MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.
A local vector has integer-typed and 0-based indices and double-typed values, stored on a single machine. MLlib supports two types of local vectors: dense and sparse. A dense vector is backed by a double array representing its entry values, while a sparse vector is backed by two parallel arrays: indices and values. For example, a vector (1.0, 0.0, 3.0)
can be represented in dense format as [1.0, 0.0, 3.0]
or in sparse format as (3, [0, 2], [1.0, 3.0])
, where 3
is the size of the vector.
The base class of local vectors is Vector
, and we provide two implementations: DenseVector
and SparseVector
. We recommend using the factory methods implemented in Vectors
to create local vectors.
{% highlight scala %} import org.apache.spark.mllib.linalg.{Vector, Vectors}
// Create a dense vector (1.0, 0.0, 3.0). val dv: Vector = Vectors.dense(1.0, 0.0, 3.0) // Create a sparse vector (1.0, 0.0, 3.0) by specifying its indices and values corresponding to nonzero entries. val sv1: Vector = Vectors.sparse(3, Array(0, 2), Array(1.0, 3.0)) // Create a sparse vector (1.0, 0.0, 3.0) by specifying its nonzero entries. val sv2: Vector = Vectors.sparse(3, Seq((0, 1.0), (2, 3.0))) {% endhighlight %}
Note: Scala imports scala.collection.immutable.Vector
by default, so you have to import org.apache.spark.mllib.linalg.Vector
explicitly to use MLlib's Vector
.
The base class of local vectors is Vector
, and we provide two implementations: DenseVector
and SparseVector
. We recommend using the factory methods implemented in Vectors
to create local vectors.
{% highlight java %} import org.apache.spark.mllib.linalg.Vector; import org.apache.spark.mllib.linalg.Vectors;
// Create a dense vector (1.0, 0.0, 3.0). Vector dv = Vectors.dense(1.0, 0.0, 3.0); // Create a sparse vector (1.0, 0.0, 3.0) by specifying its indices and values corresponding to nonzero entries. Vector sv = Vectors.sparse(3, new int[] {0, 2}, new double[] {1.0, 3.0}); {% endhighlight %}
array
[1, 2, 3]
and the following as sparse vectors:
SparseVector
.csc_matrix
with a single columnWe recommend using NumPy arrays over lists for efficiency, and using the factory methods implemented in Vectors
to create sparse vectors.
{% highlight python %} import numpy as np import scipy.sparse as sps from pyspark.mllib.linalg import Vectors
dv1 = np.array([1.0, 0.0, 3.0])
dv2 = [1.0, 0.0, 3.0]
sv1 = Vectors.sparse(3, [0, 2], [1.0, 3.0])
sv2 = sps.csc_matrix((np.array([1.0, 3.0]), np.array([0, 2]), np.array([0, 2])), shape = (3, 1)) {% endhighlight %}
A labeled point is a local vector, either dense or sparse, associated with a label/response. In MLlib, labeled points are used in supervised learning algorithms. We use a double to store a label, so we can use labeled points in both regression and classification. For binary classification, a label should be either 0
(negative) or 1
(positive). For multiclass classification, labels should be class indices starting from zero: 0, 1, 2, ...
.
A labeled point is represented by the case class LabeledPoint
.
{% highlight scala %} import org.apache.spark.mllib.linalg.Vectors import org.apache.spark.mllib.regression.LabeledPoint
// Create a labeled point with a positive label and a dense feature vector. val pos = LabeledPoint(1.0, Vectors.dense(1.0, 0.0, 3.0))
// Create a labeled point with a negative label and a sparse feature vector. val neg = LabeledPoint(0.0, Vectors.sparse(3, Array(0, 2), Array(1.0, 3.0))) {% endhighlight %}
A labeled point is represented by LabeledPoint
.
{% highlight java %} import org.apache.spark.mllib.linalg.Vectors; import org.apache.spark.mllib.regression.LabeledPoint;
// Create a labeled point with a positive label and a dense feature vector. LabeledPoint pos = new LabeledPoint(1.0, Vectors.dense(1.0, 0.0, 3.0));
// Create a labeled point with a negative label and a sparse feature vector. LabeledPoint neg = new LabeledPoint(0.0, Vectors.sparse(3, new int[] {0, 2}, new double[] {1.0, 3.0})); {% endhighlight %}
A labeled point is represented by LabeledPoint
.
