Package smile.ica

Record Class ICA

java.lang.Object
java.lang.Record
smile.ica.ICA
Record Components:
components - each row is an independent component.
All Implemented Interfaces:
Serializable
public record ICA(double[][] components) extends Record 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:

  • Nested Class Summary

    Nested Classes
    Modifier and Type
    Class
    Description
    static final record 
    ICA.Options
    ICA hyperparameters.

  • Constructor Summary

    Constructors
    Constructor
    Description
    ICA(double[][] components)
    Creates an instance of a ICA record class.

  • Method Summary

    Modifier and Type
    Method
    Description
    double[][]
    components()
    Returns the value of the components record component.
    final boolean
    equals(Object o)
    Indicates whether some other object is "equal to" this one.
    static ICA
    fit(double[][] data, int p)
    Fits independent component analysis with LogCosh contrast function.
    static ICA
    fit(double[][] data, int p, ICA.Options options)
    Fits independent component analysis.
    final int
    hashCode()
    Returns a hash code value for this object.
    final String
    toString()
    Returns a string representation of this record class.

    Methods inherited from class java.lang.Object

    clone, finalize, getClass, notify, notifyAll, wait, wait, wait

  • Constructor Details

    • ICA

      public ICA(double[][] components)
      Creates an instance of a ICA record class.
      Parameters:
      components - the value for the components record component

  • Method Details

    • fit

      public static ICA fit(double[][] data, int p)
      Fits independent component analysis with LogCosh contrast function.
      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, ICA.Options options)
      Fits independent component analysis.
      Parameters:
      data - training data.
      p - the number of independent components.
      options - the hyperparameters.
      Returns:
      the model.

    • toString

      public final String toString()
      Returns a string representation of this record class. The representation contains the name of the class, followed by the name and value of each of the record components.
      Specified by:
      toString in class Record
      Returns:
      a string representation of this object

    • hashCode

      public final int hashCode()
      Returns a hash code value for this object. The value is derived from the hash code of each of the record components.
      Specified by:
      hashCode in class Record
      Returns:
      a hash code value for this object

    • equals

      public final boolean equals(Object o)
      Indicates whether some other object is "equal to" this one. The objects are equal if the other object is of the same class and if all the record components are equal. All components in this record class are compared with Objects::equals(Object,Object).
      Specified by:
      equals in class Record
      Parameters:
      o - the object with which to compare
      Returns:
      true if this object is the same as the o argument; false otherwise.

    • components

      public double[][] components()
      Returns the value of the components record component.
      Returns:
      the value of the components record component