Repository: spark Updated Branches: refs/heads/master 8f11c6116 -> 2728c3df6
[SPARK-7578] [ML] [DOC] User guide for spark.ml Normalizer, IDF, StandardScaler Added user guide sections with code examples. Also added small Java unit tests to test Java example in guide. CC: mengxr Author: Joseph K. Bradley <jos...@databricks.com> Closes #6127 from jkbradley/feature-guide-2 and squashes the following commits: cd47f4b [Joseph K. Bradley] Updated based on code review f16bcec [Joseph K. Bradley] Fixed merge issues and update Python examples print calls for Python 3 0a862f9 [Joseph K. Bradley] Added Normalizer, StandardScaler to ml-features doc, plus small Java unit tests a21c2d6 [Joseph K. Bradley] Updated ml-features.md with IDF Project: http://git-wip-us.apache.org/repos/asf/spark/repo Commit: http://git-wip-us.apache.org/repos/asf/spark/commit/2728c3df Tree: http://git-wip-us.apache.org/repos/asf/spark/tree/2728c3df Diff: http://git-wip-us.apache.org/repos/asf/spark/diff/2728c3df Branch: refs/heads/master Commit: 2728c3df6690c2fcd4af3bd1c604c98ef6d509a5 Parents: 8f11c61 Author: Joseph K. Bradley <jos...@databricks.com> Authored: Thu May 21 22:59:45 2015 -0700 Committer: Xiangrui Meng <m...@databricks.com> Committed: Thu May 21 22:59:45 2015 -0700 ---------------------------------------------------------------------- docs/ml-features.md | 224 ++++++++++++++++--- .../spark/ml/feature/JavaHashingTFSuite.java | 17 +- .../spark/ml/feature/JavaNormalizerSuite.java | 71 ++++++ .../ml/feature/JavaStandardScalerSuite.java | 71 ++++++ 4 files changed, 351 insertions(+), 32 deletions(-) ---------------------------------------------------------------------- http://git-wip-us.apache.org/repos/asf/spark/blob/2728c3df/docs/ml-features.md ---------------------------------------------------------------------- diff --git a/docs/ml-features.md b/docs/ml-features.md index 06f1ac1..efe9b3b 100644 --- a/docs/ml-features.md +++ b/docs/ml-features.md @@ -18,30 +18,38 @@ This section covers algorithms for working with features, roughly divided into t # Feature Extractors -## Hashing Term-Frequency (HashingTF) +## TF-IDF (HashingTF and IDF) -`HashingTF` is a `Transformer` which takes sets of terms (e.g., `String` terms can be sets of words) and converts those sets into fixed-length feature vectors. -The algorithm combines [Term Frequency (TF)](http://en.wikipedia.org/wiki/Tf%E2%80%93idf) counts with the [hashing trick](http://en.wikipedia.org/wiki/Feature_hashing) for dimensionality reduction. Please refer to the [MLlib user guide on TF-IDF](mllib-feature-extraction.html#tf-idf) for more details on Term-Frequency. +[Term Frequency-Inverse Document Frequency (TF-IDF)](http://en.wikipedia.org/wiki/Tf%E2%80%93idf) is a common text pre-processing step. In Spark ML, TF-IDF is separate into two parts: TF (+hashing) and IDF. -HashingTF is implemented in -[HashingTF](api/scala/index.html#org.apache.spark.ml.feature.HashingTF). -In the following code segment, we start with a set of sentences. We split each sentence into words using `Tokenizer`. For each sentence (bag of words), we hash it into a feature vector. This feature vector could then be passed to a learning algorithm. +**TF**: `HashingTF` is a `Transformer` which takes sets of terms and converts those sets into fixed-length feature vectors. In text processing, a "set of terms" might be a bag of words. +The algorithm combines Term Frequency (TF) counts with the [hashing trick](http://en.wikipedia.org/wiki/Feature_hashing) for dimensionality reduction. + +**IDF**: `IDF` is an `Estimator` which fits on a dataset and produces an `IDFModel`. The `IDFModel` takes feature vectors (generally created from `HashingTF`) and scales each