Github user yanboliang commented on a diff in the pull request:
https://github.com/apache/spark/pull/18538#discussion_r136306135
--- Diff:
mllib/src/main/scala/org/apache/spark/ml/evaluation/ClusteringEvaluator.scala
---
@@ -0,0 +1,379 @@
+/*
+ * 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.spark.ml.evaluation
+
+import org.apache.spark.SparkContext
+import org.apache.spark.annotation.{Experimental, Since}
+import org.apache.spark.broadcast.Broadcast
+import org.apache.spark.ml.linalg.{BLAS, DenseVector, Vector, Vectors,
VectorUDT}
+import org.apache.spark.ml.param.ParamMap
+import org.apache.spark.ml.param.shared.{HasFeaturesCol, HasPredictionCol}
+import org.apache.spark.ml.util.{DefaultParamsReadable,
DefaultParamsWritable, Identifiable, SchemaUtils}
+import org.apache.spark.sql.{DataFrame, Dataset}
+import org.apache.spark.sql.functions.{avg, col, udf}
+import org.apache.spark.sql.types.IntegerType
+
+/**
+ * Evaluator for clustering results.
+ * The metric computes the Silhouette measure
+ * using the squared Euclidean distance.
+ *
+ * The Silhouette is a measure for the validation
+ * of the consistency within clusters. It ranges
+ * between 1 and -1, where a value close to 1
+ * means that the points in a cluster are close
+ * to the other points in the same cluster and
+ * far from the points of the other clusters.
+ *
+ * The implementation follows the proposal explained
+ * <a
href="https://drive.google.com/file/d/0B0Hyo%5f%5fbG%5f3fdkNvSVNYX2E3ZU0/view";>
+ * in this document</a>.
+ */
+@Experimental
+@Since("2.3.0")
+class ClusteringEvaluator (val uid: String)
+ extends Evaluator with HasPredictionCol with HasFeaturesCol with
DefaultParamsWritable {
+
+ def this() = this(Identifiable.randomUID("cluEval"))
+
+ override def copy(pMap: ParamMap): ClusteringEvaluator =
this.defaultCopy(pMap)
+
+ override def isLargerBetter: Boolean = true
+
+ /** @group setParam */
+ @Since("2.3.0")
+ def setPredictionCol(value: String): this.type = set(predictionCol,
value)
+
+ /** @group setParam */
+ @Since("2.3.0")
+ def setFeaturesCol(value: String): this.type = set(featuresCol, value)
+
+ @Since("2.3.0")
+ override def evaluate(dataset: Dataset[_]): Double = {
+ SchemaUtils.checkColumnType(dataset.schema, $(featuresCol), new
VectorUDT)
+ SchemaUtils.checkColumnType(dataset.schema, $(predictionCol),
IntegerType)
+
+ SquaredEuclideanSilhouette.computeSilhouetteScore(
+ dataset,
+ $(predictionCol),
+ $(featuresCol)
+ )
+ }
+}
+
+
+object ClusteringEvaluator
+ extends DefaultParamsReadable[ClusteringEvaluator] {
+
+ override def load(path: String): ClusteringEvaluator = super.load(path)
+
+}
+
+
+/**
+ * SquaredEuclideanSilhouette computes the average of the
+ * Silhouette over all the data of the dataset, which is
+ * a measure of how appropriately the data have been clustered.
+ *
+ * The Silhouette for each point `i` is defined as:
+ *
+ * <blockquote>
+ * s_{i} = \frac{b_{i}-a_{i}}{max\{a_{i},b_{i}\}}
+ * </blockquote>
+ *
+ * which can be rewritten as
+ *
+ * <blockquote>
+ * s_{i}=\left\{ \begin{tabular}{cc}
+ * $1-\frac{a_{i}}{b_{i}}$ & if $a_{i} \leq b_{i}$ \\
+ * $\frac{b_{i}}{a_{i}}-1$ & if $a_{i} \gt b_{i}$
+ * </blockquote>
+ *
+ * where `a(i)` is the average dissimilarity of `i` with all other data
+ * within the same cluster, `b(i)` is the lowest average dissimilarity
+ * of to any other cluster, of which `i` is not a member.
+ * `a(i)` can be interpreted as as how well `i` is assigned to its cluster
+ * (the smaller the value, the better the assignment), while `b(i)` is
+ * a measure of how well `i` has not been assigned to its "neighboring
cluster",
+ * ie. the nearest cluster to `i`.
+ *
+ * Unfortunately, the naive implementation of the algorithm requires to
compute
+ * the distance of each couple of points in the dataset. Since the
computation of
+ * the distance measure takes `D` operations - if `D` is the number of
dimensions
+ * of each point, the computational complexity of the algorithm is
`O(N^2*D)`, where
+ * `N` is the cardinality of the dataset. Of course this is not scalable
in `N`,
+ * which is the critical number in a Big Data context.
+ *
+ * The algorithm which is implemented in this object, instead, is an
efficient
+ * and parallel implementation of the Silhouette using the squared
Euclidean
+ * distance measure.
+ *
+ * With this assumption, the average of the distance of the point `X`
+ * to the points `C_{i}` belonging to the cluster `\Gamma` is:
+ *
+ * <blockquote>
+ * \sum\limits_{i=1}^N d(X, C_{i} )^2 =
+ * \sum\limits_{i=1}^N \Big( \sum\limits_{j=1}^D (x_{j}-c_{ij})^2 \Big)
+ * = \sum\limits_{i=1}^N \Big( \sum\limits_{j=1}^D x_{j}^2 +
+ * \sum\limits_{j=1}^D c_{ij}^2 -2\sum\limits_{j=1}^D x_{i}c_{ij} \Big)
+ * = \sum\limits_{i=1}^N \sum\limits_{j=1}^D x_{j}^2 +
+ * \sum\limits_{i=1}^N \sum\limits_{j=1}^D c_{ij}^2
+ * -2 \sum\limits_{i=1}^N \sum\limits_{j=1}^D x_{i}c_{ij}
+ * </blockquote>
+ *
+ * where `x_{j}` is the `j`-th dimension of the point `X` and
+ * `c_{ij} is the `j`-th dimension of the `i`-th point in cluster `\Gamma`.
+ *
+ * Then, the first term of the equation can be rewritten as:
+ *
+ * <blockquote>
+ * \sum\limits_{i=1}^N \sum\limits_{j=1}^D x_{j}^2 = N \xi_{X} ,
+ * with \xi_{X} = \sum\limits_{j=1}^D x_{j}^2
+ * </blockquote>
+ *
+ * where `\xi_{X}` is fixed for each point and it can be precomputed.
+ *
+ * Moreover, the second term is fixed for each cluster too,
+ * thus we can name it `\Psi_{\Gamma}`
+ *
+ * <blockquote>
+ * sum\limits_{i=1}^N \sum\limits_{j=1}^D c_{ij}^2 =
--- End diff --
Ditto, there is syntax error in this latex formula.
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