsolationForestModel model = new 
IsolationForestModel().setModelData(finalModelDataTable);
+        ParamUtils.updateExistingParams(model, paramMap);
+        return model;
+    }
+
+    @Override
+    public void save(String path) throws IOException {
+        ReadWriteUtils.saveMetadata(this, path);
+    }
+
+    public static IsolationForestModel load(StreamTableEnvironment tEnv, 
String path)
+            throws IOException {
+        return ReadWriteUtils.loadStageParam(path);
+    }
+
+    @Override
+    public Map<Param<?>, Object> getParamMap() {
+        return paramMap;
+    }
+
+    private static class FormatDataMapFunction implements MapFunction<Row, 
DenseVector[]> {
+        private final String featuresCol;
+        private List<DenseVector> list;
+
+        public FormatDataMapFunction(String featuresCol) {
+            this.featuresCol = featuresCol;
+        }
+
+        @Override
+        public DenseVector[] map(Row row) throws Exception {
+            list = new ArrayList<>(256);
+            DenseVector denseVector = ((Vector) 
row.getField(featuresCol)).toDense();
+            list.add(denseVector);
+            return list.toArray(new DenseVector[0]);
+        }
+    }
+
+    private static DataStream<DenseVector[]> selectRandomSample1(
+            DataStream<DenseVector[]> samplesData) {
+        DataStream<DenseVector[]> resultStream =
+                DataStreamUtils.mapPartition(
+                        DataStreamUtils.sample(samplesData, 256, 
System.currentTimeMillis()),
+                        (MapPartitionFunction<DenseVector[], DenseVector[]>)
+                                (iterable, collector) -> {
+                                    Iterator<DenseVector[]> 
samplesDataIterator =
+                                            iterable.iterator();
+                                    List<DenseVector> list = new ArrayList<>();
+                                    while (samplesDataIterator.hasNext()) {
+                                        
list.addAll(Arrays.asList(samplesDataIterator.next()));
+                                    }
+                                    collector.collect(list.toArray(new 
DenseVector[0]));
+                                },
+                        Types.OBJECT_ARRAY(DenseVectorTypeInfo.INSTANCE));
+        resultStream.getTransformation().setParallelism(1);
+        return resultStream;
+    }
+
+    private static class InitModelData implements MapFunction<DenseVector[], 
IForest> {
+        private final IForest iForest;
+
+        private InitModelData(IForest iForest) {
+            this.iForest = iForest;
+        }
+
+        @Override
+        public IForest map(DenseVector[] denseVectors) throws Exception {
+            iForest.createIForest(denseVectors);
+            DenseVector scores = iForest.calculateAnomalyScore(denseVectors);
+            iForest.classifyByCluster(scores);
+            return iForest;
+        }
+    }
+
+    private static class IsolationForestIterationBody implements IterationBody 
{
+        private final Integer iters;
+
+        public IsolationForestIterationBody(Integer iters) {
+            this.iters = iters;
+        }
+
+        @Override
+        public IterationBodyResult process(
+                DataStreamList variableStreams, DataStreamList dataStreams) {
+            DataStream<IForest> centersData = variableStreams.get(0);
+            DataStream<DenseVector[]> samplesData = dataStreams.get(0);
+            final OutputTag<IForest> modelDataOutputTag =
+                    new OutputTag<IForest>("IsolationForest") {};
+
+            SingleOutputStreamOperator terminationCriteria =
+                    centersData.flatMap(new TerminateOnMaxIter(iters));
+
+            DataStream<IForest> centers =
+                    samplesData
+                            .connect(centersData.broadcast())
+                            .transform(
+                                    "CentersUpdateAccumulator",
+                                    TypeInformation.of(IForest.class),
+                                    new 
CentersUpdateAccumulator(modelDataOutputTag));
+
+            DataStream<IsolationForestModelData> newModelData =
+                    centers.countWindowAll(centers.getParallelism())
+                            .reduce(
+                                    new ReduceFunction<IForest>() {
+                                        @Override
+                                        public IForest reduce(IForest 
iForest1, IForest iForest2)
+                                                throws Exception {
+                                            if (iForest2.center0 == null
+                                                    || iForest2.center1 == 
null) {
+                                                return iForest1;
+                                            }
+                                            return iForest2;
+                                        }
+                                    })
+                            .flatMap(
+                                    new FlatMapFunction<IForest, 
IsolationForestModelData>() {
+                                        @Override
+                                        public void flatMap(
+                                                IForest iForest,
+                                                
Collector<IsolationForestModelData> collector)
+                                                throws Exception {
+                                            if (iForest.center0 != null
+                                                    && iForest.center1 != 
null) {
+                                                collector.collect(
+                                                        new 
IsolationForestModelData(iForest));
+                                            }
+                                        }
+                                    });
+
+            DataStream<IForest> newCenters = newModelData.map(x -> 
x.iForest).setParallelism(1);
+
+            DataStream<IsolationForestModelData> finalModelData =
+                    newModelData.flatMap(new ForwardInputsOfLastRound<>());