column. Intuitively, it down-weights columns which appear frequently in a corpus. + +Please refer to the [MLlib user guide on TF-IDF](mllib-feature-extraction.html#tf-idf) for more details on Term Frequency and Inverse Document Frequency. +For API details, refer to the [HashingTF API docs](api/scala/index.html#org.apache.spark.ml.feature.HashingTF) and the [IDF API docs](api/scala/index.html#org.apache.spark.ml.feature.IDF). + +In the following code segment, we start with a set of sentences. We split each sentence into words using `Tokenizer`. For each sentence (bag of words), we use `HashingTF` to hash the sentence into a feature vector. We use `IDF` to rescale the feature vectors; this generally improves performance when using text as features. Our feature vectors could then be passed to a learning algorithm. <div class="codetabs"> <div data-lang="scala" markdown="1"> {% highlight scala %} -import org.apache.spark.ml.feature.{HashingTF, Tokenizer} +import org.apache.spark.ml.feature.{HashingTF, IDF, Tokenizer} -val sentenceDataFrame = sqlContext.createDataFrame(Seq( +val sentenceData = sqlContext.createDataFrame(Seq( (0, "Hi I heard about Spark"), (0, "I wish Java could use case classes"), (1, "Logistic regression models are neat") )).toDF("label", "sentence") val tokenizer = new Tokenizer().setInputCol("sentence").setOutputCol("words") -val wordsDataFrame = tokenizer.transform(sentenceDataFrame) -val hashingTF = new HashingTF().setInputCol("words").setOutputCol("features").setNumFeatures(20) -val featurized = hashingTF.transform(wordsDataFrame) -featurized.select("features", "label").take(3).foreach(println) +val wordsData = tokenizer.transform(sentenceData) +val hashingTF = new HashingTF().setInputCol("words").setOutputCol("rawFeatures").setNumFeatures(20) +val featurizedData = hashingTF.transform(wordsData) +val idf = new IDF().setInputCol("rawFeatures").setOutputCol("features") +val idfModel = idf.fit(featurizedData) +val rescaledData = idfModel.transform(featurizedData) +rescaledData.select("features", "label").take(3).foreach(println) {% endhighlight %} </div> @@ -51,6 +59,7 @@ import com.google.common.collect.Lists; import org.apache.spark.api.java.JavaRDD; import org.apache.spark.ml.feature.HashingTF; +import org.apache.spark.ml.feature.IDF; import org.apache.spark.ml.feature.Tokenizer; import org.apache.spark.mllib.linalg.Vector; import org.apache.spark.sql.DataFrame; @@ -70,16 +79,19 @@ StructType schema = new StructType(new StructField[]{ new StructField("label", DataTypes.DoubleType, false, Metadata.empty()), new StructField("sentence", DataTypes.StringType, false, Metadata.empty()) }); -DataFrame sentenceDataFrame = sqlContext.createDataFrame(jrdd, schema); +DataFrame sentenceData = sqlContext.createDataFrame(jrdd, schema); Tokenizer tokenizer = new Tokenizer().setInputCol("sentence").setOutputCol("words"); -DataFrame wordsDataFrame = tokenizer.transform(sentenceDataFrame); +DataFrame wordsData = tokenizer.transform(sentenceData); int numFeatures = 20; HashingTF hashingTF = new HashingTF() .setInputCol("words") - .setOutputCol("features") + .setOutputCol("rawFeatures") .setNumFeatures(numFeatures); -DataFrame featurized = hashingTF.transform(wordsDataFrame); -for (Row r : featurized.select("features", "label").take(3)) { +DataFrame featurizedData = hashingTF.transform(wordsData); +IDF idf = new IDF().setInputCol("rawFeatures").setOutputCol("features"); +IDFModel idfModel = idf.fit(featurizedData); +DataFrame rescaledData = idfModel.transform(featurizedData); +for (Row r : rescaledData.select("features", "label").take(3)) { Vector features = r.getAs(0); Double label = r.getDouble(1); System.out.println(features); @@ -89,19 +101,22 @@ for (Row r : featurized.select("features", "label").take(3)) { <div data-lang="python" markdown="1"> {% highlight python %} -from pyspark.ml.feature import HashingTF, Tokenizer +from pyspark.ml.feature import HashingTF, IDF, Tokenizer -sentenceDataFrame = sqlContext.createDataFrame([ +sentenceData = sqlContext.createDataFrame([ (0, "Hi I heard about Spark"), (0, "I wish Java could use case classes"), (1, "Logistic regression models are neat") ], ["label", "sentence"]) tokenizer = Tokenizer(inputCol="sentence", outputCol="words") -wordsDataFrame = tokenizer.transform(sentenceDataFrame) -hashingTF = HashingTF(inputCol="words", outputCol="features", numFeatures=20) -featurized = hashingTF.transform(wordsDataFrame) -for features_label in featurized.select("features", "label").take(3): - print features_label +wordsData = tokenizer.transform(sentenceData) +hashingTF = HashingTF(inputCol="words", outputCol="rawFeatures", numFeatures=20) +featurizedData = hashingTF.transform(wordsData) +idf = IDF(inputCol="rawFeatures", outputCol="features") +idfModel = idf.fit(featurizedData) +rescaledData = idfModel.transform(featurizedData) +for features_label in rescaledData.select("features", "label").take(3): + print(features_label) {% endhighlight %} </div> </div> @@ -267,11 +282,12 @@ sentenceDataFrame = sqlContext.createDataFrame([ tokenizer = Tokenizer(inputCol="sentence", outputCol="words") wordsDataFrame = tokenizer.transform(sentenceDataFrame) for words_label in wordsDataFrame.select("words", "label").take(3): - print words_label + print(words_label) {% endhighlight %} </div> </div> + ## Binarizer Binarization is the process of thresholding numerical features to binary features. As some probabilistic estimators make assumption that the input data is distributed according to [Bernoulli distribution](http://en.wikipedia.org/wiki/Bernoulli_distribution), a binarizer is useful for pre-processing the input data with continuous numerical features. @@ -352,7 +368,7 @@ binarizer = Binarizer(threshold=0.5, inputCol="feature", outputCol="binarized_fe binarizedDataFrame = binarizer.transform(continuousDataFrame) binarizedFeatures = binarizedDataFrame.select("binarized_feature") for binarized_feature, in binarizedFeatures.collect(): - print binarized_feature + print(binarized_feature) {% endhighlight %} </div> </div> @@ -618,5 +634,161 @@ indexedData = indexerModel.transform(data) </div> </div> + +## Normalizer + +`Normalizer` is a `Transformer` which transforms a dataset of `Vector` rows, normalizing each `Vector` to have unit norm. It takes parameter `p`, which specifies the [p-norm](http://en.wikipedia.org/wiki/Norm_%28mathematics%29#p-norm) used for normalization. ($p = 2$ by default.) This normalization can help standardize your input data and improve the behavior of learning algorithms. + +The following example demonstrates how to load a dataset in libsvm format and then normalize each row to have unit $L^2$ norm and unit $L^\infty$ norm. + +<div class="codetabs"> +<div data-lang="scala"> +{% highlight scala %} +import org.apache.spark.ml.feature.Normalizer +import org.apache.spark.mllib.util.MLUtils + +val data = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt") +val dataFrame = sqlContext.createDataFrame(data) + +// Normalize each Vector using $L^1$ norm. +val normalizer = new Normalizer() + .setInputCol("features") + .setOutputCol("normFeatures") + .setP(1.0) +val l1NormData = normalizer.transform(dataFrame) + +// Normalize each Vector using $L^\infty$ norm. +val lInfNormData = normalizer.transform(dataFrame, normalizer.p -> Double.PositiveInfinity) +{% endhighlight %} +</div> + +<div data-lang="java"> +{% highlight java %} +import