smile.projection

Class ICA

java.lang.Object

smile.projection.ICA

All Implemented Interfaces:

java.io.Serializable

public class ICA
extends java.lang.Object
implements java.io.Serializable

Independent Component Analysis (ICA) is a computational method for separating a multivariate signal into additive components. FastICA is an efficient algorithm for ICA invented by Aapo Hyvärinen.

Like most ICA algorithms, FastICA seeks an orthogonal rotation of prewhitened data, through a fixed-point iteration scheme, that maximizes a measure of non-Gaussianity of the rotated components. Non-gaussianity serves as a proxy for statistical independence, which is a very strong condition and requires infinite data to verify. To measure non-Gaussianity, FastICA relies on a non-quadratic nonlinear function f(u), its first derivative g(u), and its second derivative g2(u).

A simple application of ICA is the cocktail party problem, where the underlying speech signals are separated from a sample data consisting of people talking simultaneously in a room. Usually the problem is simplified by assuming no time delays or echoes. An important note to consider is that if N sources are present, at least N observations (e.g. microphones if the observed signal is audio) are needed to recover the original signals.

References

1. Aapo Hyvärinen: Fast and robust fixed-point algorithms for independent component analysis, 1999
2. Aapo Hyvärinen, Erkki Oja: Independent component analysis: Algorithms and applications, 2000

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
double[][]	components The independent components (row-wise).

Constructor Summary

Constructors

Constructor and Description
ICA(double[][] components) Constructor.

Method Summary

Modifier and Type	Method and Description
static ICA	fit(double[][] data, int p) Fits independent component analysis.
static ICA	fit(double[][] data, int p, smile.math.DifferentiableFunction contrast, double tol, int maxIter) Fits independent component analysis.
static ICA	fit(double[][] data, int p, java.util.Properties prop) Fits independent component analysis.

Methods inherited from class java.lang.Object

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

Field Detail

components

public final double[][] components

The independent components (row-wise).

Constructor Detail

ICA

public ICA(double[][] components)

Constructor.

Parameters:

components - each row is an independent component.

Method Detail

fit

public static ICA fit(double[][] data,
                      int p)

Fits independent component analysis.

Parameters:

data - training data. The number of columns corresponding with the number of samples of mixed signals and the number of rows corresponding with the number of independent source signals.

p - the number of independent components.

fit

public static ICA fit(double[][] data,
                      int p,
                      java.util.Properties prop)

Fits independent component analysis.

Parameters:

data - training data. The number of columns corresponding with the number of samples of mixed signals and the number of rows corresponding with the number of independent source signals.

p - the number of independent components.

fit

public static ICA fit(double[][] data,
                      int p,
                      smile.math.DifferentiableFunction contrast,
                      double tol,
                      int maxIter)

Fits independent component analysis.

Parameters:

data - training data.

p - the number of independent components.

contrast - the contrast function is a(statistical) functions which is capable of separating or extracting independent sources from a linear mixture. It must be a non-quadratic non-linear function that has second-order derivative.

tol - the tolerance of convergence test.

maxIter - the maximum number of iterations.