dimensionality_reduction
Class PCA

java.lang.Object
  dimensionality_reduction.PCA

public class PCA
extends java.lang.Object

The following is a simple example of how to perform basic principle component analysis in EJML.

Principal Component Analysis (PCA) is typically used to develop a linear model for a set of data (e.g. face images) which can then be used to test for membership. PCA works by converting the set of data to a new basis that is a subspace of the original set. The subspace is selected to maximize information.

PCA is typically derived as an eigenvalue problem. However in this implementation SVD is used since it can produce a more numerically stable solution. Computation using EVD requires explicitly computing the variance of each sample set. The variance is computed by squaring the residual, which can cause loss of precision.

Author:

Peter Abeles, Elefterios Spyromitros-Xioufis

Field Summary

private org.ejml.data.DenseMatrix64F	A where the data is stored
private boolean	compact
private boolean	doWhitening Whether to perform whitening.
(package private) double[]	mean mean values of each element across all the samples
private int	numComponents how many principle components are used
private int	numSamples number of samples that will be used for learning the PCA
private int	sampleIndex counts the number of currently loaded samples
private int	sampleSize number of elements in each sample
private org.ejml.data.DenseMatrix64F	V_t principle component subspace is stored in the rows
private org.ejml.data.DenseMatrix64F	W a diagonal matrix with the singular values

Constructor Summary

PCA(int numComponents, int numSamples, int sampleSize)

Method Summary

void	addSample(double[] sampleData) Adds a new sample of the raw data to internal data structure for later processing.
void	computeBasis() Computes a basis (the principle components) from the most dominant eigenvectors.
double[]	getBasisVector(int which) Returns a vector from the PCA's basis.
double[]	getEigenValues() Returns a vector with the eignevalues in descending order.
double[]	getMean()
double[]	sampleToEigenSpace(double[] sampleData) Converts a vector from sample space into eigen space.
void	setBasisMatrix(double[][] basis) Sets the PCA basis matrix.
void	setCompact(boolean compact)
void	setDoWhitening(boolean doWhitening)
void	setEigenvalues(double[] eigenvalues) Initializes the diagonal eigenvalue matrix W by using the supplied vector and then whitens the projection matrix V_t
void	setMean(double[] mean)
void	setPCAFromFile(java.lang.String PCAFileName) Initializes the PCA matrix, means vector and optionally eigenvalues matrix from the given file.

Methods inherited from class java.lang.Object

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

Field Detail

numComponents

private int numComponents

how many principle components are used

sampleSize

private int sampleSize

number of elements in each sample

numSamples

private int numSamples

number of samples that will be used for learning the PCA

sampleIndex

private int sampleIndex

counts the number of currently loaded samples

A

private org.ejml.data.DenseMatrix64F A

where the data is stored

mean

double[] mean

mean values of each element across all the samples

V_t

private org.ejml.data.DenseMatrix64F V_t

principle component subspace is stored in the rows

W

private org.ejml.data.DenseMatrix64F W

a diagonal matrix with the singular values

doWhitening

private boolean doWhitening

Whether to perform whitening.

compact

private boolean compact

Constructor Detail

PCA

public PCA(int numComponents,
           int numSamples,
           int sampleSize)

Parameters:

numComponents - Number of vectors it will use to describe the data. Typically much smaller than the number of elements in the input vector.

numSamples - Number of samples that will be processed (only important at learning).

sampleSize - Number of elements in each sample.

Method Detail

setCompact

public void setCompact(boolean compact)

addSample

public void addSample(double[] sampleData)

Adds a new sample of the raw data to internal data structure for later processing. All the samples must be added before computeBasis is called.

Parameters:

sampleData - Sample from original raw data.

computeBasis

public void computeBasis()

Computes a basis (the principle components) from the most dominant eigenvectors.

sampleToEigenSpace

public double[] sampleToEigenSpace(double[] sampleData)

Converts a vector from sample space into eigen space. If setEigenvalues(double[]) has been called, then the projected vector is also whitened.

Parameters:

sampleData - Sample space data.

Returns:

Eigen space projection.

setDoWhitening

public void setDoWhitening(boolean doWhitening)

setMean

public void setMean(double[] mean)

getMean

public double[] getMean()

setBasisMatrix

public void setBasisMatrix(double[][] basis)

Sets the PCA basis matrix.

Parameters:

basis - the basis matrix

getBasisVector

public double[] getBasisVector(int which)

Returns a vector from the PCA's basis.

Parameters:

which - Which component's vector is to be returned.

Returns:

Vector from the PCA basis.

setEigenvalues

public void setEigenvalues(double[] eigenvalues)
                    throws java.lang.Exception

Initializes the diagonal eigenvalue matrix W by using the supplied vector and then whitens the projection matrix V_t

Parameters:

eigenvalues -

Throws:

java.lang.Exception

getEigenValues

public double[] getEigenValues()

Returns a vector with the eignevalues in descending order.

Returns:

vector of eigenValues in descending order.

setPCAFromFile

public void setPCAFromFile(java.lang.String PCAFileName)
                    throws java.lang.Exception

Initializes the PCA matrix, means vector and optionally eigenvalues matrix from the given file.

Parameters:

PCAFileName - the learning file

hasEigenvalues - whether the eigenvalues are also stored in the file.

Throws:

java.lang.Exception