spark-instrumented-optimizer/docs/mllib-basics.md

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global	<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 underly linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called "labeled point" in MLlib.

Local vector

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 %}

MLlib recognizes the following types as dense vectors:

• NumPy's array
• Python's list, e.g., [1, 2, 3]

and the following as sparse vectors:

• MLlib's SparseVector.
• SciPy's csc_matrix with 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

Use a NumPy array as a dense vector.

dv1 = np.array([1.0, 0.0, 3.0])

Use a Python list as a dense vector.

dv2 = [1.0, 0.0, 3.0]

Create a SparseVector.

sv1 = Vectors.sparse(3, [0, 2], [1.0, 3.0])

Use a single-column SciPy csc_matrix as a sparse vector.

sv2 = sps.csc_matrix((np.array([1.0, 3.0]), np.array([0, 2]), np.array([0, 2])), shape = (3, 1)) {% endhighlight %}

Labeled point

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 0 (negative) or 1 (positive). For multiclass classification, labels should be class indices staring from zero: 0, 1, 2, \ldots.

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

Create a labeled point with a positive label and a dense feature vector.

pos = LabeledPoint(1.0, [1.0, 0.0, 3.0])

Create a labeled point with a negative label and a sparse feature vector.

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.loadLibSVMData 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.loadLibSVMData(sc, "mllib/data/sample_libsvm_data.txt") {% endhighlight %}

[`MLUtils.loadLibSVMData`](api/mllib/index.html#org.apache.spark.mllib.util.MLUtils$) reads training examples stored in LIBSVM format.

{% highlight java %} import org.apache.spark.mllib.regression.LabeledPoint; import org.apache.spark.mllib.util.MLUtils; import org.apache.spark.rdd.RDDimport;

RDD[LabeledPoint] training = MLUtils.loadLibSVMData(sc, "mllib/data/sample_libsvm_data.txt") {% endhighlight %}

Local matrix

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 %}

Distributed matrix

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.

RowMatrix

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.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 %}

Multivariate summary statistics

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 \mathcal{O}(n^2) storage where n is the number of columns. The total CPU time is \mathcal{O}(m n^2), where m is the number of rows, which could be faster if the rows are sparse.

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.numNonzers) // number of nonzeros in each column

// Compute the covariance matrix. val Cov: Matrix = mat.computeCovariance() {% endhighlight %}

IndexedRowMatrix

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.mllib.linalg.distributed.IndexedRow; import org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix; import org.apache.spark.mllib.linalg.distributed.RowMatrix;

JavaRDD[IndexedRow] 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 %}

CoordinateMatrix

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.mllib.linalg.distributed.CoordinateMatrix; 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 %}