{% highlight python %} from pyspark.mllib.linalg import SparseVector from pyspark.mllib.regression import LabeledPoint
pos = LabeledPoint(1.0, [1.0, 0.0, 3.0])
neg = LabeledPoint(0.0, SparseVector(3, [0, 2], [1.0, 3.0])) {% endhighlight %}
Sparse data
It is very common in practice to have sparse training data. MLlib supports reading training examples stored in LIBSVM
format, which is the default format used by LIBSVM
and LIBLINEAR
. It is a text format in which each line represents a labeled sparse feature vector using the following format:
label index1:value1 index2:value2 ...
where the indices are one-based and in ascending order. After loading, the feature indices are converted to zero-based.
MLUtils.loadLibSVMFile
reads training examples stored in LIBSVM format.
{% highlight scala %} import org.apache.spark.mllib.regression.LabeledPoint import org.apache.spark.mllib.util.MLUtils import org.apache.spark.rdd.RDD
val examples: RDD[LabeledPoint] = MLUtils.loadLibSVMFile(sc, “data/mllib/sample_libsvm_data.txt”) {% endhighlight %}
{% highlight java %} import org.apache.spark.mllib.regression.LabeledPoint; import org.apache.spark.mllib.util.MLUtils; import org.apache.spark.api.java.JavaRDD;
JavaRDD examples = MLUtils.loadLibSVMFile(jsc.sc(), “data/mllib/sample_libsvm_data.txt”).toJavaRDD(); {% endhighlight %}
{% highlight python %} from pyspark.mllib.util import MLUtils
examples = MLUtils.loadLibSVMFile(sc, “data/mllib/sample_libsvm_data.txt”) {% endhighlight %}
A local matrix has integer-typed row and column indices and double-typed values, stored on a single machine. MLlib supports dense matrices, whose entry values are stored in a single double array in column major. For example, the following matrix \[ \begin{pmatrix} 1.0 & 2.0 \\ 3.0 & 4.0 \\ 5.0 & 6.0 \end{pmatrix} \]
is stored in a one-dimensional array [1.0, 3.0, 5.0, 2.0, 4.0, 6.0]
with the matrix size (3, 2)
.
The base class of local matrices is Matrix
, and we provide one implementation: DenseMatrix
. We recommend using the factory methods implemented in Matrices
to create local matrices.
{% highlight scala %} import org.apache.spark.mllib.linalg.{Matrix, Matrices}
// Create a dense matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0)) val dm: Matrix = Matrices.dense(3, 2, Array(1.0, 3.0, 5.0, 2.0, 4.0, 6.0)) {% endhighlight %}
The base class of local matrices is Matrix
, and we provide one implementation: DenseMatrix
. We recommend using the factory methods implemented in Matrices
to create local matrices.
{% highlight java %} import org.apache.spark.mllib.linalg.Matrix; import org.apache.spark.mllib.linalg.Matrices;
// Create a dense matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0)) Matrix dm = Matrices.dense(3, 2, new double[] {1.0, 3.0, 5.0, 2.0, 4.0, 6.0}); {% endhighlight %}
A distributed matrix has long-typed row and column indices and double-typed values, stored distributively in one or more RDDs. It is very important to choose the right format to store large and distributed matrices. Converting a distributed matrix to a different format may require a global shuffle, which is quite expensive. Three types of distributed matrices have been implemented so far.
The basic type is called RowMatrix
. A RowMatrix
is a row-oriented distributed matrix without meaningful row indices, e.g., a collection of feature vectors. It is backed by an RDD of its rows, where each row is a local vector. We assume that the number of columns is not huge for a RowMatrix
so that a single local vector can be reasonably communicated to the driver and can also be stored / operated on using a single node. An IndexedRowMatrix
is similar to a RowMatrix
but with row indices, which can be used for identifying rows and executing joins. A CoordinateMatrix
is a distributed matrix stored in coordinate list (COO) format, backed by an RDD of its entries.
Note
The underlying RDDs of a distributed matrix must be deterministic, because we cache the matrix size. In general the use of non-deterministic RDDs can lead to errors.
A RowMatrix
is a row-oriented distributed matrix without meaningful row indices, backed by an RDD of its rows, where each row is a local vector. Since each row is represented by a local vector, the number of columns is limited by the integer range but it should be much smaller in practice.
A RowMatrix
can be created from an RDD[Vector]
instance. Then we can compute its column summary statistics.
{% highlight scala %} import org.apache.spark.mllib.linalg.Vector import org.apache.spark.mllib.linalg.distributed.RowMatrix
val rows: RDD[Vector] = ... // an RDD of local vectors // Create a RowMatrix from an RDD[Vector]. val mat: RowMatrix = new RowMatrix(rows)
// Get its size. val m = mat.numRows() val n = mat.numCols() {% endhighlight %}
A RowMatrix
can be created from a JavaRDD<Vector>
instance. Then we can compute its column summary statistics.
