org.openimaj.math.matrix.algorithm

Class LinearDiscriminantAnalysis

java.lang.Object

org.openimaj.math.matrix.algorithm.LinearDiscriminantAnalysis

@Reference(type=Article,
           author="Fisher, Ronald A.",
           title="{The use of multiple measurements in taxonomic problems}",
           year="1936",
           journal="Annals Eugen.",
           pages={"179","","188"},
           volume="7",
           customData={"citeulike-article-id","764226","keywords","classification","posted-at","2006-09-18 14:06:16","priority","2"})
public class LinearDiscriminantAnalysis
extends Object

Implementation of Multiclass Linear Discriminant Analysis.

Author:

Jonathon Hare (jsh2@ecs.soton.ac.uk)

Field Summary

Fields

Modifier and Type	Field and Description
protected double[]	eigenvalues
protected Jama.Matrix	eigenvectors
protected double[]	mean
protected int	numComponents

Constructor Summary

Constructors

Constructor and Description
LinearDiscriminantAnalysis(int numComponents) Construct with the given number of components.

Method Summary

Modifier and Type	Method and Description
double[]	generate(double[] scalings) Generate a new "observation" as a linear combination of the eigenvectors (ev): mean + ev * scaling.
Jama.Matrix	getBasis() Get the basis (the LDA eigenvectors)
double[]	getBasisVector(int index) Get a specific basis vector as a double array.
double	getEigenValue(int i) Get the eigen value corresponding to the ith principal component.
double[]	getEigenValues()
Jama.Matrix	getEigenVectors() Get the basis eigenvectors.
double[]	getMean()
void	learnBasis(List<double[][]> data) Learn the LDA basis.
void	learnBasis(Map<?,double[][]> data) Learn the LDA basis.
void	learnBasisIP(List<? extends IndependentPair<?,double[]>> data) Learn the LDA basis.
void	learnBasisLL(List<List<double[]>> data) Learn the LDA basis.
void	learnBasisML(Map<?,List<double[]>> data) Learn the LDA basis.
double[]	project(double[] vector) Project a vector by the basis.
Jama.Matrix	project(Jama.Matrix m) Project a matrix of row vectors by the basis.

Methods inherited from class java.lang.Object

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

Field Detail

numComponents

protected int numComponents

eigenvectors

protected Jama.Matrix eigenvectors

eigenvalues

protected double[] eigenvalues

mean

protected double[] mean

Constructor Detail

LinearDiscriminantAnalysis

public LinearDiscriminantAnalysis(int numComponents)

Construct with the given number of components.

Parameters:

numComponents - the number of components.

Method Detail

learnBasisIP

public void learnBasisIP(List<? extends IndependentPair<?,double[]>> data)

Learn the LDA basis.

Parameters:

data - data grouped by class

learnBasisML

public void learnBasisML(Map<?,List<double[]>> data)

Learn the LDA basis.

Parameters:

data - data grouped by class

learnBasisLL

public void learnBasisLL(List<List<double[]>> data)

Learn the LDA basis.

Parameters:

data - data grouped by class

learnBasis

public void learnBasis(Map<?,double[][]> data)

Learn the LDA basis.

Parameters:

data - data grouped by class

learnBasis

public void learnBasis(List<double[][]> data)

Learn the LDA basis.

Parameters:

data - data grouped by class

getBasis

public Jama.Matrix getBasis()

Get the basis (the LDA eigenvectors)

Returns:

the eigenvectors

getBasisVector

public double[] getBasisVector(int index)

Get a specific basis vector as a double array. The returned array contains a copy of the data.

Parameters:

index - the index of the vector

Returns:

the eigenvector

getEigenVectors

public Jama.Matrix getEigenVectors()

Get the basis eigenvectors. Each of column vector of the returned matrix is an eigenvector. Syntactic sugar for getBasis()

Returns:

the eigenvectors

getEigenValues

public double[] getEigenValues()

Returns:

the eigen values corresponding to the principal components

getEigenValue

public double getEigenValue(int i)

Get the eigen value corresponding to the ith principal component.

Parameters:

i - the index of the component

Returns:

the eigen value corresponding to the principal component

getMean

public double[] getMean()

Returns:

The mean values

generate

public double[] generate(double[] scalings)

Generate a new "observation" as a linear combination of the eigenvectors (ev): mean + ev * scaling.

If the scaling vector is shorter than the number of components, it will be zero-padded. If it is longer, it will be truncated.

Parameters:

scalings - the weighting for each eigenvector

Returns:

generated observation

project

public Jama.Matrix project(Jama.Matrix m)

Project a matrix of row vectors by the basis. The vectors are normalised by subtracting the mean and then multiplied by the basis. The returned matrix has a row for each vector.

Parameters:

m - the vector to project

Returns:

projected vectors

project

public double[] project(double[] vector)

Project a vector by the basis. The vector is normalised by subtracting the mean and then multiplied by the basis.

Parameters:

vector - the vector to project

Returns:

projected vector