org.apache.spark.api.java.JavaRDD; +import org.apache.spark.ml.feature.Normalizer; +import org.apache.spark.mllib.regression.LabeledPoint; +import org.apache.spark.mllib.util.MLUtils; +import org.apache.spark.sql.DataFrame; + +JavaRDD<LabeledPoint> data = + MLUtils.loadLibSVMFile(jsc.sc(), "data/mllib/sample_libsvm_data.txt").toJavaRDD(); +DataFrame dataFrame = jsql.createDataFrame(data, LabeledPoint.class); + +// Normalize each Vector using $L^1$ norm. +Normalizer normalizer = new Normalizer() + .setInputCol("features") + .setOutputCol("normFeatures") + .setP(1.0); +DataFrame l1NormData = normalizer.transform(dataFrame); + +// Normalize each Vector using $L^\infty$ norm. +DataFrame lInfNormData = + normalizer.transform(dataFrame, normalizer.p().w(Double.POSITIVE_INFINITY)); +{% endhighlight %} +</div> + +<div data-lang="python"> +{% highlight python %} +from pyspark.mllib.util import MLUtils +from pyspark.ml.feature import Normalizer + +data = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt") +dataFrame = sqlContext.createDataFrame(data) + +# Normalize each Vector using $L^1$ norm. +normalizer = Normalizer(inputCol="features", outputCol="normFeatures", p=1.0) +l1NormData = normalizer.transform(dataFrame) + +# Normalize each Vector using $L^\infty$ norm. +lInfNormData = normalizer.transform(dataFrame, {normalizer.p: float("inf")}) +{% endhighlight %} +</div> +</div> + + +## StandardScaler + +`StandardScaler` transforms a dataset of `Vector` rows, normalizing each feature to have unit standard deviation and/or zero mean. It takes parameters: + +* `withStd`: True by default. Scales the data to unit standard deviation. +* `withMean`: False by default. Centers the data with mean before scaling. It will build a dense output, so this does not work on sparse input and will raise an exception. + +`StandardScaler` is a `Model` which can be `fit` on a dataset to produce a `StandardScalerModel`; this amounts to computing summary statistics. The model can then transform a `Vector` column in a dataset to have unit standard deviation and/or zero mean features. + +Note that if the standard deviation of a feature is zero, it will return default `0.0` value in the `Vector` for that feature. + +More details can be found in the API docs for +[StandardScaler](api/scala/index.html#org.apache.spark.ml.feature.StandardScaler) and +[StandardScalerModel](api/scala/index.html#org.apache.spark.ml.feature.StandardScalerModel). + +The following example demonstrates how to load a dataset in libsvm format and then normalize each feature to have unit standard deviation. + +<div class="codetabs"> +<div data-lang="scala"> +{% highlight scala %} +import org.apache.spark.ml.feature.StandardScaler +import org.apache.spark.mllib.util.MLUtils + +val data = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt") +val dataFrame = sqlContext.createDataFrame(data) +val scaler = new StandardScaler() + .setInputCol("features") + .setOutputCol("scaledFeatures") + .setWithStd(true) + .setWithMean(false) + +// Compute summary statistics by fitting the StandardScaler +val scalerModel = scaler.fit(dataFrame) + +// Normalize each feature to have unit standard deviation. +val scaledData = scalerModel.transform(dataFrame) +{% endhighlight %} +</div> + +<div data-lang="java"> +{% highlight java %} +import org.apache.spark.api.java.JavaRDD; +import org.apache.spark.ml.feature.StandardScaler; +import org.apache.spark.mllib.regression.LabeledPoint; +import org.apache.spark.mllib.util.MLUtils; +import org.apache.spark.sql.DataFrame; + +JavaRDD<LabeledPoint> data = + MLUtils.loadLibSVMFile(jsc.sc(), "data/mllib/sample_libsvm_data.txt").toJavaRDD(); +DataFrame dataFrame = jsql.createDataFrame(data, LabeledPoint.class); +StandardScaler