# Extracting, transforming and selecting features

2020-01-21

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
• Locality Sensitive Hashing (LSH): This class of algorithms combines aspects of feature transformation with other algorithms.

# Feature Extractors

## TF-IDF

Term frequency-inverse document frequency (TF-IDF) is a feature vectorization method widely used in text mining to reflect the importance of a term to a document in the corpus. Denote a term by $t$, a document by $d$, and the corpus by $D$. Term frequency $TF(t, d)$ is the number of times that term $t$ appears in document $d$, while document frequency $DF(t, D)$ is the number of documents that contains term $t$. If we only use term frequency to measure the importance, it is very easy to over-emphasize terms that appear very often but carry little information about the document, e.g. "a", "the", and "of". If a term appears very often across the corpus, it means it doesn't carry special information about a particular document. Inverse document frequency is a numerical measure of how much information a term provides: $IDF(t, D) = \log \frac{|D| + 1}{DF(t, D) + 1},$ where $|D|$ is the total number of documents in the corpus. Since logarithm is used, if a term appears in all documents, its IDF value becomes 0. Note that a smoothing term is applied to avoid dividing by zero for terms outside the corpus. The TF-IDF measure is simply the product of TF and IDF: $TFIDF(t, d, D) = TF(t, d) \cdot IDF(t, D).$ There are several variants on the definition of term frequency and document frequency. In MLlib, we separate TF and IDF to make them flexible.

TF: Both HashingTF and CountVectorizer can be used to generate the term frequency vectors.

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. HashingTF utilizes the hashing trick. A raw feature is mapped into an index (term) by applying a hash function. The hash function used here is MurmurHash 3. Then term frequencies are calculated based on the mapped indices. This approach avoids the need to compute a global term-to-index map, which can be expensive for a large corpus, but it suffers from potential hash collisions, where different raw features may become the same term after hashing. To reduce the chance of collision, we can increase the target feature dimension, i.e. the number of buckets of the hash table. Since a simple modulo on the hashed value is used to determine the vector index, it is advisable to use a power of two as the feature dimension, otherwise the features will not be mapped evenly to the vector indices. The default feature dimension is $2^{18} = 262,144$. An optional binary toggle parameter controls term frequency counts. When set to true all nonzero frequency counts are set to 1. This is especially useful for discrete probabilistic models that model binary, rather than integer, counts.

CountVectorizer converts text documents to vectors of term counts. Refer to CountVectorizer for more details.

IDF: IDF is an Estimator which is fit on a dataset and produces an IDFModel. The IDFModel takes feature vectors (generally created from HashingTF or CountVectorizer) and scales each feature. Intuitively, it down-weights features which appear frequently in a corpus.

Note: spark.ml doesn't provide tools for text segmentation. We refer users to the Stanford NLP Group and scalanlp/chalk.

Examples

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.

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 %}
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 %}
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 %}

## 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 as features for prediction, document similarity calculations, etc. Please refer to the MLlib user guide on Word2Vec for more details.

Examples

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.

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 %}
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 %}
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 %}

## 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 affects 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. Another optional binary toggle parameter controls the output vector. If set to true all nonzero counts are set to 1. This is especially useful for discrete probabilistic models that model binary, rather than integer, counts.

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.

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 %}
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 %}
Refer to the [CountVectorizer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.CountVectorizer) and the [CountVectorizerModel Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.CountVectorizerModel) for more details on the API. {% include_example python/ml/count_vectorizer_example.py %}

## FeatureHasher

Feature hashing projects a set of categorical or numerical features into a feature vector of specified dimension (typically substantially smaller than that of the original feature space). This is done using the hashing trick to map features to indices in the feature vector.

The FeatureHasher transformer operates on multiple columns. Each column may contain either numeric or categorical features. Behavior and handling of column data types is as follows:

• Numeric columns: For numeric features, the hash value of the column name is used to map the feature value to its index in the feature vector. By default, numeric features are not treated as categorical (even when they are integers). To treat them as categorical, specify the relevant columns using the categoricalCols parameter.
• String columns: For categorical features, the hash value of the string "column_name=value" is used to map to the vector index, with an indicator value of 1.0. Thus, categorical features are "one-hot" encoded (similarly to using OneHotEncoder with dropLast=false).
• Boolean columns: Boolean values are treated in the same way as string columns. That is, boolean features are represented as "column_name=true" or "column_name=false", with an indicator value of 1.0.

Null (missing) values are ignored (implicitly zero in the resulting feature vector).

The hash function used here is also the MurmurHash 3 used in HashingTF. Since a simple modulo on the hashed value is used to determine the vector index, it is advisable to use a power of two as the numFeatures parameter; otherwise the features will not be mapped evenly to the vector indices.

Examples

Assume that we have a DataFrame with 4 input columns real, bool, stringNum, and string. These different data types as input will illustrate the behavior of the transform to produce a column of feature vectors.

real| bool|stringNum|string
----|-----|---------|------
2.2| true|        1|   foo
3.3|false|        2|   bar
4.4|false|        3|   baz
5.5|false|        4|   foo


Then the output of FeatureHasher.transform on this DataFrame is:

real|bool |stringNum|string|features
----|-----|---------|------|-------------------------------------------------------
2.2 |true |1        |foo   |(262144,[51871, 63643,174475,253195],[1.0,1.0,2.2,1.0])
3.3 |false|2        |bar   |(262144,[6031,  80619,140467,174475],[1.0,1.0,1.0,3.3])
4.4 |false|3        |baz   |(262144,[24279,140467,174475,196810],[1.0,1.0,4.4,1.0])
5.5 |false|4        |foo   |(262144,[63643,140467,168512,174475],[1.0,1.0,1.0,5.5])


The resulting feature vectors could then be passed to a learning algorithm.

