`#include <core.hpp>`

## Public Member Functions | |

void | backProject (const Mat &vec, CV_OUT Mat &result) const |

reconstructs the original vector from the projection | |

Mat | backProject (const Mat &vec) const |

reconstructs the original vector from the projection | |

PCA & | operator() (const Mat &data, const Mat &mean, int flags, int maxComponents=0) |

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

PCA (const Mat &data, const Mat &mean, int flags, int maxComponents=0) | |

the constructor that performs PCA | |

PCA () | |

default constructor | |

void | project (const Mat &vec, CV_OUT Mat &result) const |

projects vector from the original space to the principal components subspace | |

Mat | project (const Mat &vec) const |

projects vector from the original space to the principal components subspace | |

## Public Attributes | |

Mat | eigenvalues |

eigenvalues of the covariation matrix | |

Mat | eigenvectors |

eigenvectors of the covariation matrix | |

Mat | mean |

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

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; }

cv::PCA::PCA | ( | ) |

default constructor

the constructor that performs PCA

reconstructs the original vector from the projection

reconstructs the original vector from the projection

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

projects vector from the original space to the principal components subspace

projects vector from the original space to the principal components subspace

eigenvalues of the covariation matrix

eigenvectors of the covariation matrix

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

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

- /home/grier/opencv/opencv/modules/core/include/opencv2/core/core.hpp

Generated on Thu Dec 23 11:40:55 2010 for opencv by 1.6.3