+
+            return new IterationBodyResult(
+                    DataStreamList.of(newCenters),
+                    DataStreamList.of(finalModelData),
+                    terminationCriteria);
+        }
+    }
+
+    private static class CentersUpdateAccumulator extends 
AbstractStreamOperator<IForest>
+            implements TwoInputStreamOperator<DenseVector[], IForest, IForest>,
+                    IterationListener<IForest> {
+        private final OutputTag<IForest> modelDataOutputTag;
+
+        private ListStateWithCache<DenseVector[]> samplesData;
+
+        private ListState<IForest> samplesDataCenter;
+
+        private ListStateWithCache<DenseVector[]> samplesDataScores;
+
+        public CentersUpdateAccumulator(OutputTag<IForest> modelDataOutputTag) 
{
+            this.modelDataOutputTag = modelDataOutputTag;
+        }
+
+        @Override
+        public void initializeState(StateInitializationContext context) throws 
Exception {
+            super.initializeState(context);
+
+            samplesDataCenter =
+                    context.getOperatorStateStore()
+                            .getListState(
+                                    new ListStateDescriptor<IForest>(
+                                            "centers", 
TypeInformation.of(IForest.class)));
+
+            samplesData =
+                    new ListStateWithCache<>(
+                            Types.OBJECT_ARRAY(DenseVectorTypeInfo.INSTANCE)
+                                    .createSerializer(getExecutionConfig()),
+                            getContainingTask(),
+                            getRuntimeContext(),
+                            context,
+                            config.getOperatorID());
+
+            samplesDataScores =
+                    new ListStateWithCache<>(
+                            Types.OBJECT_ARRAY(DenseVectorTypeInfo.INSTANCE)
+                                    .createSerializer(getExecutionConfig()),
+                            getContainingTask(),
+                            getRuntimeContext(),
+                            context,
+                            config.getOperatorID());
+        }
+
+        @Override
+        public void snapshotState(StateSnapshotContext context) throws 
Exception {
+            super.snapshotState(context);
+            samplesData.snapshotState(context);
+        }
+
+        @Override
+        public void processElement1(StreamRecord<DenseVector[]> streamRecord) 
throws Exception {
+            samplesData.add(streamRecord.getValue());
+        }
+
+        @Override
+        public void processElement2(StreamRecord<IForest> streamRecord) throws 
Exception {
+            
Preconditions.checkState(!samplesDataCenter.get().iterator().hasNext());
+            samplesDataCenter.add(streamRecord.getValue());
+        }
+
+        @Override
+        public void onEpochWatermarkIncremented(
+                int epochWatermark, Context context, Collector<IForest> 
collector)
+                throws Exception {
+            IForest centers =
+                    Objects.requireNonNull(
+                            
OperatorStateUtils.getUniqueElement(samplesDataCenter, "centers")
+                                    .orElse(null));
+            Iterator<DenseVector[]> samplesDataIterator = 
samplesData.get().iterator();
+            List<DenseVector> list = new ArrayList<>();
+            while (samplesDataIterator.hasNext()) {
+                DenseVector[] sampleData = samplesDataIterator.next();
+                list.add(centers.calculateAnomalyScore(sampleData));
+            }
+            DenseVector[] scores = list.toArray(new DenseVector[0]);
+            samplesDataScores.add(scores);
+
+            collector.collect(samplesDataCenter.get().iterator().next());
+            samplesDataCenter.clear();
+        }
+
+        @Override
+        public void onIterationTerminated(Context context, Collector<IForest> 
collector)
+                throws Exception {
+            IForest centers =
+                    Objects.requireNonNull(
+                            
OperatorStateUtils.getUniqueElement(samplesDataCenter, "centers")
+                                    .orElse(null));
+            double centers0Sum1 = 0.0, centers1Sum1 = 0.0, centers0Sum2 = 0.0, 
centers1Sum2 = 0.0;
+            int size1 = 0, size2 = 0;
+            Iterator<DenseVector[]> samplesDataScoresIterator = 
samplesDataScores.get().iterator();
+            while (samplesDataScoresIterator.hasNext()) {
+                for (DenseVector denseVector : 
samplesDataScoresIterator.next()) {
+                    DenseVector denseVector1 = 
centers.classifyByCluster(denseVector);
+                    centers0Sum1 += denseVector1.get(0);
+                    centers1Sum1 += denseVector1.get(1);
+                    size1++;
+                }
+                centers0Sum2 = centers0Sum1 / size1;
+                centers1Sum2 = centers1Sum1 / size1;
+                size2++;
+            }
+
+            centers.center0 = centers0Sum2 / size2;
+            centers.center1 = centers1Sum2 / size2;
+
+            context.output(modelDataOutputTag, centers);
+
+            samplesDataCenter.clear();
+            samplesDataScores.clear();
+            samplesData.clear();
+        }
+    }
+
+    /** Construct isolation forest. */
+    public static class IForest implements Serializable {
+        public int treesNumber;
+        public int iters;
+        public List<ITree> iTreeList;
+        public Double center0;
+        public Double center1;
+        public int subSamplesSize;
+
+        public IForest() {}
+
+        public IForest(int treesNumber, int iters) {
+            this.iters = iters;
+            this.treesNumber = treesNumber;
+            this.iTreeList = new ArrayList<>();
+            this.center0 = null;
+            this.center1 = null;
+        }
+
+        private void createIForest(DenseVector[] samplesData) throws Exception 
{
+            this.subSamplesSize = Math.min(256, samplesData.length);
+
+            // 限制高度(向上取整)

Review Comment:
   Can you update PR so that it does not contain Chinese?