scaler = new StandardScaler() + .setInputCol("features") + .setOutputCol("scaledFeatures") + .setWithStd(true) + .setWithMean(false); + +// Compute summary statistics by fitting the StandardScaler +StandardScalerModel scalerModel = scaler.fit(dataFrame); + +// Normalize each feature to have unit standard deviation. +DataFrame scaledData = scalerModel.transform(dataFrame); +{% endhighlight %} +</div> + +<div data-lang="python"> +{% highlight python %} +from pyspark.mllib.util import MLUtils +from pyspark.ml.feature import StandardScaler + +data = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt") +dataFrame = sqlContext.createDataFrame(data) +scaler = StandardScaler(inputCol="features", outputCol="scaledFeatures", + withStd=True, withMean=False) + +# Compute summary statistics by fitting the StandardScaler +scalerModel = scaler.fit(dataFrame) + +# Normalize each feature to have unit standard deviation. +scaledData = scalerModel.transform(dataFrame) +{% endhighlight %} +</div> +</div> + + # Feature Selectors http://git-wip-us.apache.org/repos/asf/spark/blob/2728c3df/mllib/src/test/java/org/apache/spark/ml/feature/JavaHashingTFSuite.java ---------------------------------------------------------------------- diff --git a/mllib/src/test/java/org/apache/spark/ml/feature/JavaHashingTFSuite.java b/mllib/src/test/java/org/apache/spark/ml/feature/JavaHashingTFSuite.java index 23463ab..da22180 100644 --- a/mllib/src/test/java/org/apache/spark/ml/feature/JavaHashingTFSuite.java +++ b/mllib/src/test/java/org/apache/spark/ml/feature/JavaHashingTFSuite.java @@ -63,17 +63,22 @@ public class JavaHashingTFSuite { new StructField("label", DataTypes.DoubleType, false, Metadata.empty()), new StructField("sentence", DataTypes.StringType, false, Metadata.empty()) }); - DataFrame sentenceDataFrame = jsql.createDataFrame(jrdd, schema); - Tokenizer tokenizer = new Tokenizer().setInputCol("sentence").setOutputCol("words"); - DataFrame wordsDataFrame = tokenizer.transform(sentenceDataFrame); + DataFrame sentenceData = jsql.createDataFrame(jrdd, schema); + Tokenizer tokenizer = new Tokenizer() + .setInputCol("sentence") + .setOutputCol("words"); + DataFrame wordsData = tokenizer.transform(sentenceData); int numFeatures = 20; HashingTF hashingTF = new HashingTF() .setInputCol("words") - .setOutputCol("features") + .setOutputCol("rawFeatures") .setNumFeatures(numFeatures); - DataFrame featurized = hashingTF.transform(wordsDataFrame); - for (Row r : featurized.select("features", "words", "label").take(3)) { + DataFrame featurizedData = hashingTF.transform(wordsData); + IDF idf = new IDF().setInputCol("rawFeatures").setOutputCol("features"); + IDFModel idfModel = idf.fit(featurizedData); + DataFrame rescaledData = idfModel.transform(featurizedData); + for (Row r : rescaledData.select("features", "label").take(3)) { Vector features = r.getAs(0); Assert.assertEquals(features.size(), numFeatures); } http://git-wip-us.apache.org/repos/asf/spark/blob/2728c3df/mllib/src/test/java/org/apache/spark/ml/feature/JavaNormalizerSuite.java ---------------------------------------------------------------------- diff --git a/mllib/src/test/java/org/apache/spark/ml/feature/JavaNormalizerSuite.java b/mllib/src/test/java/org/apache/spark/ml/feature/JavaNormalizerSuite.java new file mode 100644 index 0000000..d82f3b7 --- /dev/null +++ b/mllib/src/test/java/org/apache/spark/ml/feature/JavaNormalizerSuite.java @@ -0,0 +1,71 @@ +/* + * 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.feature; + +import java.util.List; + +import com.google.common.collect.Lists; +import org.junit.After; +import org.junit.Before; +import org.junit.Test; + +import