Principal Component Analysis. More...
#include <opencv2/core.hpp>
Collaboration diagram for cv::PCA:
Public Types  
enum  Flags { DATA_AS_ROW = 0, DATA_AS_COL = 1, USE_AVG = 2 } 
Detailed Description
Principal Component Analysis.
The class is used to calculate a special basis for a set of vectors. The basis will consist of eigenvectors of the covariance matrix calculated from the input set of vectors. The class PCA can also transform vectors to/from the new coordinate space defined by the basis. Usually, in this new coordinate system, each vector from the original set (and any linear combination of such vectors) can be quite accurately approximated by taking its first few components, corresponding to the eigenvectors of the largest eigenvalues of the covariance matrix. Geometrically it means that you calculate a projection of the vector to a subspace formed by a few eigenvectors corresponding to the dominant eigenvalues of the covariance matrix. And usually such a projection is very close to the original vector. So, you can represent the original vector from a highdimensional space with a much shorter vector consisting of the projected vector's coordinates in the subspace. Such a transformation is also known as KarhunenLoeve Transform, or KLT. See http://en.wikipedia.org/wiki/Principal_component_analysis
The sample below is the function that takes two matrices. The first function stores a set of vectors (a row per vector) that is used to calculate PCA. The second function stores another "test" set of vectors (a row per vector). First, these vectors are 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 precomputed mean vector,
// so let the PCA engine to compute it
PCA::DATA_AS_ROW, // indicate that the vectors
// are stored as matrix rows
// (use 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, readytouse
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 ith 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;
}
cv::Mat
ndimensional dense array class
Definition mat.hpp:812
cv::Mat::row
Mat row(int y) const
Creates a matrix header for the specified matrix row.
cv::Mat::data
uchar * data
pointer to the data
Definition mat.hpp:2140
cv::Mat::create
void create(int rows, int cols, int type)
Allocates new array data if needed.
cv::Mat::cols
int cols
Definition mat.hpp:2138
cv::Mat::rows
int rows
the number of rows and columns or (1, 1) when the matrix has more than 2 dimensions
Definition mat.hpp:2138
cv::Mat::type
int type() const
Returns the type of a matrix element.
cv::PCA
Principal Component Analysis.
Definition core.hpp:2513
cv::PCA::DATA_AS_ROW
@ DATA_AS_ROW
indicates that the input samples are stored as matrix rows
Definition core.hpp:2515
cv::norm
double norm(InputArray src1, int normType=NORM_L2, InputArray mask=noArray())
Calculates the absolute norm of an array.
cv::NORM_L2
@ NORM_L2
Definition base.hpp:185
CV_Assert
#define CV_Assert(expr)
Checks a condition at runtime and throws exception if it fails.
Definition base.hpp:359
cv
"black box" representation of the file storage associated with a file on disk.
Definition core.hpp:102
 See also
 calcCovarMatrix, mulTransposed, SVD, dft, dct
 Examples
 samples/cpp/pca.cpp, and samples/cpp/tutorial_code/ml/introduction_to_pca/introduction_to_pca.cpp.
Member Enumeration Documentation
◆Flags
enum cv::PCA::Flags
Constructor & Destructor Documentation
◆PCA() [1/3]
cv::PCA::PCA  (  ) 
default constructor
The default constructor initializes an empty PCA structure. The other constructors initialize the structure and call PCA::operator()().
◆PCA() [2/3]
cv::PCA::PCA  (  InputArray  data, 
InputArray  mean,  
int  flags,  
int  maxComponents = 0  
) 
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
 Parameters

data input samples stored as matrix rows or matrix columns. mean optional mean value; if the matrix is empty ( noArray()
), the mean is computed from the data.flags operation flags; currently the parameter is only used to specify the data layout (PCA::Flags) maxComponents maximum number of components that PCA should retain; by default, all the components are retained.
◆PCA() [3/3]
cv::PCA::PCA  (  InputArray  data, 
InputArray  mean,  
int  flags,  
double  retainedVariance  
) 
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
 Parameters