##########
flink-ml-lib/src/main/java/org/apache/flink/ml/anomalydetection/isolationforest/IsolationForest.java:
##########
@@ -0,0 +1,611 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.flink.ml.anomalydetection.isolationforest;
+
+import org.apache.flink.api.common.functions.FlatMapFunction;
+import org.apache.flink.api.common.functions.MapFunction;
+import org.apache.flink.api.common.functions.MapPartitionFunction;
+import org.apache.flink.api.common.functions.ReduceFunction;
+import org.apache.flink.api.common.state.ListState;
+import org.apache.flink.api.common.state.ListStateDescriptor;
+import org.apache.flink.api.common.typeinfo.TypeInformation;
+import org.apache.flink.api.common.typeinfo.Types;
+import org.apache.flink.iteration.DataStreamList;
+import org.apache.flink.iteration.IterationBody;
+import org.apache.flink.iteration.IterationBodyResult;
+import org.apache.flink.iteration.IterationConfig;
+import org.apache.flink.iteration.IterationListener;
+import org.apache.flink.iteration.Iterations;
+import org.apache.flink.iteration.ReplayableDataStreamList;
+import org.apache.flink.iteration.datacache.nonkeyed.ListStateWithCache;
+import org.apache.flink.iteration.operator.OperatorStateUtils;
+import org.apache.flink.ml.api.Estimator;
+import org.apache.flink.ml.common.datastream.DataStreamUtils;
+import org.apache.flink.ml.common.iteration.ForwardInputsOfLastRound;
+import org.apache.flink.ml.common.iteration.TerminateOnMaxIter;
+import org.apache.flink.ml.linalg.DenseVector;
+import org.apache.flink.ml.linalg.Vector;
+import org.apache.flink.ml.linalg.typeinfo.DenseVectorTypeInfo;
+import org.apache.flink.ml.param.Param;
+import org.apache.flink.ml.util.ParamUtils;
+import org.apache.flink.ml.util.ReadWriteUtils;
+import org.apache.flink.runtime.state.StateInitializationContext;
+import org.apache.flink.runtime.state.StateSnapshotContext;
+import org.apache.flink.streaming.api.datastream.DataStream;
+import org.apache.flink.streaming.api.datastream.SingleOutputStreamOperator;
+import org.apache.flink.streaming.api.operators.AbstractStreamOperator;
+import org.apache.flink.streaming.api.operators.TwoInputStreamOperator;
+import org.apache.flink.streaming.runtime.streamrecord.StreamRecord;
+import org.apache.flink.table.api.Table;
+import org.apache.flink.table.api.bridge.java.StreamTableEnvironment;
+import org.apache.flink.table.api.internal.TableImpl;
+import org.apache.flink.types.Row;
+import org.apache.flink.util.Collector;
+import org.apache.flink.util.OutputTag;
+import org.apache.flink.util.Preconditions;
+
+import java.io.IOException;
+import java.io.Serializable;
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.HashMap;
+import java.util.Iterator;
+import java.util.List;
+import java.util.Map;
+import java.util.Objects;
+import java.util.Random;
+
+/**
+ * An Estimator which implements the Isolation Forest algorithm.
+ *
+ * <p>See https://en.wikipedia.org/wiki/Isolation_forest.
+ */
+public class IsolationForest
+        implements Estimator<IsolationForest, IsolationForestModel>,
+                IsolationForestParams<IsolationForest> {
+    private final Map<Param<?>, Object> paramMap = new HashMap<>();
+
+    public IsolationForest() {
+        ParamUtils.initializeMapWithDefaultValues(paramMap, this);
+    }
+
+    @Override
+    public IsolationForestModel fit(Table... inputs) {
+        Preconditions.checkArgument(inputs.length == 1);
+        Integer treesNumber = getTreesNumber();
+        Integer iters = getIters();
+        Preconditions.checkArgument(
+                treesNumber != null || treesNumber > 0, "Param treesNumber is 
illegal.");
+        Preconditions.checkArgument(iters != null || iters > 0, "Param iters 
is illegal.");
+        IForest iForest = new IForest(treesNumber, iters);
+        StreamTableEnvironment tEnv =
+                (StreamTableEnvironment) ((TableImpl) 
inputs[0]).getTableEnvironment();
+
+        DataStream<DenseVector[]> points =
+                tEnv.toDataStream(inputs[0]).map(new 
FormatDataMapFunction(getFeaturesCol()));
+
+        DataStream<IForest> initModelData =
+                selectRandomSample1(points).map(new 
InitModelData(iForest)).setParallelism(1);
+
+        DataStream<IsolationForestModelData> finalModelData =
+                Iterations.iterateBoundedStreamsUntilTermination(
+                                DataStreamList.of(initModelData),
+                                ReplayableDataStreamList.notReplay(points),
+                                IterationConfig.newBuilder()
+                                        .setOperatorLifeCycle(
+                                                
IterationConfig.OperatorLifeCycle.ALL_ROUND)
+                                        .build(),
+                                new IsolationForestIterationBody(iters))
+                        .get(0);
+
+        Table finalModelDataTable = tEnv.fromDataStream(finalModelData);
+        IsolationForestModel model = new 
IsolationForestModel().setModelData(finalModelDataTable);
+        ParamUtils.updateExistingParams(model, paramMap);
+        return model;
+    }
+
+    @Override
+    public void save(String path) throws IOException {
+        ReadWriteUtils.saveMetadata(this, path);
+    }
+
+    public static IsolationForestModel load(StreamTableEnvironment tEnv, 
String path)
+            throws IOException {
+        return ReadWriteUtils.loadStageParam(path);
+    }
+
+    @Override
+    public Map<Param<?>, Object> getParamMap() {
+        return paramMap;
+    }
+
+    private static class FormatDataMapFunction implements MapFunction<Row, 
DenseVector[]> {
+        private final String featuresCol;
+        private List<DenseVector> list;
+
+        public FormatDataMapFunction(String featuresCol) {
+            this.featuresCol = featuresCol;
+        }
+
+        @Override
+        public DenseVector[] map(Row row) throws Exception {
+            list = new ArrayList<>(256);
+            DenseVector denseVector = ((Vector) 
row.getField(featuresCol)).toDense();
+            list.add(denseVector);
+            return list.toArray(new DenseVector[0]);
+        }
+    }
+
+    private static DataStream<DenseVector[]> selectRandomSample1(
+            DataStream<DenseVector[]> samplesData) {
+        DataStream<DenseVector[]> resultStream =
+                DataStreamUtils.mapPartition(