Refer to the [FeatureHasher Scala docs](api/scala/index.html#org.apache.spark.ml.feature.FeatureHasher) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/FeatureHasherExample.scala %}
Refer to the [FeatureHasher Java docs](api/java/org/apache/spark/ml/feature/FeatureHasher.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaFeatureHasherExample.java %}
Refer to the [FeatureHasher Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.FeatureHasher) for more details on the API. {% include_example python/ml/feature_hasher_example.py %}

# Feature Transformers

## Tokenizer

Tokenization is the process of taking text (such as a sentence) and breaking it into individual terms (usually words). A simple Tokenizer class provides this functionality. The example below shows how to split sentences into sequences of words.

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.

Examples

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.RegexTokenizer) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/TokenizerExample.scala %}
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. {% include_example java/org/apache/spark/examples/ml/JavaTokenizerExample.java %}
Refer to the [Tokenizer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.Tokenizer) and the [RegexTokenizer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.RegexTokenizer) for more details on the API. {% include_example python/ml/tokenizer_example.py %}

## StopWordsRemover

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) and drops all the stop words from the input sequences. The list of stopwords is specified by the stopWords parameter. Default stop words for some languages are accessible by calling StopWordsRemover.loadDefaultStopWords(language), for which available options are "danish", "dutch", "english", "finnish", "french", "german", "hungarian", "italian", "norwegian", "portuguese", "russian", "spanish", "swedish" and "turkish". 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, balloon]
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, balloon]  |  [saw, red, balloon]
1  | [Mary, had, a, little, lamb]|[Mary, little, lamb]


In filtered, the stop words "I", "the", "had", and "a" have been filtered out.

Refer to the [StopWordsRemover Scala docs](api/scala/index.html#org.apache.spark.ml.feature.StopWordsRemover) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/StopWordsRemoverExample.scala %}
Refer to the [StopWordsRemover Java docs](api/java/org/apache/spark/ml/feature/StopWordsRemover.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaStopWordsRemoverExample.java %}
Refer to the [StopWordsRemover Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.StopWordsRemover) for more details on the API. {% include_example python/ml/stopwords_remover_example.py %}

## $n$-gram

An 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). 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.

Examples

Refer to the [NGram Scala docs](api/scala/index.html#org.apache.spark.ml.feature.NGram) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/NGramExample.scala %}
Refer to the [NGram Java docs](api/java/org/apache/spark/ml/feature/NGram.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaNGramExample.java %}
Refer to the [NGram Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.NGram) for more details on the API. {% include_example python/ml/n_gram_example.py %}

## 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. Both Vector and Double types are supported for inputCol.

Examples

Refer to the [Binarizer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.Binarizer) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/BinarizerExample.scala %}
Refer to the [Binarizer Java docs](api/java/org/apache/spark/ml/feature/Binarizer.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaBinarizerExample.java %}
Refer to the [Binarizer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.Binarizer) for more details on the API. {% include_example python/ml/binarizer_example.py %}

## PCA

PCA 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 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.

Examples

Refer to the [PCA Scala docs](api/scala/index.html#org.apache.spark.ml.feature.PCA) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/PCAExample.scala %}
Refer to the [PCA Java docs](api/java/org/apache/spark/ml/feature/PCA.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaPCAExample.java %}
Refer to the [PCA Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.PCA) for more details on the API. {% include_example python/ml/pca_example.py %}

## PolynomialExpansion

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 class provides this functionality. The example below shows how to expand your features into a 3-degree polynomial space.

Examples

Refer to the [PolynomialExpansion Scala docs](api/scala/index.html#org.apache.spark.ml.feature.PolynomialExpansion) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/PolynomialExpansionExample.scala %}
Refer to the [PolynomialExpansion Java docs](api/java/org/apache/spark/ml/feature/PolynomialExpansion.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaPolynomialExpansionExample.java %}
Refer to the [PolynomialExpansion Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.PolynomialExpansion) for more details on the API. {% include_example python/ml/polynomial_expansion_example.py %}

## Discrete Cosine Transform (DCT)

The 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 class provides this functionality, implementing the 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).

Examples

Refer to the [DCT Scala docs](api/scala/index.html#org.apache.spark.ml.feature.DCT) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/DCTExample.scala %}
Refer to the [DCT Java docs](api/java/org/apache/spark/ml/feature/DCT.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaDCTExample.java %}
Refer to the [DCT Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.DCT) for more details on the API. {% include_example python/ml/dct_example.py %}

## StringIndexer

StringIndexer encodes a string column of labels to a column of label indices. StringIndexer can encode multiple columns. The indices are in [0, numLabels), and four ordering options are supported: "frequencyDesc": descending order by label frequency (most frequent label assigned 0), "frequencyAsc": ascending order by label frequency (least frequent label assigned 0), "alphabetDesc": descending alphabetical order, and "alphabetAsc": ascending alphabetical order (default = "frequencyDesc"). Note that in case of equal frequency when under "frequencyDesc"/"frequencyAsc", the strings are further sorted by alphabet.

The unseen labels will be put at index numLabels if user chooses to keep them. 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.