data input samples stored as matrix rows or matrix columns. mean optional mean value; if the matrix is empty (noArray()), the mean is computed from the data. flags operation flags; currently the parameter is only used to specify the data layout (PCA::Flags) retainedVariance Percentage of variance that PCA should retain. Using this parameter will let the PCA decided how many components to retain but it will always keep at least 2.
Member Function Documentation
◆backProject() [1/2]
Mat cv::PCA::backProject  (  InputArray  vec  )  const 
Reconstructs vectors from their PC projections.
The methods are inverse operations to PCA::project. They take PC coordinates of projected vectors and reconstruct the original vectors. Unless all the principal components have been retained, the reconstructed vectors are different from the originals. But typically, the difference is small if the number of components is large enough (but still much smaller than the original vector dimensionality). As a result, PCA is used.
 Parameters

vec coordinates of the vectors in the principal component subspace, the layout and size are the same as of PCA::project output vectors.
◆backProject() [2/2]
void cv::PCA::backProject  (  InputArray  vec, 
OutputArray  result  
)  const 
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
 Parameters

vec coordinates of the vectors in the principal component subspace, the layout and size are the same as of PCA::project output vectors. result reconstructed vectors; the layout and size are the same as of PCA::project input vectors.
◆operator()() [1/2]
PCA & cv::PCA::operator()  (  InputArray  data, 
InputArray  mean,  
int  flags,  
double  retainedVariance  
) 
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
 Parameters

data input samples stored as the matrix rows or as the matrix columns. mean optional mean value; if the matrix is empty (noArray()), the mean is computed from the data. flags operation flags; currently the parameter is only used to specify the data layout. (PCA::Flags) retainedVariance Percentage of variance that PCA should retain. Using this parameter will let the PCA decided how many components to retain but it will always keep at least 2.
◆operator()() [2/2]
PCA & cv::PCA::operator()  (  InputArray  data, 
InputArray  mean,  
int  flags,  
int  maxComponents = 0  
) 
performs PCA
The operator performs PCA of the supplied dataset. It is safe to reuse the same PCA structure for multiple datasets. That is, if the structure has been previously used with another dataset, the existing internal data is reclaimed and the new eigenvalues, eigenvectors and mean are allocated and computed.
The computed eigenvalues are sorted from the largest to the smallest and the corresponding eigenvectors are stored as eigenvectors rows.
 Parameters

data input samples stored as the matrix rows or as the matrix columns. mean optional mean value; if the matrix is empty (noArray()), the mean is computed from the data. flags operation flags; currently the parameter is only used to specify the data layout. (Flags) maxComponents maximum number of components that PCA should retain; by default, all the components are retained.
◆project() [1/2]
Mat cv::PCA::project  (  InputArray  vec  )  const 
Projects vector(s) to the principal component subspace.
The methods project one or more vectors to the principal component subspace, where each vector projection is represented by coefficients in the principal component basis. The first form of the method returns the matrix that the second form writes to the result. So the first form can be used as a part of expression while the second form can be more efficient in a processing loop.
 Parameters

vec input vector(s); must have the same dimensionality and the same layout as the input data used at PCA phase, that is, if DATA_AS_ROW are specified, then vec.cols==data.cols
(vector dimensionality) andvec.rows
is the number of vectors to project, and the same is true for the PCA::DATA_AS_COL case.
◆project() [2/2]
void cv::PCA::project  (  InputArray  vec, 
OutputArray  result  
)  const 
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
 Parameters

vec input vector(s); must have the same dimensionality and the same layout as the input data used at PCA phase, that is, if DATA_AS_ROW are specified, then vec.cols==data.cols
(vector dimensionality) andvec.rows
is the number of vectors to project, and the same is true for the PCA::DATA_AS_COL case.result output vectors; in case of PCA::DATA_AS_COL, the output matrix has as many columns as the number of input vectors, this means that result.cols==vec.cols
and the number of rows match the number of principal components (for example,maxComponents
parameter passed to the constructor).
◆read()
void cv::PCA::read  (  const FileNode &  fn  ) 
load PCA objects
Loads eigenvalues eigenvectors and mean from specified FileNode
◆write()
void cv::PCA::write  (  FileStorage &  fs  )  const 
write PCA objects
Writes eigenvalues eigenvectors and mean to specified FileStorage
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
The documentation for this class was generated from the following file:
 opencv2/core.hpp