+                        DataStreamUtils.sample(samplesData, 256, 
System.currentTimeMillis()),
+                        (MapPartitionFunction<DenseVector[], DenseVector[]>)
+                                (iterable, collector) -> {
+                                    Iterator<DenseVector[]> 
samplesDataIterator =
+                                            iterable.iterator();
+                                    List<DenseVector> list = new ArrayList<>();
+                                    while (samplesDataIterator.hasNext()) {
+                                        
list.addAll(Arrays.asList(samplesDataIterator.next()));
+                                    }
+                                    collector.collect(list.toArray(new 
DenseVector[0]));
+                                },
+                        Types.OBJECT_ARRAY(DenseVectorTypeInfo.INSTANCE));
+        resultStream.getTransformation().setParallelism(1);
+        return resultStream;
+    }
+
+    private static class InitModelData implements MapFunction<DenseVector[], 
IForest> {
+        private final IForest iForest;
+
+        private InitModelData(IForest iForest) {
+            this.iForest = iForest;
+        }
+
+        @Override
+        public IForest map(DenseVector[] denseVectors) throws Exception {
+            iForest.createIForest(denseVectors);
+            DenseVector scores = iForest.calculateAnomalyScore(denseVectors);
+            iForest.classifyByCluster(scores);
+            return iForest;
+        }
+    }
+
+    private static class IsolationForestIterationBody implements IterationBody 
{
+        private final Integer iters;
+
+        public IsolationForestIterationBody(Integer iters) {
+            this.iters = iters;
+        }
+
+        @Override
+        public IterationBodyResult process(
+                DataStreamList variableStreams, DataStreamList dataStreams) {
+            DataStream<IForest> centersData = variableStreams.get(0);
+            DataStream<DenseVector[]> samplesData = dataStreams.get(0);
+            final OutputTag<IForest> modelDataOutputTag =
+                    new OutputTag<IForest>("IsolationForest") {};
+
+            SingleOutputStreamOperator terminationCriteria =
+                    centersData.flatMap(new TerminateOnMaxIter(iters));
+
+            DataStream<IForest> centers =
+                    samplesData
+                            .connect(centersData.broadcast())
+                            .transform(
+                                    "CentersUpdateAccumulator",
+                                    TypeInformation.of(IForest.class),
+                                    new 
CentersUpdateAccumulator(modelDataOutputTag));
+
+            DataStream<IsolationForestModelData> newModelData =
+                    centers.countWindowAll(centers.getParallelism())
+                            .reduce(
+                                    new ReduceFunction<IForest>() {
+                                        @Override
+                                        public IForest reduce(IForest 
iForest1, IForest iForest2)
+                                                throws Exception {
+                                            if (iForest2.center0 == null
+                                                    || iForest2.center1 == 
null) {
+                                                return iForest1;
+                                            }
+                                            return iForest2;
+                                        }
+                                    })
+                            .flatMap(
+                                    new FlatMapFunction<IForest, 
IsolationForestModelData>() {
+                                        @Override
+                                        public void flatMap(
+                                                IForest iForest,
+                                                
Collector<IsolationForestModelData> collector)
+                                                throws Exception {
+                                            if (iForest.center0 != null
+                                                    && iForest.center1 != 
null) {
+                                                collector.collect(
+                                                        new 
IsolationForestModelData(iForest));
+                                            }
+                                        }
+                                    });
+
+            DataStream<IForest> newCenters = newModelData.map(x -> 
x.iForest).setParallelism(1);
+
+            DataStream<IsolationForestModelData> finalModelData =
+                    newModelData.flatMap(new ForwardInputsOfLastRound<>());
+
+            return new IterationBodyResult(
+                    DataStreamList.of(newCenters),
+                    DataStreamList.of(finalModelData),
+                    terminationCriteria);
+        }
+    }
+
+    private static class CentersUpdateAccumulator extends 
AbstractStreamOperator<IForest>
+            implements TwoInputStreamOperator<DenseVector[], IForest, IForest>,
+                    IterationListener<IForest> {
+        private final OutputTag<IForest> modelDataOutputTag;
+
+        private ListStateWithCache<DenseVector[]> samplesData;
+
+        private ListState<IForest> samplesDataCenter;
+
+        private ListStateWithCache<DenseVector[]> samplesDataScores;
+
+        public CentersUpdateAccumulator(OutputTag<IForest> modelDataOutputTag) 
{
+            this.modelDataOutputTag = modelDataOutputTag;
+        }
+
+        @Override
+        public void initializeState(StateInitializationContext context) throws 
Exception {
+            super.initializeState(context);
+
+            samplesDataCenter =
+                    context.getOperatorStateStore()
+                            .getListState(
+                                    new ListStateDescriptor<IForest>(
+                                            "centers", 
TypeInformation.of(IForest.class)));
+
+            samplesData =
+                    new ListStateWithCache<>(
+                            Types.OBJECT_ARRAY(DenseVectorTypeInfo.INSTANCE)
+                                    .createSerializer(getExecutionConfig()),
+                            getContainingTask(),
+                            getRuntimeContext(),
+                            context,
