---
layout: global
title: Feature Extraction, Transformation, and Selection - SparkML
displayTitle: <a href="ml-guide.html">ML</a> - Features
---
This section covers algorithms for working with features, roughly divided into these groups:
* Extraction: Extracting features from "raw" data
* Transformation: Scaling, converting, or modifying features
* Selection: Selecting a subset from a larger set of features
**Table of Contents**
* This will become a table of contents (this text will be scraped).
{:toc}
# Feature Extractors
## TF-IDF (HashingTF and IDF)
[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.
**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.
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">
Refer to the [HashingTF Scala docs](api/scala/index.html#org.apache.spark.ml.feature.HashingTF) and
the [IDF Scala docs](api/scala/index.html#org.apache.spark.ml.feature.IDF) for more details on the API.
{% include_example scala/org/apache/spark/examples/ml/TfIdfExample.scala %}
</div>
<div data-lang="java" markdown="1">
Refer to the [HashingTF Java docs](api/java/org/apache/spark/ml/feature/HashingTF.html) and the
[IDF Java docs](api/java/org/apache/spark/ml/feature/IDF.html) for more details on the API.
{% include_example java/org/apache/spark/examples/ml/JavaTfIdfExample.java %}
</div>
<div data-lang="python" markdown="1">
Refer to the [HashingTF Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.HashingTF) and
the [IDF Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.IDF) for more details on the API.
{% include_example python/ml/tf_idf_example.py %}
</div>
</div>
## Word2Vec
`Word2Vec` is an `Estimator` which takes sequences of words representing documents and trains a
`Word2VecModel`. The model maps each word to a unique fixed-size vector. The `Word2VecModel`
transforms each document into a vector using the average of all words in the document; this vector
can then be used for as features for prediction, document similarity calculations, etc.
Please refer to the [MLlib user guide on Word2Vec](mllib-feature-extraction.html#Word2Vec) for more
details.
In the following code segment, we start with a set of documents, each of which is represented as a sequence of words. For each document, we transform it into a feature vector. This feature vector could then be passed to a learning algorithm.
<div class="codetabs">
<div data-lang="scala" markdown="1">
Refer to the [Word2Vec Scala docs](api/scala/index.html#org.apache.spark.ml.feature.Word2Vec)
for more details on the API.
{% include_example scala/org/apache/spark/examples/ml/Word2VecExample.scala %}
</div>
<div data-lang="java" markdown="1">
Refer to the [Word2Vec Java docs](api/java/org/apache/spark/ml/feature/Word2Vec.html)
for more details on the API.
{% include_example java/org/apache/spark/examples/ml/JavaWord2VecExample.java %}
</div>
<div data-lang="python" markdown="1">
Refer to the [Word2Vec Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.Word2Vec)
for more details on the API.
{% include_example python/ml/word2vec_example.py %}
</div>
</div>
## CountVectorizer
`CountVectorizer` and `CountVectorizerModel` aim to help convert a collection of text documents
to vectors of token counts. When an a-priori dictionary is not available, `CountVectorizer` can
be used as an `Estimator` to extract the vocabulary and generates a `CountVectorizerModel`. The
model produces sparse representations for the documents over the vocabulary, which can then be
passed to other algorithms like LDA.
During the fitting process, `CountVectorizer` will select the top `vocabSize` words ordered by
term frequency across the corpus. An optional parameter "minDF" also affect the fitting process
by specifying the minimum number (or fraction if < 1.0) of documents a term must appear in to be
included in the vocabulary.
**Examples**
Assume that we have the following DataFrame with columns `id` and `texts`:
~~~~
id | texts
----|----------
0 | Array("a", "b", "c")
1 | Array("a", "b", "b", "c", "a")
~~~~
each row in`texts` is a document of type Array[String].
Invoking fit of `CountVectorizer` produces a `CountVectorizerModel` with vocabulary (a, b, c),
then the output column "vector" after transformation contains:
~~~~
id | texts | vector
----|---------------------------------|---------------
0 | Array("a", "b", "c") | (3,[0,1,2],[1.0,1.0,1.0])
1 | Array("a", "b", "b", "c", "a") | (3,[0,1,2],[2.0,2.0,1.0])
~~~~
each vector represents the token counts of the document over the vocabulary.
<div class="codetabs">
<div data-lang="scala" markdown="1">
Refer to the [CountVectorizer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.CountVectorizer)
and the [CountVectorizerModel Scala docs](api/scala/index.html#org.apache.spark.ml.feature.CountVectorizerModel)
for more details on the API.
{% include_example scala/org/apache/spark/examples/ml/CountVectorizerExample.scala %}
</div>
<div data-lang="java" markdown="1">
Refer to the [CountVectorizer Java docs](api/java/org/apache/spark/ml/feature/CountVectorizer.html)
and the [CountVectorizerModel Java docs](api/java/org/apache/spark/ml/feature/CountVectorizerModel.html)
for more details on the API.
{% include_example java/org/apache/spark/examples/ml/JavaCountVectorizerExample.java %}
</div>
</div>
# Feature Transformers
## Tokenizer
[Tokenization](http://en.wikipedia.org/wiki/Lexical_analysis#Tokenization) is the process of taking text (such as a sentence) and breaking it into individual terms (usually words). A simple [Tokenizer](api/scala/index.html#org.apache.spark.ml.feature.Tokenizer) class provides this functionality. The example below shows how to split sentences into sequences of words.
[RegexTokenizer](api/scala/index.html#org.apache.spark.ml.feature.RegexTokenizer) allows more
advanced tokenization based on regular expression (regex) matching.
By default, the parameter "pattern" (regex, default: \\s+) is used as delimiters to split the input text.
Alternatively, users can set parameter "gaps" to false indicating the regex "pattern" denotes
"tokens" rather than splitting gaps, and find all matching occurrences as the tokenization result.
<div class="codetabs">
<div data-lang="scala" markdown="1">
Refer to the [Tokenizer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.Tokenizer)
and the [RegexTokenizer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.Tokenizer)
for more details on the API.
{% highlight scala %}
import org.apache.spark.ml.feature.{Tokenizer, RegexTokenizer}
val sentenceDataFrame = sqlContext.createDataFrame(Seq(
(0, "Hi I heard about Spark"),
(1, "I wish Java could use case classes"),
(2, "Logistic,regression,models,are,neat")
)).toDF("label", "sentence")
val tokenizer = new Tokenizer().setInputCol("sentence").setOutputCol("words")
val regexTokenizer = new RegexTokenizer()
.setInputCol("sentence")
.setOutputCol("words")
.setPattern("\\W") // alternatively .setPattern("\\w+").setGaps(false)
val tokenized = tokenizer.transform(sentenceDataFrame)
tokenized.select("words", "label").take(3).foreach(println)
val regexTokenized = regexTokenizer.transform(sentenceDataFrame)
regexTokenized.select("words", "label").take(3).foreach(println)
{% endhighlight %}
</div>
<div data-lang="java" markdown="1">
Refer to the [Tokenizer Java docs](api/java/org/apache/spark/ml/feature/Tokenizer.html)
and the [RegexTokenizer Java docs](api/java/org/apache/spark/ml/feature/RegexTokenizer.html)
for more details on the API.
{% highlight java %}
import java.util.Arrays;
import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.ml.feature.RegexTokenizer;
import org.apache.spark.ml.feature.Tokenizer;
import org.apache.spark.mllib.linalg.Vector;
import org.apache.spark.sql.DataFrame;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.types.DataTypes;
import org.apache.spark.sql.types.Metadata;
import org.apache.spark.sql.types.StructField;
import org.apache.spark.sql.types.StructType;
JavaRDD<Row> jrdd = jsc.parallelize(Arrays.asList(
RowFactory.create(0, "Hi I heard about Spark"),
RowFactory.create(1, "I wish Java could use case classes"),
RowFactory.create(2, "Logistic,regression,models,are,neat")
));
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);
Tokenizer tokenizer = new Tokenizer().setInputCol("sentence").setOutputCol("words");
DataFrame wordsDataFrame = tokenizer.transform(sentenceDataFrame);
for (Row r : wordsDataFrame.select("words", "label").take(3)) {
java.util.List<String> words = r.getList(0);
for (String word : words) System.out.print(word + " ");
System.out.println();
}
RegexTokenizer regexTokenizer = new RegexTokenizer()
.setInputCol("sentence")
.setOutputCol("words")
.setPattern("\\W"); // alternatively .setPattern("\\w+").setGaps(false);
{% endhighlight %}
</div>
<div data-lang="python" markdown="1">
Refer to the [Tokenizer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.Tokenizer) and
the the [RegexTokenizer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.RegexTokenizer)
for more details on the API.
