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Data Types - MLlib |
<a href="mllib-guide.html">MLlib</a> - Data Types |
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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 %}
- NumPy's
array - Python's list, e.g.,
[1, 2, 3]
and the following as sparse vectors:
- MLlib's
SparseVector. - SciPy's
csc_matrixwith a single column
We 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(1.0, 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 BlockMatrix is a distributed matrix backed by an RDD of MatrixBlocks, where a MatrixBlock is
a tuple of ((Int, Int), Matrix), where the (Int, Int) is the index of the block, and Matrix is
the sub-matrix at the given index with size rowsPerBlock x colsPerBlock.
BlockMatrix supports methods such as add and multiply with another BlockMatrix.
BlockMatrix also has a helper function validate which can be used to check whether the
BlockMatrix is set up properly.
A BlockMatrix can be
most easily created from an IndexedRowMatrix or CoordinateMatrix by calling toBlockMatrix.
toBlockMatrix creates blocks of size 1024 x 1024 by default.
Users may change the block size by supplying the values through toBlockMatrix(rowsPerBlock, colsPerBlock).
{% highlight scala %} import org.apache.spark.mllib.linalg.distributed.{BlockMatrix, CoordinateMatrix, MatrixEntry}
val entries: RDD[MatrixEntry] = ... // an RDD of (i, j, v) matrix entries // Create a CoordinateMatrix from an RDD[MatrixEntry]. val coordMat: CoordinateMatrix = new CoordinateMatrix(entries) // Transform the CoordinateMatrix to a BlockMatrix val matA: BlockMatrix = coordMat.toBlockMatrix().cache()
// Validate whether the BlockMatrix is set up properly. Throws an Exception when it is not valid. // Nothing happens if it is valid. matA.validate()
// Calculate A^T A. val ata = matA.transpose.multiply(matA) {% endhighlight %}
A BlockMatrix can be
most easily created from an IndexedRowMatrix or CoordinateMatrix by calling toBlockMatrix.
toBlockMatrix creates blocks of size 1024 x 1024 by default.
Users may change the block size by supplying the values through toBlockMatrix(rowsPerBlock, colsPerBlock).
{% highlight java %} import org.apache.spark.api.java.JavaRDD; import org.apache.spark.mllib.linalg.distributed.BlockMatrix; import org.apache.spark.mllib.linalg.distributed.CoordinateMatrix; import org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix;
JavaRDD entries = ... // a JavaRDD of (i, j, v) Matrix Entries // Create a CoordinateMatrix from a JavaRDD. CoordinateMatrix coordMat = new CoordinateMatrix(entries.rdd()); // Transform the CoordinateMatrix to a BlockMatrix BlockMatrix matA = coordMat.toBlockMatrix().cache();
// Validate whether the BlockMatrix is set up properly. Throws an Exception when it is not valid. // Nothing happens if it is valid. matA.validate();
// Calculate A^T A. BlockMatrix ata = matA.transpose().multiply(matA); {% endhighlight %}
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 %}