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.
Table of Contents
 This will become a table of contents (this text will be scraped). {:toc}
Feature Extractors
TFIDF
Term frequencyinverse document frequency (TFIDF) 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 overemphasize 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 TFIDF 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 fixedlength 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 termtoindex 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 downweights 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.
Word2Vec
Word2Vec
is an Estimator
which takes sequences of words representing documents and trains a Word2VecModel
. The model maps each word to a unique fixedsize 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.
CountVectorizer
CountVectorizer
and CountVectorizerModel
aim to help convert a collection of text documents to vectors of token counts. When an apriori 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.
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 "onehot" encoded (similarly to using OneHotEncoder withdropLast=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 boolstringNumstring

2.2 true 1 foo
3.3false 2 bar
4.4false 3 baz
5.5false 4 foo
Then the output of FeatureHasher.transform
on this DataFrame is:
realbool stringNumstringfeatures

2.2 true 1 foo (262144,[51871, 63643,174475,253195],[1.0,1.0,2.2,1.0])
3.3 false2 bar (262144,[6031, 80619,140467,174475],[1.0,1.0,1.0,3.3])
4.4 false3 baz (262144,[24279,140467,174475,196810],[1.0,1.0,4.4,1.0])
5.5 false4 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.
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
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.
$n$gram
An ngram 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 spacedelimited string of $n$ consecutive words. If the input sequence contains fewer than n
strings, no output is produced.
Examples
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
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 lowdimensional space using PCA. The example below shows how to project 5dimensional feature vectors into 3dimensional principal components.
Examples
PolynomialExpansion
Polynomial expansion is the process of expanding your features into a polynomial space, which is formulated by an ndegree combination of original dimensions. A PolynomialExpansion class provides this functionality. The example below shows how to expand your features into a 3degree polynomial space.
Examples
Discrete Cosine Transform (DCT)
The Discrete Cosine Transform transforms a length $N$ realvalued sequence in the time domain into another length $N$ realvalued sequence in the frequency domain. A DCT class provides this functionality, implementing the DCTII 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
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 stringindexed label, you must set the input column of the component to this stringindexed 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"
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
OneHotEncoder
Onehot encoding maps a categorical feature, represented as a label index, to a binary vector with at most a single onevalue 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 onehotencoded 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
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:
 Take an input column of type Vector and a parameter
maxCategories
.  Decide which features should be categorical based on the number of distinct values, where features with at most
maxCategories
are declared categorical.  Compute 0based category indices for each categorical feature.
 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.
Interaction
Interaction
is a Transformer
which takes vector or doublevalued 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 9dimensional vector as the output column.
Examples
Assume that we have the following DataFrame with the columns "id1", "vec1", and "vec2":
id1vec1 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:
id1vec1 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]
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 pnorm 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.
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.
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.
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 nonzero 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].
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].
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 ofsplits
areArray(Double.NegativeInfinity, 0.0, 1.0, Double.PositiveInfinity)
andArray(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 Double
s into another indexwised column.
ElementwiseProduct
ElementwiseProduct multiplies each input vector by a provided "weight" vector, using elementwise 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.
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 builtin 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
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]
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.
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 nonNaN data will be put into buckets[03], 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
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
Feature Selectors
VectorSlicer
VectorSlicer
is a transformer that takes a feature vector and outputs a new feature vector with a subarray 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,

Integer indices that represent the indices into the vector,
setIndices()
.  String indices that represent the names of features into the vector,
setNames()
. This requires the vector column to have anAttributeGroup
since the implementation matches on the name field of anAttribute
.
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"]
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 modely ~ w0 + w1 * a + w2 * b
wherew0
is the intercept andw1, w2
are coefficients.y ~ a + b + a:b  1
means modely ~ w1 * a + w2 * b + w3 * a * b
wherew1, 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 onehot 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
ChiSqSelector
ChiSqSelector
stands for ChiSquared feature selection. It operates on labeled data with categorical features. ChiSqSelector uses the ChiSquared 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 chisquared 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 pvalues are below a threshold, thus controlling the false positive rate of selection. * fdr
uses the BenjaminiHochberg procedure to choose all features whose false discovery rate is below a threshold. * fwe
chooses all features whose pvalues are below a threshold. The threshold is scaled by 1/numFeatures, thus controlling the familywise 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]
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 ORamplification 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 ANDamplification 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 userdefined threshold. Approximate similarity join supports both joining two different datasets and selfjoining. Selfjoining 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
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 userdefined 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.
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 nonzero 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 nonzero 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 nonzero entry.