{% highlight python %}
from pyspark.ml.feature import Tokenizer, RegexTokenizer
sentenceDataFrame = sqlContext.createDataFrame([
(0, "Hi I heard about Spark"),
(1, "I wish Java could use case classes"),
(2, "Logistic,regression,models,are,neat")
], ["label", "sentence"])
tokenizer = Tokenizer(inputCol="sentence", outputCol="words")
wordsDataFrame = tokenizer.transform(sentenceDataFrame)
for words_label in wordsDataFrame.select("words", "label").take(3):
print(words_label)
regexTokenizer = RegexTokenizer(inputCol="sentence", outputCol="words", pattern="\\W")
# alternatively, pattern="\\w+", gaps(False)
{% endhighlight %}
</div>
</div>
## StopWordsRemover
[Stop words](https://en.wikipedia.org/wiki/Stop_words) are words which
should be excluded from the input, typically because the words appear
frequently and don't carry as much meaning.
`StopWordsRemover` takes as input a sequence of strings (e.g. the output
of a [Tokenizer](ml-features.html#tokenizer)) and drops all the stop
words from the input sequences. The list of stopwords is specified by
the `stopWords` parameter. We provide [a list of stop
words](http://ir.dcs.gla.ac.uk/resources/linguistic_utils/stop_words) by
default, accessible by calling `getStopWords` on a newly instantiated
`StopWordsRemover` instance. A boolean parameter `caseSensitive` indicates
if the matches should be case sensitive (false by default).
**Examples**
Assume that we have the following DataFrame with columns `id` and `raw`:
~~~~
id | raw
----|----------
0 | [I, saw, the, red, baloon]
1 | [Mary, had, a, little, lamb]
~~~~
Applying `StopWordsRemover` with `raw` as the input column and `filtered` as the output
column, we should get the following:
~~~~
id | raw | filtered
----|-----------------------------|--------------------
0 | [I, saw, the, red, baloon] | [saw, red, baloon]
1 | [Mary, had, a, little, lamb]|[Mary, little, lamb]
~~~~
In `filtered`, the stop words "I", "the", "had", and "a" have been
filtered out.
<div class="codetabs">
<div data-lang="scala" markdown="1">
Refer to the [StopWordsRemover Scala docs](api/scala/index.html#org.apache.spark.ml.feature.StopWordsRemover)
for more details on the API.
{% highlight scala %}
import org.apache.spark.ml.feature.StopWordsRemover
val remover = new StopWordsRemover()
.setInputCol("raw")
.setOutputCol("filtered")
val dataSet = sqlContext.createDataFrame(Seq(
(0, Seq("I", "saw", "the", "red", "baloon")),
(1, Seq("Mary", "had", "a", "little", "lamb"))
)).toDF("id", "raw")
remover.transform(dataSet).show()
{% endhighlight %}
</div>
<div data-lang="java" markdown="1">
Refer to the [StopWordsRemover Java docs](api/java/org/apache/spark/ml/feature/StopWordsRemover.html)
for more details on the API.
{% highlight java %}
import java.util.Arrays;
import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.ml.feature.StopWordsRemover;
import org.apache.spark.sql.DataFrame;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.types.DataTypes;
import org.apache.spark.sql.types.Metadata;
import org.apache.spark.sql.types.StructField;
import org.apache.spark.sql.types.StructType;
StopWordsRemover remover = new StopWordsRemover()
.setInputCol("raw")
.setOutputCol("filtered");
JavaRDD<Row> rdd = jsc.parallelize(Arrays.asList(
RowFactory.create(Arrays.asList("I", "saw", "the", "red", "baloon")),
RowFactory.create(Arrays.asList("Mary", "had", "a", "little", "lamb"))
));
StructType schema = new StructType(new StructField[] {
new StructField("raw", DataTypes.createArrayType(DataTypes.StringType), false, Metadata.empty())
});
DataFrame dataset = jsql.createDataFrame(rdd, schema);
remover.transform(dataset).show();
{% endhighlight %}
</div>
<div data-lang="python" markdown="1">
Refer to the [StopWordsRemover Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.StopWordsRemover)
for more details on the API.
{% highlight python %}
from pyspark.ml.feature import StopWordsRemover
sentenceData = sqlContext.createDataFrame([
(0, ["I", "saw", "the", "red", "baloon"]),
(1, ["Mary", "had", "a", "little", "lamb"])
], ["label", "raw"])
remover = StopWordsRemover(inputCol="raw", outputCol="filtered")
remover.transform(sentenceData).show(truncate=False)
{% endhighlight %}
</div>
</div>
## $n$-gram
An [n-gram](https://en.wikipedia.org/wiki/N-gram) is a sequence of $n$ tokens (typically words) for some integer $n$. The `NGram` class can be used to transform input features into $n$-grams.
`NGram` takes as input a sequence of strings (e.g. the output of a [Tokenizer](ml-features.html#tokenizer)). The parameter `n` is used to determine the number of terms in each $n$-gram. The output will consist of a sequence of $n$-grams where each $n$-gram is represented by a space-delimited string of $n$ consecutive words. If the input sequence contains fewer than `n` strings, no output is produced.
<div class="codetabs">
<div data-lang="scala" markdown="1">
Refer to the [NGram Scala docs](api/scala/index.html#org.apache.spark.ml.feature.NGram)
for more details on the API.
{% highlight scala %}
import org.apache.spark.ml.feature.NGram
val wordDataFrame = sqlContext.createDataFrame(Seq(
(0, Array("Hi", "I", "heard", "about", "Spark")),
(1, Array("I", "wish", "Java", "could", "use", "case", "classes")),
(2, Array("Logistic", "regression", "models", "are", "neat"))
)).toDF("label", "words")
val ngram = new NGram().setInputCol("words").setOutputCol("ngrams")
val ngramDataFrame = ngram.transform(wordDataFrame)
ngramDataFrame.take(3).map(_.getAs[Stream[String]]("ngrams").toList).foreach(println)
{% endhighlight %}
</div>
<div data-lang="java" markdown="1">
Refer to the [NGram Java docs](api/java/org/apache/spark/ml/feature/NGram.html)
for more details on the API.
{% highlight java %}
import java.util.Arrays;
import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.ml.feature.NGram;
import org.apache.spark.mllib.linalg.Vector;
import org.apache.spark.sql.DataFrame;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.types.DataTypes;
import org.apache.spark.sql.types.Metadata;
import org.apache.spark.sql.types.StructField;
import org.apache.spark.sql.types.StructType;
JavaRDD<Row> jrdd = jsc.parallelize(Arrays.asList(
RowFactory.create(0.0, Arrays.asList("Hi", "I", "heard", "about", "Spark")),
RowFactory.create(1.0, Arrays.asList("I", "wish", "Java", "could", "use", "case", "classes")),
RowFactory.create(2.0, Arrays.asList("Logistic", "regression", "models", "are", "neat"))
));
StructType schema = new StructType(new StructField[]{
new StructField("label", DataTypes.DoubleType, false, Metadata.empty()),
new StructField("words", DataTypes.createArrayType(DataTypes.StringType), false, Metadata.empty())
});
DataFrame wordDataFrame = sqlContext.createDataFrame(jrdd, schema);
NGram ngramTransformer = new NGram().setInputCol("words").setOutputCol("ngrams");
DataFrame ngramDataFrame = ngramTransformer.transform(wordDataFrame);
for (Row r : ngramDataFrame.select("ngrams", "label").take(3)) {
java.util.List<String> ngrams = r.getList(0);
for (String ngram : ngrams) System.out.print(ngram + " --- ");
System.out.println();
}
{% endhighlight %}
</div>
<div data-lang="python" markdown="1">
Refer to the [NGram Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.NGram)
for more details on the API.
