org.openimaj.math.matrix.algorithm.pca

Class PrincipalComponentAnalysis

java.lang.Object

org.openimaj.math.matrix.algorithm.pca.PrincipalComponentAnalysis

Direct Known Subclasses:

CovarPrincipalComponentAnalysis, FeatureVectorPCA, SvdPrincipalComponentAnalysis, ThinSvdPrincipalComponentAnalysis

public abstract class PrincipalComponentAnalysis
extends Object

Abstract base class for PCA implementations.

Author:

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

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static interface	PrincipalComponentAnalysis.ComponentSelector Interface for classes capable of selecting a subset of the PCA components
static class	PrincipalComponentAnalysis.EnergyThresholdComponentSelector PrincipalComponentAnalysis.ComponentSelector that selects a subset of the principal components such that all remaining components have a cumulative energy less than the given value.
static class	PrincipalComponentAnalysis.NumberComponentSelector PrincipalComponentAnalysis.ComponentSelector that selects the n-best components.
static class	PrincipalComponentAnalysis.PercentageEnergyComponentSelector PrincipalComponentAnalysis.ComponentSelector that selects a subset of the principal components such that all remaining components have a certain percentage cumulative energy of the total.

Field Summary

Fields

Modifier and Type	Field and Description
protected Jama.Matrix	basis
protected double[]	eigenvalues
protected double[]	mean

Constructor Summary

Constructors

Constructor and Description
PrincipalComponentAnalysis()

Method Summary

Modifier and Type	Method and Description
protected Jama.Matrix	buildNormalisedDataMatrix(Jama.Matrix m) Zero-centre the data matrix and return a copy
double[]	generate(double[] scalings) Generate a new "observation" as a linear combination of the principal components (PC): mean + PC * scaling.
Jama.Matrix	getBasis() Get the principal components.
double[]	getCumulativeEnergies() Get the cumulative energies of each principal component
double	getCumulativeEnergy(int i) Get the cumulative energy of the ith principal component
double	getEigenValue(int i) Get the eigen value corresponding to the ith principal component.
double[]	getEigenValues()
Jama.Matrix	getEigenVectors() Get the principal components.
double[]	getMean()
double[]	getPrincipalComponent(int index) Get a specific principle component vector as a double array.
double[]	getStandardDeviations() Get the standard deviations (sqrt of eigenvalues) of the principal components.
double[]	getStandardDeviations(int n) Get the standard deviations (sqrt of eigenvalues) of the n top principal components.
void	learnBasis(double[][] data) Learn the principal components of the given data array.
void	learnBasis(List<double[]> data) Learn the principal components of the given data list.
void	learnBasis(Jama.Matrix data) Learn the principal components of the given data matrix.
protected abstract void	learnBasisNorm(Jama.Matrix norm) Learn the PCA basis from the centered data provided.
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.
void	selectSubset(int n) Select a subset of the principal components.
void	selectSubset(PrincipalComponentAnalysis.ComponentSelector selector) Select a subset of the principal components using a PrincipalComponentAnalysis.ComponentSelector.
void	selectSubsetEnergyThreshold(double threshold) Select a subset of the principal components such that all remaining components have a cumulative energy less than the given value.
void	selectSubsetPercentageEnergy(double percentage) Select a subset of the principal components such that all remaining components have a certain percentage cumulative energy of the total.
String	toString()

Methods inherited from class java.lang.Object

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

Field Detail

basis

protected Jama.Matrix basis

mean

protected double[] mean

eigenvalues

protected double[] eigenvalues

Constructor Detail

PrincipalComponentAnalysis

public PrincipalComponentAnalysis()

Method Detail

learnBasis

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

Learn the principal components of the given data list. Each item corresponds to an observation with the number of dimensions equal to the length of the array.

Parameters:

data - the data

learnBasis

public void learnBasis(double[][] data)

Learn the principal components of the given data array. Each row corresponds to an observation with the number of dimensions equal to the number of columns.

Parameters:

data - the data

learnBasis

public void learnBasis(Jama.Matrix data)

Learn the principal components of the given data matrix. Each row corresponds to an observation with the number of dimensions equal to the number of columns.

Parameters:

data - the data

learnBasisNorm

protected abstract void learnBasisNorm(Jama.Matrix norm)

Learn the PCA basis from the centered data provided. Each row corresponds to an observation with the number of dimensions equal to the number of columns.

Parameters:

norm -

buildNormalisedDataMatrix

protected Jama.Matrix buildNormalisedDataMatrix(Jama.Matrix m)

Zero-centre the data matrix and return a copy

Parameters:

data - the data matrix

Returns:

the normalised data

getBasis

public Jama.Matrix getBasis()

Get the principal components. The principal components are the column vectors of the returned matrix.

Returns:

the principal components

getPrincipalComponent

public double[] getPrincipalComponent(int index)

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

Parameters:

index - the index of the principle component

Returns:

the principle component

getEigenVectors

public Jama.Matrix getEigenVectors()

Get the principal components. The principal components are the column vectors of the returned matrix. Syntactic sugar for getBasis()

Returns:

the principal components

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

getCumulativeEnergy

public double getCumulativeEnergy(int i)

Get the cumulative energy of the ith principal component

Parameters:

i - the index of the component

Returns:

the cumulative energy of the component

getCumulativeEnergies

public double[] getCumulativeEnergies()

Get the cumulative energies of each principal component

Returns:

the cumulative energies of the components

getMean

public double[] getMean()

Returns:

The mean values

selectSubset

public void selectSubset(PrincipalComponentAnalysis.ComponentSelector selector)

Select a subset of the principal components using a PrincipalComponentAnalysis.ComponentSelector. Calling this method throws away any extra basis vectors and eigenvalues.

Parameters:

selector - the PrincipalComponentAnalysis.ComponentSelector to apply

selectSubset

public void selectSubset(int n)

Select a subset of the principal components. Calling this method throws away any extra basis vectors and eigenvalues.

Parameters:

n -

selectSubsetEnergyThreshold

public void selectSubsetEnergyThreshold(double threshold)

Select a subset of the principal components such that all remaining components have a cumulative energy less than the given value. Calling this method throws away any extra basis vectors and eigenvalues.

Parameters:

threshold - threshold on the cumulative energy.

selectSubsetPercentageEnergy

public void selectSubsetPercentageEnergy(double percentage)

Select a subset of the principal components such that all remaining components have a certain percentage cumulative energy of the total. The percentage is calculated relative to the total energy of the eigenvalues. Bear in mind that if not all the eigenvalues were calculated, or if some have previously been removed through selectSubset(int), selectSubsetEnergyThreshold(double) or selectSubsetPercentageEnergy(double), then the percentage calculation only factors in the remaining eigenvalues that are available to it. Calling this method throws away any extra basis vectors and eigenvalues.

Parameters:

percentage - percentage of the total cumulative energy to retain [0..1].

generate

public double[] generate(double[] scalings)

Generate a new "observation" as a linear combination of the principal components (PC): mean + PC * 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 PC

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

getStandardDeviations

public double[] getStandardDeviations()

Get the standard deviations (sqrt of eigenvalues) of the principal components.

Returns:

vector of standard deviations

getStandardDeviations

public double[] getStandardDeviations(int n)

Get the standard deviations (sqrt of eigenvalues) of the n top principal components.

Parameters:

n - number of principal components

Returns:

vector of standard deviations

toString

public String toString()

Overrides:

toString in class Object