Package smile.ica

Class ICA

java.lang.Object

smile.ica.ICA

All Implemented Interfaces:

Serializable

public class ICA
extends Object
implements 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	Description
final double[][]	components	The independent components (row-wise).

Method Summary

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

Methods inherited from class java.lang.Object

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

Field Details

components

public final double[][] components

The independent components (row-wise).

Method Details

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.

Returns:

the model.

fit

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

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.

params - the hyperparameters.

Returns:

the model.

fit

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

Fits independent component analysis.

Parameters:

data - training data.

p - the number of independent components.

contrast - the contrast function 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.

Returns:

the model.