{% highlight python %}
from pyspark.ml.feature import NGram
wordDataFrame = sqlContext.createDataFrame([
(0, ["Hi", "I", "heard", "about", "Spark"]),
(1, ["I", "wish", "Java", "could", "use", "case", "classes"]),
(2, ["Logistic", "regression", "models", "are", "neat"])
], ["label", "words"])
ngram = NGram(inputCol="words", outputCol="ngrams")
ngramDataFrame = ngram.transform(wordDataFrame)
for ngrams_label in ngramDataFrame.select("ngrams", "label").take(3):
print(ngrams_label)
{% endhighlight %}
</div>
</div>
## Binarizer
Binarization is the process of thresholding numerical features to binary (0/1) features.
`Binarizer` takes the common parameters `inputCol` and `outputCol`, as well as the `threshold` for binarization. Feature values greater than the threshold are binarized to 1.0; values equal to or less than the threshold are binarized to 0.0.
<div class="codetabs">
<div data-lang="scala" markdown="1">
Refer to the [Binarizer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.Binarizer)
for more details on the API.
{% highlight scala %}
import org.apache.spark.ml.feature.Binarizer
import org.apache.spark.sql.DataFrame
val data = Array(
(0, 0.1),
(1, 0.8),
(2, 0.2)
)
val dataFrame: DataFrame = sqlContext.createDataFrame(data).toDF("label", "feature")
val binarizer: Binarizer = new Binarizer()
.setInputCol("feature")
.setOutputCol("binarized_feature")
.setThreshold(0.5)
val binarizedDataFrame = binarizer.transform(dataFrame)
val binarizedFeatures = binarizedDataFrame.select("binarized_feature")
binarizedFeatures.collect().foreach(println)
{% endhighlight %}
</div>
<div data-lang="java" markdown="1">
Refer to the [Binarizer Java docs](api/java/org/apache/spark/ml/feature/Binarizer.html)
for more details on the API.
{% highlight java %}
import java.util.Arrays;
import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.ml.feature.Binarizer;
import org.apache.spark.sql.DataFrame;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.types.DataTypes;
import org.apache.spark.sql.types.Metadata;
import org.apache.spark.sql.types.StructField;
import org.apache.spark.sql.types.StructType;
JavaRDD<Row> jrdd = jsc.parallelize(Arrays.asList(
RowFactory.create(0, 0.1),
RowFactory.create(1, 0.8),
RowFactory.create(2, 0.2)
));
StructType schema = new StructType(new StructField[]{
new StructField("label", DataTypes.DoubleType, false, Metadata.empty()),
new StructField("feature", DataTypes.DoubleType, false, Metadata.empty())
});
DataFrame continuousDataFrame = jsql.createDataFrame(jrdd, schema);
Binarizer binarizer = new Binarizer()
.setInputCol("feature")
.setOutputCol("binarized_feature")
.setThreshold(0.5);
DataFrame binarizedDataFrame = binarizer.transform(continuousDataFrame);
DataFrame binarizedFeatures = binarizedDataFrame.select("binarized_feature");
for (Row r : binarizedFeatures.collect()) {
Double binarized_value = r.getDouble(0);
System.out.println(binarized_value);
}
{% endhighlight %}
</div>
<div data-lang="python" markdown="1">
Refer to the [Binarizer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.Binarizer)
for more details on the API.
{% highlight python %}
from pyspark.ml.feature import Binarizer
continuousDataFrame = sqlContext.createDataFrame([
(0, 0.1),
(1, 0.8),
(2, 0.2)
], ["label", "feature"])
binarizer = Binarizer(threshold=0.5, inputCol="feature", outputCol="binarized_feature")
binarizedDataFrame = binarizer.transform(continuousDataFrame)
binarizedFeatures = binarizedDataFrame.select("binarized_feature")
for binarized_feature, in binarizedFeatures.collect():
print(binarized_feature)
{% endhighlight %}
</div>
</div>
## PCA
[PCA](http://en.wikipedia.org/wiki/Principal_component_analysis) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. A [PCA](api/scala/index.html#org.apache.spark.ml.feature.PCA) class trains a model to project vectors to a low-dimensional space using PCA. The example below shows how to project 5-dimensional feature vectors into 3-dimensional principal components.
<div class="codetabs">
<div data-lang="scala" markdown="1">
Refer to the [PCA Scala docs](api/scala/index.html#org.apache.spark.ml.feature.PCA)
for more details on the API.
{% highlight scala %}
import org.apache.spark.ml.feature.PCA
import org.apache.spark.mllib.linalg.Vectors
val data = Array(
Vectors.sparse(5, Seq((1, 1.0), (3, 7.0))),
Vectors.dense(2.0, 0.0, 3.0, 4.0, 5.0),
Vectors.dense(4.0, 0.0, 0.0, 6.0, 7.0)
)
val df = sqlContext.createDataFrame(data.map(Tuple1.apply)).toDF("features")
val pca = new PCA()
.setInputCol("features")
.setOutputCol("pcaFeatures")
.setK(3)
.fit(df)
val pcaDF = pca.transform(df)
val result = pcaDF.select("pcaFeatures")
result.show()
{% endhighlight %}
</div>
<div data-lang="java" markdown="1">
Refer to the [PCA Java docs](api/java/org/apache/spark/ml/feature/PCA.html)
for more details on the API.
{% highlight java %}
import java.util.Arrays;
import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.api.java.JavaSparkContext;
import org.apache.spark.ml.feature.PCA
import org.apache.spark.ml.feature.PCAModel
import org.apache.spark.mllib.linalg.VectorUDT;
import org.apache.spark.mllib.linalg.Vectors;
import org.apache.spark.sql.DataFrame;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.SQLContext;
import org.apache.spark.sql.types.Metadata;
import org.apache.spark.sql.types.StructField;
import org.apache.spark.sql.types.StructType;
JavaSparkContext jsc = ...
SQLContext jsql = ...
JavaRDD<Row> data = jsc.parallelize(Arrays.asList(
RowFactory.create(Vectors.sparse(5, new int[]{1, 3}, new double[]{1.0, 7.0})),
RowFactory.create(Vectors.dense(2.0, 0.0, 3.0, 4.0, 5.0)),
RowFactory.create(Vectors.dense(4.0, 0.0, 0.0, 6.0, 7.0))
));
StructType schema = new StructType(new StructField[] {
new StructField("features", new VectorUDT(), false, Metadata.empty()),
});
DataFrame df = jsql.createDataFrame(data, schema);
PCAModel pca = new PCA()
.setInputCol("features")
.setOutputCol("pcaFeatures")
.setK(3)
.fit(df);
DataFrame result = pca.transform(df).select("pcaFeatures");
result.show();
{% endhighlight %}
</div>
<div data-lang="python" markdown="1">
Refer to the [PCA Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.PCA)
for more details on the API.
{% highlight python %}
from pyspark.ml.feature import PCA
from pyspark.mllib.linalg import Vectors
data = [(Vectors.sparse(5, [(1, 1.0), (3, 7.0)]),),
(Vectors.dense([2.0, 0.0, 3.0, 4.0, 5.0]),),
(Vectors.dense([4.0, 0.0, 0.0, 6.0, 7.0]),)]
df = sqlContext.createDataFrame(data,["features"])
pca = PCA(k=3, inputCol="features", outputCol="pcaFeatures")
model = pca.fit(df)
result = model.transform(df).select("pcaFeatures")
result.show(truncate=False)
{% endhighlight %}
</div>
</div>
## PolynomialExpansion
[Polynomial expansion](http://en.wikipedia.org/wiki/Polynomial_expansion) is the process of expanding your features into a polynomial space, which is formulated by an n-degree combination of original dimensions. A [PolynomialExpansion](api/scala/index.html#org.apache.spark.ml.feature.PolynomialExpansion) class provides this functionality. The example below shows how to expand your features into a 3-degree polynomial space.
<div class="codetabs">
<div data-lang="scala" markdown="1">
Refer to the [PolynomialExpansion Scala docs](api/scala/index.html#org.apache.spark.ml.feature.PolynomialExpansion)
for more details on the API.