+                            config.getOperatorID());
+
+            samplesDataScores =
+                    new ListStateWithCache<>(
+                            Types.OBJECT_ARRAY(DenseVectorTypeInfo.INSTANCE)
+                                    .createSerializer(getExecutionConfig()),
+                            getContainingTask(),
+                            getRuntimeContext(),
+                            context,
+                            config.getOperatorID());
+        }
+
+        @Override
+        public void snapshotState(StateSnapshotContext context) throws 
Exception {
+            super.snapshotState(context);
+            samplesData.snapshotState(context);
+        }
+
+        @Override
+        public void processElement1(StreamRecord<DenseVector[]> streamRecord) 
throws Exception {
+            samplesData.add(streamRecord.getValue());
+        }
+
+        @Override
+        public void processElement2(StreamRecord<IForest> streamRecord) throws 
Exception {
+            
Preconditions.checkState(!samplesDataCenter.get().iterator().hasNext());
+            samplesDataCenter.add(streamRecord.getValue());
+        }
+
+        @Override
+        public void onEpochWatermarkIncremented(
+                int epochWatermark, Context context, Collector<IForest> 
collector)
+                throws Exception {
+            IForest centers =
+                    Objects.requireNonNull(
+                            
OperatorStateUtils.getUniqueElement(samplesDataCenter, "centers")
+                                    .orElse(null));
+            Iterator<DenseVector[]> samplesDataIterator = 
samplesData.get().iterator();
+            List<DenseVector> list = new ArrayList<>();
+            while (samplesDataIterator.hasNext()) {
+                DenseVector[] sampleData = samplesDataIterator.next();
+                list.add(centers.calculateAnomalyScore(sampleData));
+            }
+            DenseVector[] scores = list.toArray(new DenseVector[0]);
+            samplesDataScores.add(scores);
+
+            collector.collect(samplesDataCenter.get().iterator().next());
+            samplesDataCenter.clear();
+        }
+
+        @Override
+        public void onIterationTerminated(Context context, Collector<IForest> 
collector)
+                throws Exception {
+            IForest centers =
+                    Objects.requireNonNull(
+                            
OperatorStateUtils.getUniqueElement(samplesDataCenter, "centers")
+                                    .orElse(null));
+            double centers0Sum1 = 0.0, centers1Sum1 = 0.0, centers0Sum2 = 0.0, 
centers1Sum2 = 0.0;
+            int size1 = 0, size2 = 0;
+            Iterator<DenseVector[]> samplesDataScoresIterator = 
samplesDataScores.get().iterator();
+            while (samplesDataScoresIterator.hasNext()) {
+                for (DenseVector denseVector : 
samplesDataScoresIterator.next()) {
+                    DenseVector denseVector1 = 
centers.classifyByCluster(denseVector);
+                    centers0Sum1 += denseVector1.get(0);
+                    centers1Sum1 += denseVector1.get(1);
+                    size1++;
+                }
+                centers0Sum2 = centers0Sum1 / size1;
+                centers1Sum2 = centers1Sum1 / size1;
+                size2++;
+            }
+
+            centers.center0 = centers0Sum2 / size2;
+            centers.center1 = centers1Sum2 / size2;
+
+            context.output(modelDataOutputTag, centers);
+
+            samplesDataCenter.clear();
+            samplesDataScores.clear();
+            samplesData.clear();
+        }
+    }
+
+    /** Construct isolation forest. */
+    public static class IForest implements Serializable {
+        public int treesNumber;
+        public int iters;
+        public List<ITree> iTreeList;
+        public Double center0;
+        public Double center1;
+        public int subSamplesSize;
+
+        public IForest() {}
+
+        public IForest(int treesNumber, int iters) {
+            this.iters = iters;
+            this.treesNumber = treesNumber;
+            this.iTreeList = new ArrayList<>();
+            this.center0 = null;
+            this.center1 = null;
+        }
+
+        private void createIForest(DenseVector[] samplesData) throws Exception 
{
+            this.subSamplesSize = Math.min(256, samplesData.length);
+
+            // 限制高度(向上取整)
+            int limitHeight = (int) Math.ceil(Math.log(subSamplesSize) / 
Math.log(2));
+
+            int rows = samplesData.length;
+
+            Random random = new Random(System.currentTimeMillis());
+            for (int i = 0; i < this.treesNumber; i++) {
+                DenseVector[] subSamples = new DenseVector[subSamplesSize];
+                for (int j = 0; j < subSamplesSize; j++) {
+                    int r = random.nextInt(rows);
+                    subSamples[j] = samplesData[r];
+                }
+                ITree iTree = ITree.createITree(subSamples, 0, limitHeight);
+                this.iTreeList.add(iTree);
+            }
+        }
+
+        private DenseVector calculateAnomalyScore(DenseVector[] samplesData) 
throws Exception {
+            int n = samplesData.length;
+
+            DenseVector scores = new DenseVector(n);
+            for (int i = 0; i < n; i++) {
+                double pathLengthSum = 0;
+                for (ITree iTree : iTreeList) {
+                    pathLengthSum += calculatePathLength(samplesData[i], 
iTree);
+                }
+
+                double pathLengthAvg = pathLengthSum / iTreeList.size();
+                double cn = calculateCn(subSamplesSize);
+                double index = pathLengthAvg / cn;
+                scores.set(i, Math.pow(2, -index));
+            }
+            return scores;
+        }
+
+        private double calculatePathLength(DenseVector sampleData, ITree 
iTree) throws Exception {
+            double pathLength = -1;
+            ITree tmpITree = iTree;
+            while (tmpITree != null) {
+                pathLength += 1;
+                if (tmpITree.leftTree == null
+                        || tmpITree.rightTree == null
+                        || sampleData.get(tmpITree.attributeIndex)
+                                == tmpITree.splitAttributeValue) {
+                    break;
+                } else if (sampleData.get(tmpITree.attributeIndex) < 
tmpITree.splitAttributeValue) {