Additionally, there are three strategies regarding how StringIndexer will handle unseen labels when you have fit a StringIndexer on one dataset and then use it to transform another:

• throw an exception (which is the default)
• skip the row containing the unseen label entirely
• put unseen labels in a special additional bucket, at index numLabels

Examples

Let's go back to our previous example but this time reuse our previously defined StringIndexer on the following dataset:

 id | category
----|----------
0  | a
1  | b
2  | c
3  | d
4  | e


If you've not set how StringIndexer handles unseen labels or set it to "error", an exception will be thrown. However, if you had called setHandleInvalid("skip"), the following dataset will be generated:

 id | category | categoryIndex
----|----------|---------------
0  | a        | 0.0
1  | b        | 2.0
2  | c        | 1.0


Notice that the rows containing "d" or "e" do not appear.

If you call setHandleInvalid("keep"), the following dataset will be generated:

 id | category | categoryIndex
----|----------|---------------
0  | a        | 0.0
1  | b        | 2.0
2  | c        | 1.0
3  | d        | 3.0
4  | e        | 3.0


Notice that the rows containing "d" or "e" are mapped to index "3.0"

Refer to the [StringIndexer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.StringIndexer) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/StringIndexerExample.scala %}
Refer to the [StringIndexer Java docs](api/java/org/apache/spark/ml/feature/StringIndexer.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaStringIndexerExample.java %}
Refer to the [StringIndexer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.StringIndexer) for more details on the API. {% include_example python/ml/string_indexer_example.py %}

## IndexToString

Symmetrically to StringIndexer, IndexToString maps a column of label indices back to a column containing the original labels as strings. A common use case is to produce indices from labels with StringIndexer, train a model with those indices and retrieve the original labels from the column of predicted indices with IndexToString. However, you are free to supply your own labels.

Examples

Building on the StringIndexer example, let's assume we have the following DataFrame with columns id and categoryIndex:

 id | categoryIndex
----|---------------
0  | 0.0
1  | 2.0
2  | 1.0
3  | 0.0
4  | 0.0
5  | 1.0


Applying IndexToString with categoryIndex as the input column, originalCategory as the output column, we are able to retrieve our original labels (they will be inferred from the columns' metadata):

 id | categoryIndex | originalCategory
----|---------------|-----------------
0  | 0.0           | a
1  | 2.0           | b
2  | 1.0           | c
3  | 0.0           | a
4  | 0.0           | a
5  | 1.0           | c

Refer to the [IndexToString Scala docs](api/scala/index.html#org.apache.spark.ml.feature.IndexToString) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/IndexToStringExample.scala %}
Refer to the [IndexToString Java docs](api/java/org/apache/spark/ml/feature/IndexToString.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaIndexToStringExample.java %}
Refer to the [IndexToString Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.IndexToString) for more details on the API. {% include_example python/ml/index_to_string_example.py %}

## OneHotEncoder

One-hot encoding maps a categorical feature, represented as a label index, to a binary vector with at most a single one-value indicating the presence of a specific feature value from among the set of all feature values. This encoding allows algorithms which expect continuous features, such as Logistic Regression, to use categorical features. For string type input data, it is common to encode categorical features using StringIndexer first.

OneHotEncoder can transform multiple columns, returning an one-hot-encoded output vector column for each input column. It is common to merge these vectors into a single feature vector using VectorAssembler.

OneHotEncoder supports the handleInvalid parameter to choose how to handle invalid input during transforming data. Available options include 'keep' (any invalid inputs are assigned to an extra categorical index) and 'error' (throw an error).

Examples

Refer to the [OneHotEncoder Scala docs](api/scala/index.html#org.apache.spark.ml.feature.OneHotEncoder) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/OneHotEncoderExample.scala %}
Refer to the [OneHotEncoder Java docs](api/java/org/apache/spark/ml/feature/OneHotEncoder.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaOneHotEncoderExample.java %}
Refer to the [OneHotEncoder Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.OneHotEncoder) for more details on the API. {% include_example python/ml/onehot_encoder_example.py %}

## VectorIndexer

VectorIndexer helps index categorical features in datasets of Vectors. 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 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.

Examples

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.

Refer to the [VectorIndexer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.VectorIndexer) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/VectorIndexerExample.scala %}
Refer to the [VectorIndexer Java docs](api/java/org/apache/spark/ml/feature/VectorIndexer.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaVectorIndexerExample.java %}
Refer to the [VectorIndexer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.VectorIndexer) for more details on the API. {% include_example python/ml/vector_indexer_example.py %}

## Interaction

Interaction is a Transformer which takes vector or double-valued columns, and generates a single vector column that contains the product of all combinations of one value from each input column.

For example, if you have 2 vector type columns each of which has 3 dimensions as input columns, then you'll get a 9-dimensional vector as the output column.