{% highlight scala %}
import org.apache.spark.ml.feature.PolynomialExpansion
import org.apache.spark.mllib.linalg.Vectors
val data = Array(
Vectors.dense(-2.0, 2.3),
Vectors.dense(0.0, 0.0),
Vectors.dense(0.6, -1.1)
)
val df = sqlContext.createDataFrame(data.map(Tuple1.apply)).toDF("features")
val polynomialExpansion = new PolynomialExpansion()
.setInputCol("features")
.setOutputCol("polyFeatures")
.setDegree(3)
val polyDF = polynomialExpansion.transform(df)
polyDF.select("polyFeatures").take(3).foreach(println)
{% endhighlight %}
</div>
<div data-lang="java" markdown="1">
Refer to the [PolynomialExpansion Java docs](api/java/org/apache/spark/ml/feature/PolynomialExpansion.html)
for more details on the API.
{% highlight java %}
import java.util.Arrays;
import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.api.java.JavaSparkContext;
import org.apache.spark.mllib.linalg.Vector;
import org.apache.spark.mllib.linalg.VectorUDT;
import org.apache.spark.mllib.linalg.Vectors;
import org.apache.spark.sql.DataFrame;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.SQLContext;
import org.apache.spark.sql.types.Metadata;
import org.apache.spark.sql.types.StructField;
import org.apache.spark.sql.types.StructType;
JavaSparkContext jsc = ...
SQLContext jsql = ...
PolynomialExpansion polyExpansion = new PolynomialExpansion()
.setInputCol("features")
.setOutputCol("polyFeatures")
.setDegree(3);
JavaRDD<Row> data = jsc.parallelize(Arrays.asList(
RowFactory.create(Vectors.dense(-2.0, 2.3)),
RowFactory.create(Vectors.dense(0.0, 0.0)),
RowFactory.create(Vectors.dense(0.6, -1.1))
));
StructType schema = new StructType(new StructField[] {
new StructField("features", new VectorUDT(), false, Metadata.empty()),
});
DataFrame df = jsql.createDataFrame(data, schema);
DataFrame polyDF = polyExpansion.transform(df);
Row[] row = polyDF.select("polyFeatures").take(3);
for (Row r : row) {
System.out.println(r.get(0));
}
{% endhighlight %}
</div>
<div data-lang="python" markdown="1">
Refer to the [PolynomialExpansion Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.PolynomialExpansion)
for more details on the API.
{% highlight python %}
from pyspark.ml.feature import PolynomialExpansion
from pyspark.mllib.linalg import Vectors
df = sqlContext.createDataFrame(
[(Vectors.dense([-2.0, 2.3]), ),
(Vectors.dense([0.0, 0.0]), ),
(Vectors.dense([0.6, -1.1]), )],
["features"])
px = PolynomialExpansion(degree=2, inputCol="features", outputCol="polyFeatures")
polyDF = px.transform(df)
for expanded in polyDF.select("polyFeatures").take(3):
print(expanded)
{% endhighlight %}
</div>
</div>
## Discrete Cosine Transform (DCT)
The [Discrete Cosine
Transform](https://en.wikipedia.org/wiki/Discrete_cosine_transform)
transforms a length $N$ real-valued sequence in the time domain into
another length $N$ real-valued sequence in the frequency domain. A
[DCT](api/scala/index.html#org.apache.spark.ml.feature.DCT) class
provides this functionality, implementing the
[DCT-II](https://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT-II)
and scaling the result by $1/\sqrt{2}$ such that the representing matrix
for the transform is unitary. No shift is applied to the transformed
sequence (e.g. the $0$th element of the transformed sequence is the
$0$th DCT coefficient and _not_ the $N/2$th).
<div class="codetabs">
<div data-lang="scala" markdown="1">
Refer to the [DCT Scala docs](api/scala/index.html#org.apache.spark.ml.feature.DCT)
for more details on the API.
{% highlight scala %}
import org.apache.spark.ml.feature.DCT
import org.apache.spark.mllib.linalg.Vectors
val data = Seq(
Vectors.dense(0.0, 1.0, -2.0, 3.0),
Vectors.dense(-1.0, 2.0, 4.0, -7.0),
Vectors.dense(14.0, -2.0, -5.0, 1.0))
val df = sqlContext.createDataFrame(data.map(Tuple1.apply)).toDF("features")
val dct = new DCT()
.setInputCol("features")
.setOutputCol("featuresDCT")
.setInverse(false)
val dctDf = dct.transform(df)
dctDf.select("featuresDCT").show(3)
{% endhighlight %}
</div>
<div data-lang="java" markdown="1">
Refer to the [DCT Java docs](api/java/org/apache/spark/ml/feature/DCT.html)
for more details on the API.
{% highlight java %}
import java.util.Arrays;
import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.api.java.JavaSparkContext;
import org.apache.spark.ml.feature.DCT;
import org.apache.spark.mllib.linalg.Vector;
import org.apache.spark.mllib.linalg.VectorUDT;
import org.apache.spark.mllib.linalg.Vectors;
import org.apache.spark.sql.DataFrame;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.SQLContext;
import org.apache.spark.sql.types.Metadata;
import org.apache.spark.sql.types.StructField;
import org.apache.spark.sql.types.StructType;
JavaRDD<Row> data = jsc.parallelize(Arrays.asList(
RowFactory.create(Vectors.dense(0.0, 1.0, -2.0, 3.0)),
RowFactory.create(Vectors.dense(-1.0, 2.0, 4.0, -7.0)),
RowFactory.create(Vectors.dense(14.0, -2.0, -5.0, 1.0))
));
StructType schema = new StructType(new StructField[] {
new StructField("features", new VectorUDT(), false, Metadata.empty()),
});
DataFrame df = jsql.createDataFrame(data, schema);
DCT dct = new DCT()
.setInputCol("features")
.setOutputCol("featuresDCT")
.setInverse(false);
DataFrame dctDf = dct.transform(df);
dctDf.select("featuresDCT").show(3);
{% endhighlight %}
</div>
</div>
## StringIndexer
`StringIndexer` encodes a string column of labels to a column of label indices.
The indices are in `[0, numLabels)`, ordered by label frequencies.
So the most frequent label gets index `0`.
If the input column is numeric, we cast it to string and index the string
values. When downstream pipeline components such as `Estimator` or
`Transformer` make use of this string-indexed label, you must set the input
column of the component to this string-indexed column name. In many cases,
you can set the input column with `setInputCol`.
**Examples**
Assume that we have the following DataFrame with columns `id` and `category`:
~~~~
id | category
----|----------
0 | a
1 | b
2 | c
3 | a
4 | a
5 | c
~~~~
`category` is a string column with three labels: "a", "b", and "c".
Applying `StringIndexer` with `category` as the input column and `categoryIndex` as the output
column, we should get the following:
~~~~
id | category | categoryIndex
----|----------|---------------
0 | a | 0.0
1 | b | 2.0
2 | c | 1.0
3 | a | 0.0
4 | a | 0.0
5 | c | 1.0
~~~~
"a" gets index `0` because it is the most frequent, followed by "c" with index `1` and "b" with
index `2`.
<div class="codetabs">
<div data-lang="scala" markdown="1">
Refer to the [StringIndexer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.StringIndexer)
for more details on the API.
{% highlight scala %}
import org.apache.spark.ml.feature.StringIndexer
val df = sqlContext.createDataFrame(
Seq((0, "a"), (1, "b"), (2, "c"), (3, "a"), (4, "a"), (5, "c"))
).toDF("id", "category")
val indexer = new StringIndexer()
.setInputCol("category")
.setOutputCol("categoryIndex")
val indexed = indexer.fit(df).transform(df)
indexed.show()
{% endhighlight %}
</div>
<div data-lang="java" markdown="1">
Refer to the [StringIndexer Java docs](api/java/org/apache/spark/ml/feature/StringIndexer.html)
for more details on the API.
{% highlight java %}
import java.util.Arrays;
import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.ml.feature.StringIndexer;
import org.apache.spark.sql.DataFrame;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.types.StructField;
import org.apache.spark.sql.types.StructType;
import static org.apache.spark.sql.types.DataTypes.*;
JavaRDD<Row> jrdd = jsc.parallelize(Arrays.asList(
RowFactory.create(0, "a"),
RowFactory.create(1, "b"),
RowFactory.create(2, "c"),
RowFactory.create(3, "a"),
RowFactory.create(4, "a"),
RowFactory.create(5, "c")
));
StructType schema = new StructType(new StructField[] {
createStructField("id", DoubleType, false),
createStructField("category", StringType, false)
});
DataFrame df = sqlContext.createDataFrame(jrdd, schema);
StringIndexer indexer = new StringIndexer()
.setInputCol("category")
.setOutputCol("categoryIndex");
DataFrame indexed = indexer.fit(df).transform(df);
indexed.show();
{% endhighlight %}
</div>
<div data-lang="python" markdown="1">
Refer to the [StringIndexer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.StringIndexer)
for more details on the API.