+                    tmpITree = tmpITree.leftTree;
+                } else {
+                    tmpITree = tmpITree.rightTree;
+                }
+            }
+
+            return pathLength + calculateCn(tmpITree.leafNodesNum);
+        }
+
+        private double calculateCn(double n) {
+            if (n <= 1) {
+                return 0;
+            }
+            return 2.0 * (Math.log(n - 1.0) + 0.5772156649015329) - 2.0 * (n - 
1.0) / n;
+        }
+
+        private DenseVector classifyByCluster(DenseVector scores) {
+            int scoresSize = scores.size();
+            this.center0 = scores.get(0); // Cluster center of abnormal
+            this.center1 = scores.get(0); // Cluster center of normal
+
+            for (int p = 1; p < scores.size(); p++) {
+                if (scores.get(p) > center0) {
+                    center0 = scores.get(p);
+                }
+
+                if (scores.get(p) < center1) {
+                    center1 = scores.get(p);
+                }
+            }
+
+            int cnt0, cnt1;
+            double diff0, diff1;
+            int[] labels = new int[scoresSize];
+
+            for (int i = 0; i < iters; i++) {
+                cnt0 = 0;
+                cnt1 = 0;
+
+                for (int j = 0; j < scoresSize; j++) {
+                    diff0 = Math.abs(scores.get(j) - center0);
+                    diff1 = Math.abs(scores.get(j) - center1);
+
+                    if (diff0 < diff1) {
+                        labels[j] = 0;
+                        cnt0++;
+                    } else {
+                        labels[j] = 1;
+                        cnt1++;
+                    }
+                }
+
+                diff0 = center0;
+                diff1 = center1;
+
+                center0 = 0.0;
+                center1 = 0.0;
+                for (int k = 0; k < scoresSize; k++) {
+                    if (labels[k] == 0) {
+                        center0 += scores.get(k);
+                    } else {
+                        center1 += scores.get(k);
+                    }
+                }
+
+                center0 /= cnt0;
+                center1 /= cnt1;
+
+                if (center0 - diff0 <= 1e-6 && center1 - diff1 <= 1e-6) {
+                    break;
+                }
+            }
+            return new DenseVector(new double[] {center0, center1});
+        }
+    }
+
+    /** Construct isolation tree. */
+    public static class ITree implements Serializable {
+        public int attributeIndex;
+        public double splitAttributeValue;
+        public ITree leftTree, rightTree;
+        public int currentHeight;
+        public int leafNodesNum;
+
+        public ITree() {}
+
+        public ITree(int attributeIndex, double splitAttributeValue) {
+            this.attributeIndex = attributeIndex;
+            this.splitAttributeValue = splitAttributeValue;
+            this.leftTree = null;
+            this.rightTree = null;
+            this.currentHeight = 0;
+            this.leafNodesNum = 1;
+        }
+
+        public static ITree createITree(

Review Comment:
   If `ITree` is used to describe model data, it might be better to move the 
logic of computing/processing `ITree` out of this class.
   
   Ideally, the description of the model data should be put in the 
`IsolationForestModelData.java` and the training logic should be put in the 
corresponding estimator class.
   
   Same for `IForest`.



##########
flink-ml-lib/src/main/java/org/apache/flink/ml/anomalydetection/isolationforest/IsolationForest.java:
##########
@@ -0,0 +1,611 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.flink.ml.anomalydetection.isolationforest;
+
+import org.apache.flink.api.common.functions.FlatMapFunction;
+import org.apache.flink.api.common.functions.MapFunction;
+import org.apache.flink.api.common.functions.MapPartitionFunction;
+import org.apache.flink.api.common.functions.ReduceFunction;
+import org.apache.flink.api.common.state.ListState;
+import org.apache.flink.api.common.state.ListStateDescriptor;
+import org.apache.flink.api.common.typeinfo.TypeInformation;
+import org.apache.flink.api.common.typeinfo.Types;
+import org.apache.flink.iteration.DataStreamList;
+import org.apache.flink.iteration.IterationBody;
+import org.apache.flink.iteration.IterationBodyResult;
+import org.apache.flink.iteration.IterationConfig;
+import org.apache.flink.iteration.IterationListener;
+import org.apache.flink.iteration.Iterations;
+import org.apache.flink.iteration.ReplayableDataStreamList;
+import org.apache.flink.iteration.datacache.nonkeyed.ListStateWithCache;
+import org.apache.flink.iteration.operator.OperatorStateUtils;
+import org.apache.flink.ml.api.Estimator;
+import org.apache.flink.ml.common.datastream.DataStreamUtils;
+import org.apache.flink.ml.common.iteration.ForwardInputsOfLastRound;
+import org.apache.flink.ml.common.iteration.TerminateOnMaxIter;
+import org.apache.flink.ml.linalg.DenseVector;
+import org.apache.flink.ml.linalg.Vector;
+import org.apache.flink.ml.linalg.typeinfo.DenseVectorTypeInfo;
+import org.apache.flink.ml.param.Param;
+import org.apache.flink.ml.util.ParamUtils;
+import org.apache.flink.ml.util.ReadWriteUtils;
+import org.apache.flink.runtime.state.StateInitializationContext;
+import org.apache.flink.runtime.state.StateSnapshotContext;
+import org.apache.flink.streaming.api.datastream.DataStream;
+import org.apache.flink.streaming.api.datastream.SingleOutputStreamOperator;
+import org.apache.flink.streaming.api.operators.AbstractStreamOperator;
+import org.apache.flink.streaming.api.operators.TwoInputStreamOperator;
+import org.apache.flink.streaming.runtime.streamrecord.StreamRecord;
+import org.apache.flink.table.api.Table;
+import org.apache.flink.table.api.bridge.java.StreamTableEnvironment;
+import org.apache.flink.table.api.internal.TableImpl;
+import org.apache.flink.types.Row;
+import org.apache.flink.util.Collector;
+import org.apache.flink.util.OutputTag;
+import org.apache.flink.util.Preconditions;
+
+import java.io.IOException;
+import java.io.Serializable;
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.HashMap;
+import java.util.Iterator;
+import java.util.List;
+import java.util.Map;
+import java.util.Objects;
+import java.util.Random;
+
+/**
+ * An Estimator which implements the Isolation Forest algorithm.
+ *
+ * <p>See https://en.wikipedia.org/wiki/Isolation_forest.
