org.apache.spark.mllib.optimization

Class NNLS

Object

org.apache.spark.mllib.optimization.NNLS

public class NNLS
extends Object

Object used to solve nonnegative least squares problems using a modified projected gradient method.

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	NNLS.Workspace

Constructor Summary

Constructors

Constructor and Description
NNLS()

Method Summary

Modifier and Type	Method and Description
static NNLS.Workspace	createWorkspace(int n)
static double[]	solve(double[] ata, double[] atb, NNLS.Workspace ws) Solve a least squares problem, possibly with nonnegativity constraints, by a modified projected gradient method.

Methods inherited from class Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

NNLS

public NNLS()

Method Detail

createWorkspace

public static NNLS.Workspace createWorkspace(int n)

solve

public static double[] solve(double[] ata,
                             double[] atb,
                             NNLS.Workspace ws)

Solve a least squares problem, possibly with nonnegativity constraints, by a modified projected gradient method. That is, find x minimising ||Ax - b||_2 given A^T A and A^T b.

We solve the problem

$$ min_x 1/2 x^T ata x^T - x^T atb $$

where x is nonnegative.

The method used is similar to one described by Polyak (B. T. Polyak, The conjugate gradient method in extremal problems, Zh. Vychisl. Mat. Mat. Fiz. 9(4)(1969), pp. 94-112) for bound- constrained nonlinear programming. Polyak unconditionally uses a conjugate gradient direction, however, while this method only uses a conjugate gradient direction if the last iteration did not cause a previously-inactive constraint to become active.

Parameters:

ata - (undocumented)

atb - (undocumented)

ws - (undocumented)

Returns:

(undocumented)