{% highlight python %}
from pyspark.ml.feature import StringIndexer
df = sqlContext.createDataFrame(
[(0, "a"), (1, "b"), (2, "c"), (3, "a"), (4, "a"), (5, "c")],
["id", "category"])
indexer = StringIndexer(inputCol="category", outputCol="categoryIndex")
indexed = indexer.fit(df).transform(df)
indexed.show()
{% endhighlight %}
</div>
</div>
## OneHotEncoder
[One-hot encoding](http://en.wikipedia.org/wiki/One-hot) maps a column of label indices to a column of binary vectors, with at most a single one-value. This encoding allows algorithms which expect continuous features, such as Logistic Regression, to use categorical features
<div class="codetabs">
<div data-lang="scala" markdown="1">
Refer to the [OneHotEncoder Scala docs](api/scala/index.html#org.apache.spark.ml.feature.OneHotEncoder)
for more details on the API.
{% highlight scala %}
import org.apache.spark.ml.feature.{OneHotEncoder, StringIndexer}
val df = sqlContext.createDataFrame(Seq(
(0, "a"),
(1, "b"),
(2, "c"),
(3, "a"),
(4, "a"),
(5, "c")
)).toDF("id", "category")
val indexer = new StringIndexer()
.setInputCol("category")
.setOutputCol("categoryIndex")
.fit(df)
val indexed = indexer.transform(df)
val encoder = new OneHotEncoder().setInputCol("categoryIndex").
setOutputCol("categoryVec")
val encoded = encoder.transform(indexed)
encoded.select("id", "categoryVec").foreach(println)
{% endhighlight %}
</div>
<div data-lang="java" markdown="1">
Refer to the [OneHotEncoder Java docs](api/java/org/apache/spark/ml/feature/OneHotEncoder.html)
for more details on the API.
{% highlight java %}
import java.util.Arrays;
import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.ml.feature.OneHotEncoder;
import org.apache.spark.ml.feature.StringIndexer;
import org.apache.spark.ml.feature.StringIndexerModel;
import org.apache.spark.sql.DataFrame;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.types.DataTypes;
import org.apache.spark.sql.types.Metadata;
import org.apache.spark.sql.types.StructField;
import org.apache.spark.sql.types.StructType;
JavaRDD<Row> jrdd = jsc.parallelize(Arrays.asList(
RowFactory.create(0, "a"),
RowFactory.create(1, "b"),
RowFactory.create(2, "c"),
RowFactory.create(3, "a"),
RowFactory.create(4, "a"),
RowFactory.create(5, "c")
));
StructType schema = new StructType(new StructField[]{
new StructField("id", DataTypes.DoubleType, false, Metadata.empty()),
new StructField("category", DataTypes.StringType, false, Metadata.empty())
});
DataFrame df = sqlContext.createDataFrame(jrdd, schema);
StringIndexerModel indexer = new StringIndexer()
.setInputCol("category")
.setOutputCol("categoryIndex")
.fit(df);
DataFrame indexed = indexer.transform(df);
OneHotEncoder encoder = new OneHotEncoder()
.setInputCol("categoryIndex")
.setOutputCol("categoryVec");
DataFrame encoded = encoder.transform(indexed);
{% endhighlight %}
</div>
<div data-lang="python" markdown="1">
Refer to the [OneHotEncoder Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.OneHotEncoder)
for more details on the API.
{% highlight python %}
from pyspark.ml.feature import OneHotEncoder, StringIndexer
df = sqlContext.createDataFrame([
(0, "a"),
(1, "b"),
(2, "c"),
(3, "a"),
(4, "a"),
(5, "c")
], ["id", "category"])
stringIndexer = StringIndexer(inputCol="category", outputCol="categoryIndex")
model = stringIndexer.fit(df)
indexed = model.transform(df)
encoder = OneHotEncoder(includeFirst=False, inputCol="categoryIndex", outputCol="categoryVec")
encoded = encoder.transform(indexed)
{% endhighlight %}
</div>
</div>
## VectorIndexer
`VectorIndexer` helps index categorical features in datasets of `Vector`s.
It can both automatically decide which features are categorical and convert original values to category indices. Specifically, it does the following:
1. Take an input column of type [Vector](api/scala/index.html#org.apache.spark.mllib.linalg.Vector) and a parameter `maxCategories`.
2. Decide which features should be categorical based on the number of distinct values, where features with at most `maxCategories` are declared categorical.
3. Compute 0-based category indices for each categorical feature.
4. Index categorical features and transform original feature values to indices.
Indexing categorical features allows algorithms such as Decision Trees and Tree Ensembles to treat categorical features appropriately, improving performance.
In the example below, we read in a dataset of labeled points and then use `VectorIndexer` to decide which features should be treated as categorical. We transform the categorical feature values to their indices. This transformed data could then be passed to algorithms such as `DecisionTreeRegressor` that handle categorical features.
<div class="codetabs">
<div data-lang="scala" markdown="1">
Refer to the [VectorIndexer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.VectorIndexer)
for more details on the API.
{% highlight scala %}
import org.apache.spark.ml.feature.VectorIndexer
val data = sqlContext.read.format("libsvm")
.load("data/mllib/sample_libsvm_data.txt")
val indexer = new VectorIndexer()
.setInputCol("features")
.setOutputCol("indexed")
.setMaxCategories(10)
val indexerModel = indexer.fit(data)
val categoricalFeatures: Set[Int] = indexerModel.categoryMaps.keys.toSet
println(s"Chose ${categoricalFeatures.size} categorical features: " +
categoricalFeatures.mkString(", "))
// Create new column "indexed" with categorical values transformed to indices
val indexedData = indexerModel.transform(data)
{% endhighlight %}
</div>
<div data-lang="java" markdown="1">
Refer to the [VectorIndexer Java docs](api/java/org/apache/spark/ml/feature/VectorIndexer.html)
for more details on the API.
{% highlight java %}
import java.util.Map;
import org.apache.spark.ml.feature.VectorIndexer;
import org.apache.spark.ml.feature.VectorIndexerModel;
import org.apache.spark.sql.DataFrame;
DataFrame data = sqlContext.read().format("libsvm")
.load("data/mllib/sample_libsvm_data.txt");
VectorIndexer indexer = new VectorIndexer()
.setInputCol("features")
.setOutputCol("indexed")
.setMaxCategories(10);
VectorIndexerModel indexerModel = indexer.fit(data);
Map<Integer, Map<Double, Integer>> categoryMaps = indexerModel.javaCategoryMaps();
System.out.print("Chose " + categoryMaps.size() + "categorical features:");
for (Integer feature : categoryMaps.keySet()) {
System.out.print(" " + feature);
}
System.out.println();
// Create new column "indexed" with categorical values transformed to indices
DataFrame indexedData = indexerModel.transform(data);
{% endhighlight %}
</div>
<div data-lang="python" markdown="1">
Refer to the [VectorIndexer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.VectorIndexer)
for more details on the API.
{% highlight python %}
from pyspark.ml.feature import VectorIndexer
data = sqlContext.read.format("libsvm")
.load("data/mllib/sample_libsvm_data.txt")
indexer = VectorIndexer(inputCol="features", outputCol="indexed", maxCategories=10)
indexerModel = indexer.fit(data)
# Create new column "indexed" with categorical values transformed to indices
indexedData = indexerModel.transform(data)
{% endhighlight %}
</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">
Refer to the [Normalizer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.Normalizer)
for more details on the API.
{% highlight scala %}
import org.apache.spark.ml.feature.Normalizer
val dataFrame = sqlContext.read.format("libsvm")
.load("data/mllib/sample_libsvm_data.txt")
// 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">
Refer to the [Normalizer Java docs](api/java/org/apache/spark/ml/feature/Normalizer.html)
for more details on the API.
{% highlight java %}
import org.apache.spark.ml.feature.Normalizer;
import org.apache.spark.sql.DataFrame;
DataFrame dataFrame = sqlContext.read().format("libsvm")
.load("data/mllib/sample_libsvm_data.txt");
// 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">
Refer to the [Normalizer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.Normalizer)
for more details on the API.