Examples

Assume that we have the following DataFrame with the columns "id1", "vec1", and "vec2":

  id1|vec1          |vec2
---|--------------|--------------
1  |[1.0,2.0,3.0] |[8.0,4.0,5.0]
2  |[4.0,3.0,8.0] |[7.0,9.0,8.0]
3  |[6.0,1.0,9.0] |[2.0,3.0,6.0]
4  |[10.0,8.0,6.0]|[9.0,4.0,5.0]
5  |[9.0,2.0,7.0] |[10.0,7.0,3.0]
6  |[1.0,1.0,4.0] |[2.0,8.0,4.0]


Applying Interaction with those input columns, then interactedCol as the output column contains:

  id1|vec1          |vec2          |interactedCol
---|--------------|--------------|------------------------------------------------------
1  |[1.0,2.0,3.0] |[8.0,4.0,5.0] |[8.0,4.0,5.0,16.0,8.0,10.0,24.0,12.0,15.0]
2  |[4.0,3.0,8.0] |[7.0,9.0,8.0] |[56.0,72.0,64.0,42.0,54.0,48.0,112.0,144.0,128.0]
3  |[6.0,1.0,9.0] |[2.0,3.0,6.0] |[36.0,54.0,108.0,6.0,9.0,18.0,54.0,81.0,162.0]
4  |[10.0,8.0,6.0]|[9.0,4.0,5.0] |[360.0,160.0,200.0,288.0,128.0,160.0,216.0,96.0,120.0]
5  |[9.0,2.0,7.0] |[10.0,7.0,3.0]|[450.0,315.0,135.0,100.0,70.0,30.0,350.0,245.0,105.0]
6  |[1.0,1.0,4.0] |[2.0,8.0,4.0] |[12.0,48.0,24.0,12.0,48.0,24.0,48.0,192.0,96.0]

Refer to the [Interaction Scala docs](api/scala/index.html#org.apache.spark.ml.feature.Interaction) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/InteractionExample.scala %}
Refer to the [Interaction Java docs](api/java/org/apache/spark/ml/feature/Interaction.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaInteractionExample.java %}
Refer to the [Interaction Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.Interaction) for more details on the API. {% include_example python/ml/interaction_example.py %}

## 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 used for normalization. ($p = 2$ by default.) This normalization can help standardize your input data and improve the behavior of learning algorithms.

Examples

The following example demonstrates how to load a dataset in libsvm format and then normalize each row to have unit $L^1$ norm and unit $L^\infty$ norm.

Refer to the [Normalizer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.Normalizer) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/NormalizerExample.scala %}
Refer to the [Normalizer Java docs](api/java/org/apache/spark/ml/feature/Normalizer.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaNormalizerExample.java %}
Refer to the [Normalizer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.Normalizer) for more details on the API. {% include_example python/ml/normalizer_example.py %}

## 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 take care when applying to sparse input.

StandardScaler is an Estimator 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.

Examples

The following example demonstrates how to load a dataset in libsvm format and then normalize each feature to have unit standard deviation.

Refer to the [StandardScaler Scala docs](api/scala/index.html#org.apache.spark.ml.feature.StandardScaler) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/StandardScalerExample.scala %}
Refer to the [StandardScaler Java docs](api/java/org/apache/spark/ml/feature/StandardScaler.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaStandardScalerExample.java %}
Refer to the [StandardScaler Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.StandardScaler) for more details on the API. {% include_example python/ml/standard_scaler_example.py %}

## RobustScaler

RobustScaler transforms a dataset of Vector rows, removing the median and scaling the data according to a specific quantile range (by default the IQR: Interquartile Range, quantile range between the 1st quartile and the 3rd quartile). Its behavior is quite similar to StandardScaler, however the median and the quantile range are used instead of mean and standard deviation, which make it robust to outliers. It takes parameters:

• lower: 0.25 by default. Lower quantile to calculate quantile range, shared by all features.
• upper: 0.75 by default. Upper quantile to calculate quantile range, shared by all features.
• withScaling: True by default. Scales the data to quantile range.
• withCentering: False by default. Centers the data with median before scaling. It will build a dense output, so take care when applying to sparse input.

RobustScaler is an Estimator which can be fit on a dataset to produce a RobustScalerModel; this amounts to computing quantile statistics. The model can then transform a Vector column in a dataset to have unit quantile range and/or zero median features.

Note that if the quantile range of a feature is zero, it will return default 0.0 value in the Vector for that feature.

Examples

The following example demonstrates how to load a dataset in libsvm format and then normalize each feature to have unit quantile range.

Refer to the [RobustScaler Scala docs](api/scala/index.html#org.apache.spark.ml.feature.RobustScaler) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/RobustScalerExample.scala %}
Refer to the [RobustScaler Java docs](api/java/org/apache/spark/ml/feature/RobustScaler.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaRobustScalerExample.java %}
Refer to the [RobustScaler Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.RobustScaler) for more details on the API. {% include_example python/ml/robust_scaler_example.py %}

## 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, $$Rescaled(e_i) = \frac{e_i - E_{min}}{E_{max} - E_{min}} * (max - min) + min$$ 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.

Examples

The following example demonstrates how to load a dataset in libsvm format and then rescale each feature to [0, 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. {% include_example scala/org/apache/spark/examples/ml/MinMaxScalerExample.scala %}
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. {% include_example java/org/apache/spark/examples/ml/JavaMinMaxScalerExample.java %}
Refer to the [MinMaxScaler Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.MinMaxScaler) and the [MinMaxScalerModel Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.MinMaxScalerModel) for more details on the API. {% include_example python/ml/min_max_scaler_example.py %}

## MaxAbsScaler

MaxAbsScaler transforms a dataset of Vector rows, rescaling each feature to range [-1, 1] by dividing through the maximum absolute value in each feature. It does not shift/center the data, and thus does not destroy any sparsity.

MaxAbsScaler computes summary statistics on a data set and produces a MaxAbsScalerModel. The model can then transform each feature individually to range [-1, 1].

Examples

The following example demonstrates how to load a dataset in libsvm format and then rescale each feature to [-1, 1].