org.apache.spark.api.java.JavaSparkContext; +import org.apache.spark.mllib.linalg.Vectors; +import org.apache.spark.sql.DataFrame; +import org.apache.spark.sql.SQLContext; + +public class JavaNormalizerSuite { + private transient JavaSparkContext jsc; + private transient SQLContext jsql; + + @Before + public void setUp() { + jsc = new JavaSparkContext("local", "JavaNormalizerSuite"); + jsql = new SQLContext(jsc); + } + + @After + public void tearDown() { + jsc.stop(); + jsc = null; + } + + @Test + public void normalizer() { + // The tests are to check Java compatibility. + List<VectorIndexerSuite.FeatureData> points = Lists.newArrayList( + new VectorIndexerSuite.FeatureData(Vectors.dense(0.0, -2.0)), + new VectorIndexerSuite.FeatureData(Vectors.dense(1.0, 3.0)), + new VectorIndexerSuite.FeatureData(Vectors.dense(1.0, 4.0)) + ); + DataFrame dataFrame = jsql.createDataFrame(jsc.parallelize(points, 2), + VectorIndexerSuite.FeatureData.class); + Normalizer normalizer = new Normalizer() + .setInputCol("features") + .setOutputCol("normFeatures"); + + // Normalize each Vector using $L^2$ norm. + DataFrame l2NormData = normalizer.transform(dataFrame, normalizer.p().w(2)); + l2NormData.count(); + + // Normalize each Vector using $L^\infty$ norm. + DataFrame lInfNormData = + normalizer.transform(dataFrame, normalizer.p().w(Double.POSITIVE_INFINITY)); + lInfNormData.count(); + } +} http://git-wip-us.apache.org/repos/asf/spark/blob/2728c3df/mllib/src/test/java/org/apache/spark/ml/feature/JavaStandardScalerSuite.java ---------------------------------------------------------------------- diff --git a/mllib/src/test/java/org/apache/spark/ml/feature/JavaStandardScalerSuite.java b/mllib/src/test/java/org/apache/spark/ml/feature/JavaStandardScalerSuite.java new file mode 100644 index 0000000..74eb273 --- /dev/null +++ b/mllib/src/test/java/org/apache/spark/ml/feature/JavaStandardScalerSuite.java @@ -0,0 +1,71 @@ +/* + * 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.feature; + +import java.util.List; + +import com.google.common.collect.Lists; +import org.junit.After; +import org.junit.Before; +import org.junit.Test; + +import org.apache.spark.api.java.JavaSparkContext; +import org.apache.spark.mllib.linalg.Vectors; +import org.apache.spark.sql.DataFrame; +import org.apache.spark.sql.SQLContext; + +public class JavaStandardScalerSuite { + private transient JavaSparkContext jsc; + private transient SQLContext jsql; + + @Before + public void setUp() { + jsc = new JavaSparkContext("local", "JavaStandardScalerSuite"); + jsql = new SQLContext(jsc); + } + + @After + public void tearDown() { + jsc.stop(); + jsc = null; + } + + @Test + public void standardScaler() { + // The tests are to check Java compatibility. + List<VectorIndexerSuite.FeatureData> points = Lists.newArrayList( + new VectorIndexerSuite.FeatureData(Vectors.dense(0.0, -2.0)), + new VectorIndexerSuite.FeatureData(Vectors.dense(1.0, 3.0)), + new VectorIndexerSuite.FeatureData(Vectors.dense(1.0, 4.0)) + ); + DataFrame dataFrame = jsql.createDataFrame(jsc.parallelize(points, 2), + VectorIndexerSuite.FeatureData.class); + StandardScaler scaler = new StandardScaler() + .setInputCol("features") + .setOutputCol("scaledFeatures") + .setWithStd(true) + .setWithMean(false); + + // Compute summary statistics by fitting the StandardScaler + StandardScalerModel scalerModel = scaler.fit(dataFrame); + + // Normalize each feature to have unit standard deviation. + DataFrame scaledData = scalerModel.transform(dataFrame); + scaledData.count(); + } +} --------------------------------------------------------------------- To unsubscribe, e-mail: commits-unsubscr...@spark.apache.org For additional commands, e-mail: commits-h...@spark.apache.org
