pub struct PCA { /* private fields */ }Expand 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 high-dimensional space with a much shorter vector consisting of the projected vector’s coordinates in the subspace. Such a transformation is also known as Karhunen-Loeve 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 pre-computed 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, 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;
}See also
calcCovarMatrix, mulTransposed, SVD, dft, dct
Implementations
sourceimpl PCA
impl PCA
sourcepub fn default() -> Result<PCA>
pub fn default() -> Result<PCA>
default constructor
The default constructor initializes an empty %PCA structure. The other constructors initialize the structure and call PCA::operator()().
sourcepub fn new(
data: &dyn ToInputArray,
mean: &dyn ToInputArray,
flags: i32,
max_components: i32
) -> Result<PCA>
pub fn new(
data: &dyn ToInputArray,
mean: &dyn ToInputArray,
flags: i32,
max_components: i32
) -> Result<PCA>
default constructor
The default constructor initializes an empty %PCA structure. The other constructors initialize the structure and call PCA::operator()().
Overloaded parameters
Parameters
- data: input samples stored as matrix rows or matrix columns.
- mean: optional mean value; if the matrix is empty (@c 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.
C++ default parameters
- max_components: 0
sourcepub fn new_with_variance(
data: &dyn ToInputArray,
mean: &dyn ToInputArray,
flags: i32,
retained_variance: f64
) -> Result<PCA>
pub fn new_with_variance(
data: &dyn ToInputArray,
mean: &dyn ToInputArray,
flags: i32,
retained_variance: f64
) -> Result<PCA>
default constructor
The default constructor initializes an empty %PCA structure. The other constructors initialize the structure and call PCA::operator()().
Overloaded parameters
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.