Refer to the [MaxAbsScaler Scala docs](api/scala/index.html#org.apache.spark.ml.feature.MaxAbsScaler) and the [MaxAbsScalerModel Scala docs](api/scala/index.html#org.apache.spark.ml.feature.MaxAbsScalerModel) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/MaxAbsScalerExample.scala %}
Refer to the [MaxAbsScaler Java docs](api/java/org/apache/spark/ml/feature/MaxAbsScaler.html) and the [MaxAbsScalerModel Java docs](api/java/org/apache/spark/ml/feature/MaxAbsScalerModel.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaMaxAbsScalerExample.java %}
Refer to the [MaxAbsScaler Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.MaxAbsScaler) and the [MaxAbsScalerModel Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.MaxAbsScalerModel) for more details on the API. {% include_example python/ml/max_abs_scaler_example.py %}

## 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 and lower bounds of the targeted column, you should add Double.NegativeInfinity and Double.PositiveInfinity as the bounds of your splits to prevent a potential 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.

Examples

The following example demonstrates how to bucketize a column of Doubles into another index-wised column.

Refer to the [Bucketizer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.Bucketizer) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/BucketizerExample.scala %}
Refer to the [Bucketizer Java docs](api/java/org/apache/spark/ml/feature/Bucketizer.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaBucketizerExample.java %}
Refer to the [Bucketizer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.Bucketizer) for more details on the API. {% include_example python/ml/bucketizer_example.py %}

## 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 between the input vector, v and transforming vector, w, to yield a result vector.

$\begin{pmatrix} v_1 \\ \vdots \\ v_N \end{pmatrix} \circ \begin{pmatrix} w_1 \\ \vdots \\ w_N \end{pmatrix} = \begin{pmatrix} v_1 w_1 \\ \vdots \\ v_N w_N \end{pmatrix}$

Examples

This example below demonstrates how to transform vectors using a transforming vector value.

Refer to the [ElementwiseProduct Scala docs](api/scala/index.html#org.apache.spark.ml.feature.ElementwiseProduct) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/ElementwiseProductExample.scala %}
Refer to the [ElementwiseProduct Java docs](api/java/org/apache/spark/ml/feature/ElementwiseProduct.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaElementwiseProductExample.java %}
Refer to the [ElementwiseProduct Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.ElementwiseProduct) for more details on the API. {% include_example python/ml/elementwise_product_example.py %}

## SQLTransformer

SQLTransformer implements the transformations which are defined by SQL statement. Currently, we only support SQL syntax like "SELECT ... FROM __THIS__ ..." where "__THIS__" represents the underlying table of the input dataset. The select clause specifies the fields, constants, and expressions to display in the output, and can be any select clause that Spark SQL supports. Users can also use Spark SQL built-in function and UDFs to operate on these selected columns. For example, SQLTransformer supports statements like:

• SELECT a, a + b AS a_b FROM __THIS__
• SELECT a, SQRT(b) AS b_sqrt FROM __THIS__ where a > 5
• SELECT a, b, SUM(c) AS c_sum FROM __THIS__ GROUP BY a, b

Examples

Assume that we have the following DataFrame with columns id, v1 and v2:

 id |  v1 |  v2
----|-----|-----
0  | 1.0 | 3.0
2  | 2.0 | 5.0


This is the output of the SQLTransformer with statement "SELECT *, (v1 + v2) AS v3, (v1 * v2) AS v4 FROM __THIS__":

 id |  v1 |  v2 |  v3 |  v4
----|-----|-----|-----|-----
0  | 1.0 | 3.0 | 4.0 | 3.0
2  | 2.0 | 5.0 | 7.0 |10.0

Refer to the [SQLTransformer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.SQLTransformer) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/SQLTransformerExample.scala %}
Refer to the [SQLTransformer Java docs](api/java/org/apache/spark/ml/feature/SQLTransformer.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaSQLTransformerExample.java %}
Refer to the [SQLTransformer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.SQLTransformer) for more details on the API. {% include_example python/ml/sql_transformer.py %}

## 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]

Refer to the [VectorAssembler Scala docs](api/scala/index.html#org.apache.spark.ml.feature.VectorAssembler) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/VectorAssemblerExample.scala %}
Refer to the [VectorAssembler Java docs](api/java/org/apache/spark/ml/feature/VectorAssembler.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaVectorAssemblerExample.java %}
Refer to the [VectorAssembler Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.VectorAssembler) for more details on the API. {% include_example python/ml/vector_assembler_example.py %}

## VectorSizeHint

It can sometimes be useful to explicitly specify the size of the vectors for a column of VectorType. For example, VectorAssembler uses size information from its input columns to produce size information and metadata for its output column. While in some cases this information can be obtained by inspecting the contents of the column, in a streaming dataframe the contents are not available until the stream is started. VectorSizeHint allows a user to explicitly specify the vector size for a column so that VectorAssembler, or other transformers that might need to know vector size, can use that column as an input.

To use VectorSizeHint a user must set the inputCol and size parameters. Applying this transformer to a dataframe produces a new dataframe with updated metadata for inputCol specifying the vector size. Downstream operations on the resulting dataframe can get this size using the metadata.

VectorSizeHint can also take an optional handleInvalid parameter which controls its behaviour when the vector column contains nulls or vectors of the wrong size. By default handleInvalid is set to "error", indicating an exception should be thrown. This parameter can also be set to "skip", indicating that rows containing invalid values should be filtered out from the resulting dataframe, or "optimistic", indicating that the column should not be checked for invalid values and all rows should be kept. Note that the use of "optimistic" can cause the resulting dataframe to be in an inconsistent state, meaning the metadata for the column VectorSizeHint was applied to does not match the contents of that column. Users should take care to avoid this kind of inconsistent state.

