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<a href="mllib-guide.html">MLlib</a> - Basics |
- Table of contents {:toc}
MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. In the current implementation, local vectors and matrices are simple data models to serve public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called "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] 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, label should be either
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. 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 training: RDD[LabeledPoint] = MLUtils.loadLibSVMFile(sc, "mllib/data/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.rdd.RDDimport;
RDD training = MLUtils.loadLibSVMFile(jsc, "mllib/data/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 matrix, 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).
We are going to add sparse matrix in the next release.
The base class of local matrices is
Matrix, and we provide one
implementation: DenseMatrix.
Sparse matrix will be added in the next release. 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.
Sparse matrix will be added in the next release. 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. We implemented three types of distributed matrices in this release and will add more types in the future.
Note
The underlying RDDs of a distributed matrix must be deterministic, because we cache the matrix size. It is always error-prone to have non-deterministic RDDs.
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. This is similar to data matrix in the context of
multivariate statistics. 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 %}
We provide column summary statistics for RowMatrix.
If the number of columns is not large, say, smaller than 3000, you can also compute
the covariance matrix as a local matrix, which requires
RowMatrix#computeColumnSummaryStatistics returns an instance of
MultivariateStatisticalSummary,
which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the
total count.
{% highlight scala %} import org.apache.spark.mllib.linalg.Matrix import org.apache.spark.mllib.linalg.distributed.RowMatrix import org.apache.spark.mllib.stat.MultivariateStatisticalSummary
val mat: RowMatrix = ... // a RowMatrix
// Compute column summary statistics. val summary: MultivariateStatisticalSummary = mat.computeColumnSummaryStatistics() println(summary.mean) // a dense vector containing the mean value for each column println(summary.variance) // column-wise variance println(summary.numNonzeros) // number of nonzeros in each column
// Compute the covariance matrix. val cov: Matrix = mat.computeCovariance() {% endhighlight %}
An IndexedRowMatrix is similar to a RowMatrix but with meaningful row indices. It is backed by
an RDD of indexed rows, which 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 in the case 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 a IndexedRowMatrix
with sparse rows by calling toIndexedRowMatrix. In this release, we do not provide other
computation for CoordinateMatrix.
{% 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 a IndexedRowMatrix
with sparse rows by calling toIndexedRowMatrix.
{% highlight scala %} 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);
// 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 %}