{% highlight python %}
from pyspark.ml.feature import Normalizer
dataFrame = sqlContext.read.format("libsvm")
.load("data/mllib/sample_libsvm_data.txt")
# 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.
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">
Refer to the [StandardScaler Scala docs](api/scala/index.html#org.apache.spark.ml.feature.StandardScaler)
for more details on the API.
{% highlight scala %}
import org.apache.spark.ml.feature.StandardScaler
val dataFrame = sqlContext.read.format("libsvm")
.load("data/mllib/sample_libsvm_data.txt")
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">
Refer to the [StandardScaler Java docs](api/java/org/apache/spark/ml/feature/StandardScaler.html)
for more details on the API.
{% highlight java %}
import org.apache.spark.ml.feature.StandardScaler;
import org.apache.spark.ml.feature.StandardScalerModel;
import org.apache.spark.sql.DataFrame;
DataFrame dataFrame = sqlContext.read().format("libsvm")
.load("data/mllib/sample_libsvm_data.txt");
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">
Refer to the [StandardScaler Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.StandardScaler)
for more details on the API.
{% highlight python %}
from pyspark.ml.feature import StandardScaler
dataFrame = sqlContext.read.format("libsvm")
.load("data/mllib/sample_libsvm_data.txt")
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>
## MinMaxScaler
`MinMaxScaler` transforms a dataset of `Vector` rows, rescaling each feature to a specific range (often [0, 1]). It takes parameters:
* `min`: 0.0 by default. Lower bound after transformation, shared by all features.
* `max`: 1.0 by default. Upper bound after transformation, shared by all features.
`MinMaxScaler` computes summary statistics on a data set and produces a `MinMaxScalerModel`. The model can then transform each feature individually such that it is in the given range.
The rescaled value for a feature E is calculated as,
`\begin{equation}
Rescaled(e_i) = \frac{e_i - E_{min}}{E_{max} - E_{min}} * (max - min) + min
\end{equation}`
For the case `E_{max} == E_{min}`, `Rescaled(e_i) = 0.5 * (max + min)`
Note that since zero values will probably be transformed to non-zero values, output of the transformer will be DenseVector even for sparse input.
The following example demonstrates how to load a dataset in libsvm format and then rescale each feature to [0, 1].
<div class="codetabs">
<div data-lang="scala" markdown="1">
Refer to the [MinMaxScaler Scala docs](api/scala/index.html#org.apache.spark.ml.feature.MinMaxScaler)
and the [MinMaxScalerModel Scala docs](api/scala/index.html#org.apache.spark.ml.feature.MinMaxScalerModel)
for more details on the API.
{% highlight scala %}
import org.apache.spark.ml.feature.MinMaxScaler
val dataFrame = sqlContext.read.format("libsvm")
.load("data/mllib/sample_libsvm_data.txt")
val scaler = new MinMaxScaler()
.setInputCol("features")
.setOutputCol("scaledFeatures")
// Compute summary statistics and generate MinMaxScalerModel
val scalerModel = scaler.fit(dataFrame)
// rescale each feature to range [min, max].
val scaledData = scalerModel.transform(dataFrame)
{% endhighlight %}
</div>
<div data-lang="java" markdown="1">
Refer to the [MinMaxScaler Java docs](api/java/org/apache/spark/ml/feature/MinMaxScaler.html)
and the [MinMaxScalerModel Java docs](api/java/org/apache/spark/ml/feature/MinMaxScalerModel.html)
for more details on the API.
{% highlight java %}
import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.ml.feature.MinMaxScaler;
import org.apache.spark.ml.feature.MinMaxScalerModel;
import org.apache.spark.sql.DataFrame;
DataFrame dataFrame = sqlContext.read().format("libsvm")
.load("data/mllib/sample_libsvm_data.txt");
MinMaxScaler scaler = new MinMaxScaler()
.setInputCol("features")
.setOutputCol("scaledFeatures");
// Compute summary statistics and generate MinMaxScalerModel
MinMaxScalerModel scalerModel = scaler.fit(dataFrame);
// rescale each feature to range [min, max].
DataFrame scaledData = scalerModel.transform(dataFrame);
{% endhighlight %}
</div>
</div>
## Bucketizer
`Bucketizer` transforms a column of continuous features to a column of feature buckets, where the buckets are specified by users. It takes a parameter:
* `splits`: Parameter for mapping continuous features into buckets. With n+1 splits, there are n buckets. A bucket defined by splits x,y holds values in the range [x,y) except the last bucket, which also includes y. Splits should be strictly increasing. Values at -inf, inf must be explicitly provided to cover all Double values; Otherwise, values outside the splits specified will be treated as errors. Two examples of `splits` are `Array(Double.NegativeInfinity, 0.0, 1.0, Double.PositiveInfinity)` and `Array(0.0, 1.0, 2.0)`.
Note that if you have no idea of the upper bound and lower bound of the targeted column, you would better add the `Double.NegativeInfinity` and `Double.PositiveInfinity` as the bounds of your splits to prevent a potenial out of Bucketizer bounds exception.
Note also that the splits that you provided have to be in strictly increasing order, i.e. `s0 < s1 < s2 < ... < sn`.
More details can be found in the API docs for [Bucketizer](api/scala/index.html#org.apache.spark.ml.feature.Bucketizer).
The following example demonstrates how to bucketize a column of `Double`s into another index-wised column.
<div class="codetabs">
<div data-lang="scala">
Refer to the [Bucketizer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.Bucketizer)
for more details on the API.
{% highlight scala %}
import org.apache.spark.ml.feature.Bucketizer
import org.apache.spark.sql.DataFrame
val splits = Array(Double.NegativeInfinity, -0.5, 0.0, 0.5, Double.PositiveInfinity)
val data = Array(-0.5, -0.3, 0.0, 0.2)
val dataFrame = sqlContext.createDataFrame(data.map(Tuple1.apply)).toDF("features")
val bucketizer = new Bucketizer()
.setInputCol("features")
.setOutputCol("bucketedFeatures")
.setSplits(splits)
// Transform original data into its bucket index.
val bucketedData = bucketizer.transform(dataFrame)
{% endhighlight %}
</div>
<div data-lang="java">
Refer to the [Bucketizer Java docs](api/java/org/apache/spark/ml/feature/Bucketizer.html)
for more details on the API.
{% highlight java %}
import java.util.Arrays;
import org.apache.spark.sql.DataFrame;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.types.DataTypes;
import org.apache.spark.sql.types.Metadata;
import org.apache.spark.sql.types.StructField;
import org.apache.spark.sql.types.StructType;
double[] splits = {Double.NEGATIVE_INFINITY, -0.5, 0.0, 0.5, Double.POSITIVE_INFINITY};
JavaRDD<Row> data = jsc.parallelize(Arrays.asList(
RowFactory.create(-0.5),
RowFactory.create(-0.3),
RowFactory.create(0.0),
RowFactory.create(0.2)
));
StructType schema = new StructType(new StructField[] {
new StructField("features", DataTypes.DoubleType, false, Metadata.empty())
});
DataFrame dataFrame = jsql.createDataFrame(data, schema);
Bucketizer bucketizer = new Bucketizer()
.setInputCol("features")
.setOutputCol("bucketedFeatures")
.setSplits(splits);
// Transform original data into its bucket index.
DataFrame bucketedData = bucketizer.transform(dataFrame);
{% endhighlight %}
</div>
<div data-lang="python">
Refer to the [Bucketizer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.Bucketizer)
for more details on the API.
{% highlight python %}
from pyspark.ml.feature import Bucketizer
splits = [-float("inf"), -0.5, 0.0, 0.5, float("inf")]
data = [(-0.5,), (-0.3,), (0.0,), (0.2,)]
dataFrame = sqlContext.createDataFrame(data, ["features"])
bucketizer = Bucketizer(splits=splits, inputCol="features", outputCol="bucketedFeatures")
# Transform original data into its bucket index.
bucketedData = bucketizer.transform(dataFrame)
{% endhighlight %}
</div>
</div>
## ElementwiseProduct
ElementwiseProduct multiplies each input vector by a provided "weight" vector, using element-wise multiplication. In other words, it scales each column of the dataset by a scalar multiplier. This represents the [Hadamard product](https://en.wikipedia.org/wiki/Hadamard_product_%28matrices%29) between the input vector, `v` and transforming vector, `w`, to yield a result vector.