Refer to the [VectorSizeHint Scala docs](api/scala/index.html#org.apache.spark.ml.feature.VectorSizeHint) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/VectorSizeHintExample.scala %}
Refer to the [VectorSizeHint Java docs](api/java/org/apache/spark/ml/feature/VectorSizeHint.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaVectorSizeHintExample.java %}
Refer to the [VectorSizeHint Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.VectorSizeHint) for more details on the API. {% include_example python/ml/vector_size_hint_example.py %}

## QuantileDiscretizer

QuantileDiscretizer takes a column with continuous features and outputs a column with binned categorical features. The number of bins is set by the numBuckets parameter. It is possible that the number of buckets used will be smaller than this value, for example, if there are too few distinct values of the input to create enough distinct quantiles.

NaN values: NaN values will be removed from the column during QuantileDiscretizer fitting. This will produce a Bucketizer model for making predictions. During the transformation, Bucketizer will raise an error when it finds NaN values in the dataset, but the user can also choose to either keep or remove NaN values within the dataset by setting handleInvalid. If the user chooses to keep NaN values, they will be handled specially and placed into their own bucket, for example, if 4 buckets are used, then non-NaN data will be put into buckets[0-3], but NaNs will be counted in a special bucket[4].

Algorithm: The bin ranges are chosen using an approximate algorithm (see the documentation for approxQuantile for a detailed description). The precision of the approximation can be controlled with the relativeError parameter. When set to zero, exact quantiles are calculated (Note: Computing exact quantiles is an expensive operation). The lower and upper bin bounds will be -Infinity and +Infinity covering all real values.

Examples

Assume that we have a DataFrame with the columns id, hour:

 id | hour
----|------
0  | 18.0
----|------
1  | 19.0
----|------
2  | 8.0
----|------
3  | 5.0
----|------
4  | 2.2


hour is a continuous feature with Double type. We want to turn the continuous feature into a categorical one. Given numBuckets = 3, we should get the following DataFrame:

 id | hour | result
----|------|------
0  | 18.0 | 2.0
----|------|------
1  | 19.0 | 2.0
----|------|------
2  | 8.0  | 1.0
----|------|------
3  | 5.0  | 1.0
----|------|------
4  | 2.2  | 0.0

Refer to the [QuantileDiscretizer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.QuantileDiscretizer) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/QuantileDiscretizerExample.scala %}
Refer to the [QuantileDiscretizer Java docs](api/java/org/apache/spark/ml/feature/QuantileDiscretizer.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaQuantileDiscretizerExample.java %}
Refer to the [QuantileDiscretizer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.QuantileDiscretizer) for more details on the API. {% include_example python/ml/quantile_discretizer_example.py %}

## Imputer

The Imputer estimator completes missing values in a dataset, either using the mean or the median of the columns in which the missing values are located. The input columns should be of DoubleType or FloatType. Currently Imputer does not support categorical features and possibly creates incorrect values for columns containing categorical features. Imputer can impute custom values other than 'NaN' by .setMissingValue(custom_value). For example, .setMissingValue(0) will impute all occurrences of (0).

Note all null values in the input columns are treated as missing, and so are also imputed.

Examples

Suppose that we have a DataFrame with the columns a and b:

      a     |      b
------------|-----------
1.0    | Double.NaN
2.0    | Double.NaN
Double.NaN |     3.0
4.0    |     4.0
5.0    |     5.0


In this example, Imputer will replace all occurrences of Double.NaN (the default for the missing value) with the mean (the default imputation strategy) computed from the other values in the corresponding columns. In this example, the surrogate values for columns a and b are 3.0 and 4.0 respectively. After transformation, the missing values in the output columns will be replaced by the surrogate value for the relevant column.

      a     |      b     | out_a | out_b
------------|------------|-------|-------
1.0    | Double.NaN |  1.0  |  4.0
2.0    | Double.NaN |  2.0  |  4.0
Double.NaN |     3.0    |  3.0  |  3.0
4.0    |     4.0    |  4.0  |  4.0
5.0    |     5.0    |  5.0  |  5.0

Refer to the [Imputer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.Imputer) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/ImputerExample.scala %}
Refer to the [Imputer Java docs](api/java/org/apache/spark/ml/feature/Imputer.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaImputerExample.java %}
Refer to the [Imputer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.Imputer) for more details on the API. {% include_example python/ml/imputer_example.py %}

# 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 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 represent the indices into the vector, setIndices().

2. String indices that represent 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 thrown if empty input attributes are encountered.

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. Assume that the first column of userFeatures are all zeros, so we want to remove it and select only the last two columns. 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 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"]

Refer to the [VectorSlicer Scala docs](api/scala/index.html#org.apache.spark.ml.feature.VectorSlicer) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/VectorSlicerExample.scala %}
Refer to the [VectorSlicer Java docs](api/java/org/apache/spark/ml/feature/VectorSlicer.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaVectorSlicerExample.java %}
Refer to the [VectorSlicer Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.VectorSlicer) for more details on the API. {% include_example python/ml/vector_slicer_example.py %}

## RFormula

RFormula selects columns specified by an R model formula. Currently we support a limited subset of the R operators, including '~', '.', ':', '+', and '-'. The basic operators are:

• ~ separate target and terms
• + concat terms, "+ 0" means removing intercept
• - remove a term, "- 1" means removing intercept
• : interaction (multiplication for numeric values, or binarized categorical values)
• . all columns except target

Suppose a and b are double columns, we use the following simple examples to illustrate the effect of RFormula:

• y ~ a + b means model y ~ w0 + w1 * a + w2 * b where w0 is the intercept and w1, w2 are coefficients.
• y ~ a + b + a:b - 1 means model y ~ w1 * a + w2 * b + w3 * a * b where w1, w2, w3 are coefficients.