{% highlight java %} import org.apache.spark.api.java.JavaRDD; import org.apache.spark.mllib.linalg.Vector; import org.apache.spark.mllib.linalg.distributed.RowMatrix;
JavaRDD rows = ... // a JavaRDD of local vectors // Create a RowMatrix from an JavaRDD. RowMatrix mat = new RowMatrix(rows.rdd());
// Get its size. long m = mat.numRows(); long n = mat.numCols(); {% endhighlight %}
An IndexedRowMatrix
is similar to a RowMatrix
but with meaningful row indices. It is backed by an RDD of indexed rows, so that each row is represented by its index (long-typed) and a local vector.
An IndexedRowMatrix
can be created from an RDD[IndexedRow]
instance, where IndexedRow
is a wrapper over (Long, Vector)
. An IndexedRowMatrix
can be converted to a RowMatrix
by dropping its row indices.
{% highlight scala %} import org.apache.spark.mllib.linalg.distributed.{IndexedRow, IndexedRowMatrix, RowMatrix}
val rows: RDD[IndexedRow] = ... // an RDD of indexed rows // Create an IndexedRowMatrix from an RDD[IndexedRow]. val mat: IndexedRowMatrix = new IndexedRowMatrix(rows)
// Get its size. val m = mat.numRows() val n = mat.numCols()
// Drop its row indices. val rowMat: RowMatrix = mat.toRowMatrix() {% endhighlight %}
An IndexedRowMatrix
can be created from an JavaRDD<IndexedRow>
instance, where IndexedRow
is a wrapper over (long, Vector)
. An IndexedRowMatrix
can be converted to a RowMatrix
by dropping its row indices.
{% highlight java %} import org.apache.spark.api.java.JavaRDD; import org.apache.spark.mllib.linalg.distributed.IndexedRow; import org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix; import org.apache.spark.mllib.linalg.distributed.RowMatrix;
JavaRDD rows = ... // a JavaRDD of indexed rows // Create an IndexedRowMatrix from a JavaRDD. IndexedRowMatrix mat = new IndexedRowMatrix(rows.rdd());
// Get its size. long m = mat.numRows(); long n = mat.numCols();
// Drop its row indices. RowMatrix rowMat = mat.toRowMatrix(); {% endhighlight %}
A CoordinateMatrix
is a distributed matrix backed by an RDD of its entries. Each entry is a tuple of (i: Long, j: Long, value: Double)
, where i
is the row index, j
is the column index, and value
is the entry value. A CoordinateMatrix
should be used only when both dimensions of the matrix are huge and the matrix is very sparse.
A CoordinateMatrix
can be created from an RDD[MatrixEntry]
instance, where MatrixEntry
is a wrapper over (Long, Long, Double)
. A CoordinateMatrix
can be converted to an IndexedRowMatrix
with sparse rows by calling toIndexedRowMatrix
. Other computations for CoordinateMatrix
are not currently supported.
{% highlight scala %} import org.apache.spark.mllib.linalg.distributed.{CoordinateMatrix, MatrixEntry}
val entries: RDD[MatrixEntry] = ... // an RDD of matrix entries // Create a CoordinateMatrix from an RDD[MatrixEntry]. val mat: CoordinateMatrix = new CoordinateMatrix(entries)
// Get its size. val m = mat.numRows() val n = mat.numCols()
// Convert it to an IndexRowMatrix whose rows are sparse vectors. val indexedRowMatrix = mat.toIndexedRowMatrix() {% endhighlight %}
A CoordinateMatrix
can be created from a JavaRDD<MatrixEntry>
instance, where MatrixEntry
is a wrapper over (long, long, double)
. A CoordinateMatrix
can be converted to an IndexedRowMatrix
with sparse rows by calling toIndexedRowMatrix
. Other computations for CoordinateMatrix
are not currently supported.
{% highlight java %} import org.apache.spark.api.java.JavaRDD; import org.apache.spark.mllib.linalg.distributed.CoordinateMatrix; import org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix; import org.apache.spark.mllib.linalg.distributed.MatrixEntry;
JavaRDD entries = ... // a JavaRDD of matrix entries // Create a CoordinateMatrix from a JavaRDD. CoordinateMatrix mat = new CoordinateMatrix(entries.rdd());
// Get its size. long m = mat.numRows(); long n = mat.numCols();
// Convert it to an IndexRowMatrix whose rows are sparse vectors. IndexedRowMatrix indexedRowMatrix = mat.toIndexedRowMatrix(); {% endhighlight %}