`\[ \begin{pmatrix}
v_1 \\
\vdots \\
v_N
\end{pmatrix} \circ \begin{pmatrix}
w_1 \\
\vdots \\
w_N
\end{pmatrix}
= \begin{pmatrix}
v_1 w_1 \\
\vdots \\
v_N w_N
\end{pmatrix}
\]`
This example below demonstrates how to transform vectors using a transforming vector value.
<div class="codetabs">
<div data-lang="scala" markdown="1">
Refer to the [ElementwiseProduct Scala docs](api/scala/index.html#org.apache.spark.ml.feature.ElementwiseProduct)
for more details on the API.
{% highlight scala %}
import org.apache.spark.ml.feature.ElementwiseProduct
import org.apache.spark.mllib.linalg.Vectors
// Create some vector data; also works for sparse vectors
val dataFrame = sqlContext.createDataFrame(Seq(
("a", Vectors.dense(1.0, 2.0, 3.0)),
("b", Vectors.dense(4.0, 5.0, 6.0)))).toDF("id", "vector")
val transformingVector = Vectors.dense(0.0, 1.0, 2.0)
val transformer = new ElementwiseProduct()
.setScalingVec(transformingVector)
.setInputCol("vector")
.setOutputCol("transformedVector")
// Batch transform the vectors to create new column:
transformer.transform(dataFrame).show()
{% endhighlight %}
</div>
<div data-lang="java" markdown="1">
Refer to the [ElementwiseProduct Java docs](api/java/org/apache/spark/ml/feature/ElementwiseProduct.html)
for more details on the API.
{% highlight java %}
import java.util.Arrays;
import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.ml.feature.ElementwiseProduct;
import org.apache.spark.mllib.linalg.Vector;
import org.apache.spark.mllib.linalg.Vectors;
import org.apache.spark.sql.DataFrame;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.SQLContext;
import org.apache.spark.sql.types.DataTypes;
import org.apache.spark.sql.types.Metadata;
import org.apache.spark.sql.types.StructField;
import org.apache.spark.sql.types.StructType;
// Create some vector data; also works for sparse vectors
JavaRDD<Row> jrdd = jsc.parallelize(Arrays.asList(
RowFactory.create("a", Vectors.dense(1.0, 2.0, 3.0)),
RowFactory.create("b", Vectors.dense(4.0, 5.0, 6.0))
));
List<StructField> fields = new ArrayList<StructField>(2);
fields.add(DataTypes.createStructField("id", DataTypes.StringType, false));
fields.add(DataTypes.createStructField("vector", DataTypes.StringType, false));
StructType schema = DataTypes.createStructType(fields);
DataFrame dataFrame = sqlContext.createDataFrame(jrdd, schema);
Vector transformingVector = Vectors.dense(0.0, 1.0, 2.0);
ElementwiseProduct transformer = new ElementwiseProduct()
.setScalingVec(transformingVector)
.setInputCol("vector")
.setOutputCol("transformedVector");
// Batch transform the vectors to create new column:
transformer.transform(dataFrame).show();
{% endhighlight %}
</div>
<div data-lang="python" markdown="1">
Refer to the [ElementwiseProduct Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.ElementwiseProduct)
for more details on the API.
{% highlight python %}
from pyspark.ml.feature import ElementwiseProduct
from pyspark.mllib.linalg import Vectors
data = [(Vectors.dense([1.0, 2.0, 3.0]),), (Vectors.dense([4.0, 5.0, 6.0]),)]
df = sqlContext.createDataFrame(data, ["vector"])
transformer = ElementwiseProduct(scalingVec=Vectors.dense([0.0, 1.0, 2.0]),
inputCol="vector", outputCol="transformedVector")
transformer.transform(df).show()
{% endhighlight %}
</div>
</div>
## VectorAssembler
`VectorAssembler` is a transformer that combines a given list of columns into a single vector
column.
It is useful for combining raw features and features generated by different feature transformers
into a single feature vector, in order to train ML models like logistic regression and decision
trees.
`VectorAssembler` accepts the following input column types: all numeric types, boolean type,
and vector type.
In each row, the values of the input columns will be concatenated into a vector in the specified
order.
**Examples**
Assume that we have a DataFrame with the columns `id`, `hour`, `mobile`, `userFeatures`,
and `clicked`:
~~~
id | hour | mobile | userFeatures | clicked
----|------|--------|------------------|---------
0 | 18 | 1.0 | [0.0, 10.0, 0.5] | 1.0
~~~
`userFeatures` is a vector column that contains three user features.
We want to combine `hour`, `mobile`, and `userFeatures` into a single feature vector
called `features` and use it to predict `clicked` or not.
If we set `VectorAssembler`'s input columns to `hour`, `mobile`, and `userFeatures` and
output column to `features`, after transformation we should get the following DataFrame:
~~~
id | hour | mobile | userFeatures | clicked | features
----|------|--------|------------------|---------|-----------------------------
0 | 18 | 1.0 | [0.0, 10.0, 0.5] | 1.0 | [18.0, 1.0, 0.0, 10.0, 0.5]
~~~
<div class="codetabs">
<div data-lang="scala" markdown="1">
Refer to the [VectorAssembler Scala docs](api/scala/index.html#org.apache.spark.ml.feature.VectorAssembler)
for more details on the API.
{% highlight scala %}
import org.apache.spark.mllib.linalg.Vectors
import org.apache.spark.ml.feature.VectorAssembler
val dataset = sqlContext.createDataFrame(
Seq((0, 18, 1.0, Vectors.dense(0.0, 10.0, 0.5), 1.0))
).toDF("id", "hour", "mobile", "userFeatures", "clicked")
val assembler = new VectorAssembler()
.setInputCols(Array("hour", "mobile", "userFeatures"))
.setOutputCol("features")
val output = assembler.transform(dataset)
println(output.select("features", "clicked").first())
{% endhighlight %}
</div>
<div data-lang="java" markdown="1">
Refer to the [VectorAssembler Java docs](api/java/org/apache/spark/ml/feature/VectorAssembler.html)
for more details on the API.
{% highlight java %}
import java.util.Arrays;
import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.mllib.linalg.VectorUDT;
import org.apache.spark.mllib.linalg.Vectors;
import org.apache.spark.sql.DataFrame;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.types.*;
import static org.apache.spark.sql.types.DataTypes.*;
StructType schema = createStructType(new StructField[] {
createStructField("id", IntegerType, false),
createStructField("hour", IntegerType, false),
createStructField("mobile", DoubleType, false),
createStructField("userFeatures", new VectorUDT(), false),
createStructField("clicked", DoubleType, false)
});
Row row = RowFactory.create(0, 18, 1.0, Vectors.dense(0.0, 10.0, 0.5), 1.0);
JavaRDD<Row> rdd = jsc.parallelize(Arrays.asList(row));
DataFrame dataset = sqlContext.createDataFrame(rdd, schema);
VectorAssembler assembler = new VectorAssembler()
.setInputCols(new String[] {"hour", "mobile", "userFeatures"})
.setOutputCol("features");
DataFrame output = assembler.transform(dataset);
System.out.println(output.select("features", "clicked").first());
{% endhighlight %}
</div>
<div data-lang="python" markdown="1">
Refer to the [VectorAssembler Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.VectorAssembler)
for more details on the API.
{% highlight python %}
from pyspark.mllib.linalg import Vectors
from pyspark.ml.feature import VectorAssembler
dataset = sqlContext.createDataFrame(
[(0, 18, 1.0, Vectors.dense([0.0, 10.0, 0.5]), 1.0)],
["id", "hour", "mobile", "userFeatures", "clicked"])
assembler = VectorAssembler(
inputCols=["hour", "mobile", "userFeatures"],
outputCol="features")
output = assembler.transform(dataset)
print(output.select("features", "clicked").first())
{% endhighlight %}
</div>
</div>
# Feature Selectors
## VectorSlicer
`VectorSlicer` is a transformer that takes a feature vector and outputs a new feature vector with a
sub-array of the original features. It is useful for extracting features from a vector column.