RFormula produces a vector column of features and a double or string column of label. Like when formulas are used in R for linear regression, numeric columns will be cast to doubles. As to string input columns, they will first be transformed with StringIndexer using ordering determined by stringOrderType, and the last category after ordering is dropped, then the doubles will be one-hot encoded.

Suppose a string feature column containing values {'b', 'a', 'b', 'a', 'c', 'b'}, we set stringOrderType to control the encoding:

stringOrderType | Category mapped to 0 by StringIndexer |  Category dropped by RFormula
----------------|---------------------------------------|---------------------------------
'frequencyDesc' | most frequent category ('b')          | least frequent category ('c')
'frequencyAsc'  | least frequent category ('c')         | most frequent category ('b')
'alphabetDesc'  | last alphabetical category ('c')      | first alphabetical category ('a')
'alphabetAsc'   | first alphabetical category ('a')     | last alphabetical category ('c')


If the label column is of type string, it will be first transformed to double with StringIndexer using frequencyDesc ordering. If the label column does not exist in the DataFrame, the output label column will be created from the specified response variable in the formula.

Note: The ordering option stringOrderType is NOT used for the label column. When the label column is indexed, it uses the default descending frequency ordering in StringIndexer.

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

Refer to the [RFormula Scala docs](api/scala/index.html#org.apache.spark.ml.feature.RFormula) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/RFormulaExample.scala %}
Refer to the [RFormula Java docs](api/java/org/apache/spark/ml/feature/RFormula.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaRFormulaExample.java %}
Refer to the [RFormula Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.RFormula) for more details on the API. {% include_example python/ml/rformula_example.py %}

## ChiSqSelector

ChiSqSelector stands for Chi-Squared feature selection. It operates on labeled data with categorical features. ChiSqSelector uses the Chi-Squared test of independence to decide which features to choose. It supports five selection methods: numTopFeatures, percentile, fpr, fdr, fwe: * numTopFeatures chooses a fixed number of top features according to a chi-squared test. This is akin to yielding the features with the most predictive power. * percentile is similar to numTopFeatures but chooses a fraction of all features instead of a fixed number. * fpr chooses all features whose p-values are below a threshold, thus controlling the false positive rate of selection. * fdr uses the Benjamini-Hochberg procedure to choose all features whose false discovery rate is below a threshold. * fwe chooses all features whose p-values are below a threshold. The threshold is scaled by 1/numFeatures, thus controlling the family-wise error rate of selection. By default, the selection method is numTopFeatures, with the default number of top features set to 50. The user can choose a selection method using setSelectorType.

Examples

Assume that we have a DataFrame with the columns id, features, and clicked, which is used as our target to be predicted:

id | features              | clicked
---|-----------------------|---------
7 | [0.0, 0.0, 18.0, 1.0] | 1.0
8 | [0.0, 1.0, 12.0, 0.0] | 0.0
9 | [1.0, 0.0, 15.0, 0.1] | 0.0


If we use ChiSqSelector with numTopFeatures = 1, then according to our label clicked the last column in our features is chosen as the most useful feature:

id | features              | clicked | selectedFeatures
---|-----------------------|---------|------------------
7 | [0.0, 0.0, 18.0, 1.0] | 1.0     | [1.0]
8 | [0.0, 1.0, 12.0, 0.0] | 0.0     | [0.0]
9 | [1.0, 0.0, 15.0, 0.1] | 0.0     | [0.1]

Refer to the [ChiSqSelector Scala docs](api/scala/index.html#org.apache.spark.ml.feature.ChiSqSelector) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/ChiSqSelectorExample.scala %}
Refer to the [ChiSqSelector Java docs](api/java/org/apache/spark/ml/feature/ChiSqSelector.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaChiSqSelectorExample.java %}
Refer to the [ChiSqSelector Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.ChiSqSelector) for more details on the API. {% include_example python/ml/chisq_selector_example.py %}

# Locality Sensitive Hashing

Locality Sensitive Hashing (LSH) is an important class of hashing techniques, which is commonly used in clustering, approximate nearest neighbor search and outlier detection with large datasets.

The general idea of LSH is to use a family of functions ("LSH families") to hash data points into buckets, so that the data points which are close to each other are in the same buckets with high probability, while data points that are far away from each other are very likely in different buckets. An LSH family is formally defined as follows.

In a metric space (M, d), where M is a set and d is a distance function on M, an LSH family is a family of functions h that satisfy the following properties: $\forall p, q \in M,\\ d(p,q) \leq r1 \Rightarrow Pr(h(p)=h(q)) \geq p1\\ d(p,q) \geq r2 \Rightarrow Pr(h(p)=h(q)) \leq p2$ This LSH family is called (r1, r2, p1, p2)-sensitive.

In Spark, different LSH families are implemented in separate classes (e.g., MinHash), and APIs for feature transformation, approximate similarity join and approximate nearest neighbor are provided in each class.