+ */
+public class IsolationForest
+        implements Estimator<IsolationForest, IsolationForestModel>,
+                IsolationForestParams<IsolationForest> {
+    private final Map<Param<?>, Object> paramMap = new HashMap<>();
+
+    public IsolationForest() {
+        ParamUtils.initializeMapWithDefaultValues(paramMap, this);
+    }
+
+    @Override
+    public IsolationForestModel fit(Table... inputs) {
+        Preconditions.checkArgument(inputs.length == 1);
+        Integer treesNumber = getTreesNumber();
+        Integer iters = getIters();
+        Preconditions.checkArgument(
+                treesNumber != null || treesNumber > 0, "Param treesNumber is 
illegal.");
+        Preconditions.checkArgument(iters != null || iters > 0, "Param iters 
is illegal.");
+        IForest iForest = new IForest(treesNumber, iters);
+        StreamTableEnvironment tEnv =
+                (StreamTableEnvironment) ((TableImpl) 
inputs[0]).getTableEnvironment();
+
+        DataStream<DenseVector[]> points =
+                tEnv.toDataStream(inputs[0]).map(new 
FormatDataMapFunction(getFeaturesCol()));
+
+        DataStream<IForest> initModelData =
+                selectRandomSample1(points).map(new 
InitModelData(iForest)).setParallelism(1);
+
+        DataStream<IsolationForestModelData> finalModelData =
+                Iterations.iterateBoundedStreamsUntilTermination(
+                                DataStreamList.of(initModelData),
+                                ReplayableDataStreamList.notReplay(points),
+                                IterationConfig.newBuilder()
+                                        .setOperatorLifeCycle(
+                                                
IterationConfig.OperatorLifeCycle.ALL_ROUND)
+                                        .build(),
+                                new IsolationForestIterationBody(iters))
+                        .get(0);
+
+        Table finalModelDataTable = tEnv.fromDataStream(finalModelData);
+        IsolationForestModel model = new 
IsolationForestModel().setModelData(finalModelDataTable);
+        ParamUtils.updateExistingParams(model, paramMap);
+        return model;
+    }
+
+    @Override
+    public void save(String path) throws IOException {
+        ReadWriteUtils.saveMetadata(this, path);
+    }
+
+    public static IsolationForestModel load(StreamTableEnvironment tEnv, 
String path)
+            throws IOException {
+        return ReadWriteUtils.loadStageParam(path);
+    }
+
+    @Override
+    public Map<Param<?>, Object> getParamMap() {
+        return paramMap;
+    }
+
+    private static class FormatDataMapFunction implements MapFunction<Row, 
DenseVector[]> {
+        private final String featuresCol;
+        private List<DenseVector> list;
+
+        public FormatDataMapFunction(String featuresCol) {
+            this.featuresCol = featuresCol;
+        }
+
+        @Override
+        public DenseVector[] map(Row row) throws Exception {
+            list = new ArrayList<>(256);
+            DenseVector denseVector = ((Vector) 
row.getField(featuresCol)).toDense();
+            list.add(denseVector);
+            return list.toArray(new DenseVector[0]);
+        }
+    }
+
+    private static DataStream<DenseVector[]> selectRandomSample1(
+            DataStream<DenseVector[]> samplesData) {
+        DataStream<DenseVector[]> resultStream =
+                DataStreamUtils.mapPartition(
+                        DataStreamUtils.sample(samplesData, 256, 
System.currentTimeMillis()),
+                        (MapPartitionFunction<DenseVector[], DenseVector[]>)
+                                (iterable, collector) -> {
+                                    Iterator<DenseVector[]> 
samplesDataIterator =
+                                            iterable.iterator();
+                                    List<DenseVector> list = new ArrayList<>();
+                                    while (samplesDataIterator.hasNext()) {
+                                        
list.addAll(Arrays.asList(samplesDataIterator.next()));
+                                    }
+                                    collector.collect(list.toArray(new 
DenseVector[0]));
+                                },
+                        Types.OBJECT_ARRAY(DenseVectorTypeInfo.INSTANCE));
+        resultStream.getTransformation().setParallelism(1);
+        return resultStream;
+    }
+
+    private static class InitModelData implements MapFunction<DenseVector[], 
IForest> {
+        private final IForest iForest;
+
+        private InitModelData(IForest iForest) {
+            this.iForest = iForest;
+        }
+
+        @Override
+        public IForest map(DenseVector[] denseVectors) throws Exception {
+            iForest.createIForest(denseVectors);
+            DenseVector scores = iForest.calculateAnomalyScore(denseVectors);
+            iForest.classifyByCluster(scores);
+            return iForest;
+        }
+    }
+
+    private static class IsolationForestIterationBody implements IterationBody 
{
+        private final Integer iters;
+
+        public IsolationForestIterationBody(Integer iters) {
+            this.iters = iters;
+        }
+
+        @Override
+        public IterationBodyResult process(
+                DataStreamList variableStreams, DataStreamList dataStreams) {
+            DataStream<IForest> centersData = variableStreams.get(0);
+            DataStream<DenseVector[]> samplesData = dataStreams.get(0);
+            final OutputTag<IForest> modelDataOutputTag =
+                    new OutputTag<IForest>("IsolationForest") {};
+
+            SingleOutputStreamOperator terminationCriteria =
+                    centersData.flatMap(new TerminateOnMaxIter(iters));
+
+            DataStream<IForest> centers =
+                    samplesData
+                            .connect(centersData.broadcast())
+                            .transform(
+                                    "CentersUpdateAccumulator",
+                                    TypeInformation.of(IForest.class),
+                                    new 
CentersUpdateAccumulator(modelDataOutputTag));
+
+            DataStream<IsolationForestModelData> newModelData =
+                    centers.countWindowAll(centers.getParallelism())
+                            .reduce(
+                                    new ReduceFunction<IForest>() {
+                                        @Override
+                                        public IForest reduce(IForest 
iForest1, IForest iForest2)
+                                                throws Exception {
+                                            if (iForest2.center0 == null
+                                                    || iForest2.center1 == 
null) {
+                                                return iForest1;
+                                            }
+                                            return iForest2;