`VectorSlicer` accepts a vector column with a specified indices, then outputs a new vector column
whose values are selected via those indices. There are two types of indices,
1. Integer indices that represents the indices into the vector, `setIndices()`;
2. String indices that represents the names of features into the vector, `setNames()`.
*This requires the vector column to have an `AttributeGroup` since the implementation matches on
the name field of an `Attribute`.*
Specification by integer and string are both acceptable. Moreover, you can use integer index and
string name simultaneously. At least one feature must be selected. Duplicate features are not
allowed, so there can be no overlap between selected indices and names. Note that if names of
features are selected, an exception will be threw out when encountering with empty input attributes.
The output vector will order features with the selected indices first (in the order given),
followed by the selected names (in the order given).
**Examples**
Suppose that we have a DataFrame with the column `userFeatures`:
~~~
userFeatures
------------------
[0.0, 10.0, 0.5]
~~~
`userFeatures` is a vector column that contains three user features. Assuming that the first column
of `userFeatures` are all zeros, so we want to remove it and only the last two columns are selected.
The `VectorSlicer` selects the last two elements with `setIndices(1, 2)` then produces a new vector
column named `features`:
~~~
userFeatures | features
------------------|-----------------------------
[0.0, 10.0, 0.5] | [10.0, 0.5]
~~~
Suppose also that we have a potential input attributes for the `userFeatures`, i.e.
`["f1", "f2", "f3"]`, then we can use `setNames("f2", "f3")` to select them.
~~~
userFeatures | features
------------------|-----------------------------
[0.0, 10.0, 0.5] | [10.0, 0.5]
["f1", "f2", "f3"] | ["f2", "f3"]
~~~
<div class="codetabs">
<div data-lang="scala" markdown="1">
Refer to the [VectorSlicer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.VectorSlicer)
for more details on the API.
{% highlight scala %}
import org.apache.spark.mllib.linalg.Vectors
import org.apache.spark.ml.attribute.{Attribute, AttributeGroup, NumericAttribute}
import org.apache.spark.ml.feature.VectorSlicer
import org.apache.spark.sql.types.StructType
import org.apache.spark.sql.{DataFrame, Row, SQLContext}
val data = Array(
Vectors.sparse(3, Seq((0, -2.0), (1, 2.3))),
Vectors.dense(-2.0, 2.3, 0.0)
)
val defaultAttr = NumericAttribute.defaultAttr
val attrs = Array("f1", "f2", "f3").map(defaultAttr.withName)
val attrGroup = new AttributeGroup("userFeatures", attrs.asInstanceOf[Array[Attribute]])
val dataRDD = sc.parallelize(data).map(Row.apply)
val dataset = sqlContext.createDataFrame(dataRDD, StructType(attrGroup.toStructField()))
val slicer = new VectorSlicer().setInputCol("userFeatures").setOutputCol("features")
slicer.setIndices(1).setNames("f3")
// or slicer.setIndices(Array(1, 2)), or slicer.setNames(Array("f2", "f3"))
val output = slicer.transform(dataset)
println(output.select("userFeatures", "features").first())
{% endhighlight %}
</div>
<div data-lang="java" markdown="1">
Refer to the [VectorSlicer Java docs](api/java/org/apache/spark/ml/feature/VectorSlicer.html)
for more details on the API.
{% highlight java %}
import java.util.Arrays;
import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.mllib.linalg.Vectors;
import org.apache.spark.sql.DataFrame;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.types.*;
import static org.apache.spark.sql.types.DataTypes.*;
Attribute[] attrs = new Attribute[]{
NumericAttribute.defaultAttr().withName("f1"),
NumericAttribute.defaultAttr().withName("f2"),
NumericAttribute.defaultAttr().withName("f3")
};
AttributeGroup group = new AttributeGroup("userFeatures", attrs);
JavaRDD<Row> jrdd = jsc.parallelize(Lists.newArrayList(
RowFactory.create(Vectors.sparse(3, new int[]{0, 1}, new double[]{-2.0, 2.3})),
RowFactory.create(Vectors.dense(-2.0, 2.3, 0.0))
));
DataFrame dataset = jsql.createDataFrame(jrdd, (new StructType()).add(group.toStructField()));
VectorSlicer vectorSlicer = new VectorSlicer()
.setInputCol("userFeatures").setOutputCol("features");
vectorSlicer.setIndices(new int[]{1}).setNames(new String[]{"f3"});
// or slicer.setIndices(new int[]{1, 2}), or slicer.setNames(new String[]{"f2", "f3"})
DataFrame output = vectorSlicer.transform(dataset);
System.out.println(output.select("userFeatures", "features").first());
{% endhighlight %}
</div>
</div>
## RFormula
`RFormula` selects columns specified by an [R model formula](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/formula.html). It produces a vector column of features and a double column of labels. Like when formulas are used in R for linear regression, string input columns will be one-hot encoded, and numeric columns will be cast to doubles. If not already present in the DataFrame, the output label column will be created from the specified response variable in the formula.
**Examples**
Assume that we have a DataFrame with the columns `id`, `country`, `hour`, and `clicked`:
~~~
id | country | hour | clicked
---|---------|------|---------
7 | "US" | 18 | 1.0
8 | "CA" | 12 | 0.0
9 | "NZ" | 15 | 0.0
~~~
If we use `RFormula` with a formula string of `clicked ~ country + hour`, which indicates that we want to
predict `clicked` based on `country` and `hour`, after transformation we should get the following DataFrame:
~~~
id | country | hour | clicked | features | label
---|---------|------|---------|------------------|-------
7 | "US" | 18 | 1.0 | [0.0, 0.0, 18.0] | 1.0
8 | "CA" | 12 | 0.0 | [0.0, 1.0, 12.0] | 0.0
9 | "NZ" | 15 | 0.0 | [1.0, 0.0, 15.0] | 0.0
~~~
<div class="codetabs">
<div data-lang="scala" markdown="1">
Refer to the [RFormula Scala docs](api/scala/index.html#org.apache.spark.ml.feature.RFormula)
for more details on the API.
{% highlight scala %}
import org.apache.spark.ml.feature.RFormula
val dataset = sqlContext.createDataFrame(Seq(
(7, "US", 18, 1.0),
(8, "CA", 12, 0.0),
(9, "NZ", 15, 0.0)
)).toDF("id", "country", "hour", "clicked")
val formula = new RFormula()
.setFormula("clicked ~ country + hour")
.setFeaturesCol("features")
.setLabelCol("label")
val output = formula.fit(dataset).transform(dataset)
output.select("features", "label").show()
{% endhighlight %}
</div>
<div data-lang="java" markdown="1">
Refer to the [RFormula Java docs](api/java/org/apache/spark/ml/feature/RFormula.html)
for more details on the API.
{% highlight java %}
import java.util.Arrays;
import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.ml.feature.RFormula;
import org.apache.spark.sql.DataFrame;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.types.*;
import static org.apache.spark.sql.types.DataTypes.*;
StructType schema = createStructType(new StructField[] {
createStructField("id", IntegerType, false),
createStructField("country", StringType, false),
createStructField("hour", IntegerType, false),
createStructField("clicked", DoubleType, false)
});
JavaRDD<Row> rdd = jsc.parallelize(Arrays.asList(
RowFactory.create(7, "US", 18, 1.0),
RowFactory.create(8, "CA", 12, 0.0),
RowFactory.create(9, "NZ", 15, 0.0)
));
DataFrame dataset = sqlContext.createDataFrame(rdd, schema);
RFormula formula = new RFormula()
.setFormula("clicked ~ country + hour")
.setFeaturesCol("features")
.setLabelCol("label");
DataFrame output = formula.fit(dataset).transform(dataset);
output.select("features", "label").show();
{% endhighlight %}
</div>
<div data-lang="python" markdown="1">
Refer to the [RFormula Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.RFormula)
for more details on the API.
{% highlight python %}
from pyspark.ml.feature import RFormula
dataset = sqlContext.createDataFrame(
[(7, "US", 18, 1.0),
(8, "CA", 12, 0.0),
(9, "NZ", 15, 0.0)],
["id", "country", "hour", "clicked"])
formula = RFormula(
formula="clicked ~ country + hour",
featuresCol="features",
labelCol="label")
output = formula.fit(dataset).transform(dataset)
output.select("features", "label").show()
{% endhighlight %}
</div>
</div>