In LSH, we define a false positive as a pair of distant input features (with $d(p,q) \geq r2$) which are hashed into the same bucket, and we define a false negative as a pair of nearby features (with $d(p,q) \leq r1$) which are hashed into different buckets.

## LSH Operations

We describe the major types of operations which LSH can be used for. A fitted LSH model has methods for each of these operations.

### Feature Transformation

Feature transformation is the basic functionality to add hashed values as a new column. This can be useful for dimensionality reduction. Users can specify input and output column names by setting inputCol and outputCol.

LSH also supports multiple LSH hash tables. Users can specify the number of hash tables by setting numHashTables. This is also used for OR-amplification in approximate similarity join and approximate nearest neighbor. Increasing the number of hash tables will increase the accuracy but will also increase communication cost and running time.

The type of outputCol is Seq[Vector] where the dimension of the array equals numHashTables, and the dimensions of the vectors are currently set to 1. In future releases, we will implement AND-amplification so that users can specify the dimensions of these vectors.

### Approximate Similarity Join

Approximate similarity join takes two datasets and approximately returns pairs of rows in the datasets whose distance is smaller than a user-defined threshold. Approximate similarity join supports both joining two different datasets and self-joining. Self-joining will produce some duplicate pairs.

Approximate similarity join accepts both transformed and untransformed datasets as input. If an untransformed dataset is used, it will be transformed automatically. In this case, the hash signature will be created as outputCol.

In the joined dataset, the origin datasets can be queried in datasetA and datasetB. A distance column will be added to the output dataset to show the true distance between each pair of rows returned.

Approximate nearest neighbor search takes a dataset (of feature vectors) and a key (a single feature vector), and it approximately returns a specified number of rows in the dataset that are closest to the vector.

Approximate nearest neighbor search accepts both transformed and untransformed datasets as input. If an untransformed dataset is used, it will be transformed automatically. In this case, the hash signature will be created as outputCol.

A distance column will be added to the output dataset to show the true distance between each output row and the searched key.

Note: Approximate nearest neighbor search will return fewer than k rows when there are not enough candidates in the hash bucket.

## LSH Algorithms

### Bucketed Random Projection for Euclidean Distance

Bucketed Random Projection is an LSH family for Euclidean distance. The Euclidean distance is defined as follows: $d(\mathbf{x}, \mathbf{y}) = \sqrt{\sum_i (x_i - y_i)^2}$ Its LSH family projects feature vectors $\mathbf{x}$ onto a random unit vector $\mathbf{v}$ and portions the projected results into hash buckets: $h(\mathbf{x}) = \Big\lfloor \frac{\mathbf{x} \cdot \mathbf{v}}{r} \Big\rfloor$ where r is a user-defined bucket length. The bucket length can be used to control the average size of hash buckets (and thus the number of buckets). A larger bucket length (i.e., fewer buckets) increases the probability of features being hashed to the same bucket (increasing the numbers of true and false positives).

Bucketed Random Projection accepts arbitrary vectors as input features, and supports both sparse and dense vectors.

Refer to the [BucketedRandomProjectionLSH Scala docs](api/scala/index.html#org.apache.spark.ml.feature.BucketedRandomProjectionLSH) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/BucketedRandomProjectionLSHExample.scala %}
Refer to the [BucketedRandomProjectionLSH Java docs](api/java/org/apache/spark/ml/feature/BucketedRandomProjectionLSH.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaBucketedRandomProjectionLSHExample.java %}
Refer to the [BucketedRandomProjectionLSH Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.BucketedRandomProjectionLSH) for more details on the API. {% include_example python/ml/bucketed_random_projection_lsh_example.py %}

### MinHash for Jaccard Distance

MinHash is an LSH family for Jaccard distance where input features are sets of natural numbers. Jaccard distance of two sets is defined by the cardinality of their intersection and union: $d(\mathbf{A}, \mathbf{B}) = 1 - \frac{|\mathbf{A} \cap \mathbf{B}|}{|\mathbf{A} \cup \mathbf{B}|}$ MinHash applies a random hash function g to each element in the set and take the minimum of all hashed values: $h(\mathbf{A}) = \min_{a \in \mathbf{A}}(g(a))$

The input sets for MinHash are represented as binary vectors, where the vector indices represent the elements themselves and the non-zero values in the vector represent the presence of that element in the set. While both dense and sparse vectors are supported, typically sparse vectors are recommended for efficiency. For example, Vectors.sparse(10, Array[(2, 1.0), (3, 1.0), (5, 1.0)]) means there are 10 elements in the space. This set contains elem 2, elem 3 and elem 5. All non-zero values are treated as binary "1" values.

Note: Empty sets cannot be transformed by MinHash, which means any input vector must have at least 1 non-zero entry.

Refer to the [MinHashLSH Scala docs](api/scala/index.html#org.apache.spark.ml.feature.MinHashLSH) for more details on the API. {% include_example scala/org/apache/spark/examples/ml/MinHashLSHExample.scala %}
Refer to the [MinHashLSH Java docs](api/java/org/apache/spark/ml/feature/MinHashLSH.html) for more details on the API. {% include_example java/org/apache/spark/examples/ml/JavaMinHashLSHExample.java %}
Refer to the [MinHashLSH Python docs](api/python/pyspark.ml.html#pyspark.ml.feature.MinHashLSH) for more details on the API. {% include_example python/ml/min_hash_lsh_example.py %}