+                                        }
+                                    })
+                            .flatMap(
+                                    new FlatMapFunction<IForest, 
IsolationForestModelData>() {
+                                        @Override
+                                        public void flatMap(
+                                                IForest iForest,
+                                                
Collector<IsolationForestModelData> collector)
+                                                throws Exception {
+                                            if (iForest.center0 != null
+                                                    && iForest.center1 != 
null) {
+                                                collector.collect(
+                                                        new 
IsolationForestModelData(iForest));
+                                            }
+                                        }
+                                    });
+
+            DataStream<IForest> newCenters = newModelData.map(x -> 
x.iForest).setParallelism(1);
+
+            DataStream<IsolationForestModelData> finalModelData =
+                    newModelData.flatMap(new ForwardInputsOfLastRound<>());
+
+            return new IterationBodyResult(
+                    DataStreamList.of(newCenters),
+                    DataStreamList.of(finalModelData),
+                    terminationCriteria);
+        }
+    }
+
+    private static class CentersUpdateAccumulator extends 
AbstractStreamOperator<IForest>
+            implements TwoInputStreamOperator<DenseVector[], IForest, IForest>,
+                    IterationListener<IForest> {
+        private final OutputTag<IForest> modelDataOutputTag;
+
+        private ListStateWithCache<DenseVector[]> samplesData;
+
+        private ListState<IForest> samplesDataCenter;
+
+        private ListStateWithCache<DenseVector[]> samplesDataScores;
+
+        public CentersUpdateAccumulator(OutputTag<IForest> modelDataOutputTag) 
{
+            this.modelDataOutputTag = modelDataOutputTag;
+        }
+
+        @Override
+        public void initializeState(StateInitializationContext context) throws 
Exception {
+            super.initializeState(context);
+
+            samplesDataCenter =
+                    context.getOperatorStateStore()
+                            .getListState(
+                                    new ListStateDescriptor<IForest>(
+                                            "centers", 
TypeInformation.of(IForest.class)));
+
+            samplesData =
+                    new ListStateWithCache<>(
+                            Types.OBJECT_ARRAY(DenseVectorTypeInfo.INSTANCE)
+                                    .createSerializer(getExecutionConfig()),
+                            getContainingTask(),
+                            getRuntimeContext(),
+                            context,
+                            config.getOperatorID());
+
+            samplesDataScores =
+                    new ListStateWithCache<>(
+                            Types.OBJECT_ARRAY(DenseVectorTypeInfo.INSTANCE)
+                                    .createSerializer(getExecutionConfig()),
+                            getContainingTask(),
+                            getRuntimeContext(),
+                            context,
+                            config.getOperatorID());
+        }
+
+        @Override
+        public void snapshotState(StateSnapshotContext context) throws 
Exception {
+            super.snapshotState(context);
+            samplesData.snapshotState(context);
+        }
+
+        @Override
+        public void processElement1(StreamRecord<DenseVector[]> streamRecord) 
throws Exception {
+            samplesData.add(streamRecord.getValue());
+        }
+
+        @Override
+        public void processElement2(StreamRecord<IForest> streamRecord) throws 
Exception {
+            
Preconditions.checkState(!samplesDataCenter.get().iterator().hasNext());
+            samplesDataCenter.add(streamRecord.getValue());
+        }
+
+        @Override
+        public void onEpochWatermarkIncremented(
+                int epochWatermark, Context context, Collector<IForest> 
collector)
+                throws Exception {
+            IForest centers =
+                    Objects.requireNonNull(
+                            
OperatorStateUtils.getUniqueElement(samplesDataCenter, "centers")
+                                    .orElse(null));
+            Iterator<DenseVector[]> samplesDataIterator = 
samplesData.get().iterator();
+            List<DenseVector> list = new ArrayList<>();
+            while (samplesDataIterator.hasNext()) {
+                DenseVector[] sampleData = samplesDataIterator.next();
+                list.add(centers.calculateAnomalyScore(sampleData));
+            }
+            DenseVector[] scores = list.toArray(new DenseVector[0]);
+            samplesDataScores.add(scores);
+
+            collector.collect(samplesDataCenter.get().iterator().next());
+            samplesDataCenter.clear();
+        }
+
+        @Override
+        public void onIterationTerminated(Context context, Collector<IForest> 
collector)
+                throws Exception {
+            IForest centers =
+                    Objects.requireNonNull(
+                            
OperatorStateUtils.getUniqueElement(samplesDataCenter, "centers")
+                                    .orElse(null));
+            double centers0Sum1 = 0.0, centers1Sum1 = 0.0, centers0Sum2 = 0.0, 
centers1Sum2 = 0.0;
+            int size1 = 0, size2 = 0;
+            Iterator<DenseVector[]> samplesDataScoresIterator = 
samplesDataScores.get().iterator();
+            while (samplesDataScoresIterator.hasNext()) {
+                for (DenseVector denseVector : 
samplesDataScoresIterator.next()) {
+                    DenseVector denseVector1 = 
centers.classifyByCluster(denseVector);
+                    centers0Sum1 += denseVector1.get(0);
+                    centers1Sum1 += denseVector1.get(1);
+                    size1++;
+                }
+                centers0Sum2 = centers0Sum1 / size1;
+                centers1Sum2 = centers1Sum1 / size1;
+                size2++;
+            }
+
+            centers.center0 = centers0Sum2 / size2;
+            centers.center1 = centers1Sum2 / size2;
+
+            context.output(modelDataOutputTag, centers);
+
+            samplesDataCenter.clear();
+            samplesDataScores.clear();
+            samplesData.clear();
+        }
+    }
+
+    /** Construct isolation forest. */
+    public static class IForest implements Serializable {
+        public int treesNumber;
+        public int iters;

Review Comment:
   Given that `IForest` is used as the model data, it seems a bit weird to have 
`iters` in the model data. 



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