cv::PCA Class Reference

#include <core.hpp>

Public Member Functions
	PCA ()
	default constructor More...
	PCA (InputArray data, InputArray mean, int flags, int maxComponents=0)
	the constructor that performs PCA More...
	PCA (InputArray data, InputArray mean, int flags, double retainedVariance)
PCA &	operator() (InputArray data, InputArray mean, int flags, int maxComponents=0)
	operator that performs PCA. The previously stored data, if any, is released More...
PCA &	computeVar (InputArray data, InputArray mean, int flags, double retainedVariance)
Mat	project (InputArray vec) const
	projects vector from the original space to the principal components subspace More...
void	project (InputArray vec, OutputArray result) const
	projects vector from the original space to the principal components subspace More...
Mat	backProject (InputArray vec) const
	reconstructs the original vector from the projection More...
void	backProject (InputArray vec, OutputArray result) const
	reconstructs the original vector from the projection More...

Public Attributes
Mat	eigenvectors
	eigenvectors of the covariation matrix More...
Mat	eigenvalues
	eigenvalues of the covariation matrix More...
Mat	mean
	mean value subtracted before the projection and added after the back projection More...

Detailed Description

Principal Component Analysis

The class PCA is used to compute the special basis for a set of vectors. The basis will consist of eigenvectors of the covariance matrix computed from the input set of vectors. After PCA is performed, vectors can be transformed from the original high-dimensional space to the subspace formed by a few most prominent eigenvectors (called the principal components), corresponding to the largest eigenvalues of the covariation matrix. Thus the dimensionality of the vector and the correlation between the coordinates is reduced.

The following sample is the function that takes two matrices. The first one stores the set of vectors (a row per vector) that is used to compute PCA, the second one stores another "test" set of vectors (a row per vector) that are first compressed with PCA, then reconstructed back and then the reconstruction error norm is computed and printed for each vector.

using namespace cv;

PCA compressPCA(const Mat& pcaset, int maxComponents,
                const Mat& testset, Mat& compressed)
{
    PCA pca(pcaset, // pass the data
            Mat(), // we do not have a pre-computed mean vector,
                   // so let the PCA engine to compute it
            CV_PCA_DATA_AS_ROW, // indicate that the vectors
                                // are stored as matrix rows
                                // (use CV_PCA_DATA_AS_COL if the vectors are
                                // the matrix columns)
            maxComponents // specify, how many principal components to retain
            );
    // if there is no test data, just return the computed basis, ready-to-use
    if( !testset.data )
        return pca;
    CV_Assert( testset.cols == pcaset.cols );

    compressed.create(testset.rows, maxComponents, testset.type());

    Mat reconstructed;
    for( int i = 0; i < testset.rows; i++ )
    {
        Mat vec = testset.row(i), coeffs = compressed.row(i), reconstructed;
        // compress the vector, the result will be stored
        // in the i-th row of the output matrix
        pca.project(vec, coeffs);
        // and then reconstruct it
        pca.backProject(coeffs, reconstructed);
        // and measure the error
        printf("%d. diff = %g\n", i, norm(vec, reconstructed, NORM_L2));
    }
    return pca;
}

Constructor & Destructor Documentation

PCA() [1/3]

cv::PCA::PCA

(

)

default constructor

PCA() [2/3]

cv::PCA::PCA	(	InputArray	data,
		InputArray	mean,
		int	flags,
		int	maxComponents = 0
	)

the constructor that performs PCA

PCA() [3/3]

cv::PCA::PCA	(	InputArray	data,
		InputArray	mean,
		int	flags,
		double	retainedVariance
	)

Member Function Documentation

backProject() [1/2]

Mat cv::PCA::backProject

(

InputArray

vec

)

const

reconstructs the original vector from the projection

backProject() [2/2]

void cv::PCA::backProject	(	InputArray	vec,
		OutputArray	result
	)		const

reconstructs the original vector from the projection

computeVar()

PCA& cv::PCA::computeVar	(	InputArray	data,
		InputArray	mean,
		int	flags,
		double	retainedVariance
	)

operator()()

PCA& cv::PCA::operator()	(	InputArray	data,
		InputArray	mean,
		int	flags,
		int	maxComponents = 0
	)

operator that performs PCA. The previously stored data, if any, is released

project() [1/2]

Mat cv::PCA::project

(

InputArray

vec

)

const

projects vector from the original space to the principal components subspace

project() [2/2]

void cv::PCA::project	(	InputArray	vec,
		OutputArray	result
	)		const

projects vector from the original space to the principal components subspace

Member Data Documentation

eigenvalues

Mat cv::PCA::eigenvalues

eigenvalues of the covariation matrix

eigenvectors

Mat cv::PCA::eigenvectors

eigenvectors of the covariation matrix

mean

Mat cv::PCA::mean

mean value subtracted before the projection and added after the back projection

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The documentation for this class was generated from the following file:

• core/core.hpp