Struct opencv::core::PCA

pub struct PCA { /* private fields */ }

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

impl 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()().

pub fn new( data: &impl ToInputArray, mean: &impl 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

pub fn new_def( data: &impl ToInputArray, mean: &impl ToInputArray, flags: i32, ) -> Result<PCA>

@overload

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.

Note

This alternative version of [new] function uses the following default values for its arguments:

• max_components: 0

pub fn new_with_variance( data: &impl ToInputArray, mean: &impl 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.

Trait Implementations

impl Boxed for PCA

unsafe fn from_raw(ptr: <PCA as OpenCVFromExtern>::ExternReceive) -> Self

Wrap the specified raw pointer

fn into_raw(self) -> <PCA as OpenCVTypeExternContainer>::ExternSendMut

Return the underlying raw pointer while consuming this wrapper.

fn as_raw(&self) -> <PCA as OpenCVTypeExternContainer>::ExternSend

Return the underlying raw pointer.

fn as_raw_mut(&mut self) -> <PCA as OpenCVTypeExternContainer>::ExternSendMut

Return the underlying mutable raw pointer

impl Debug for PCA

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Drop for PCA

fn drop(&mut self)

Executes the destructor for this type.

impl PCATrait for PCA

fn as_raw_mut_PCA(&mut self) -> *mut c_void

fn set_eigenvectors(&mut self, val: Mat)

eigenvectors of the covariation matrix

fn set_eigenvalues(&mut self, val: Mat)

eigenvalues of the covariation matrix

fn set_mean(&mut self, val: Mat)

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

fn apply( &mut self, data: &impl ToInputArray, mean: &impl ToInputArray, flags: i32, max_components: i32, ) -> Result<PCA>

performs %PCA

fn apply_def( &mut self, data: &impl ToInputArray, mean: &impl ToInputArray, flags: i32, ) -> Result<PCA>

performs %PCA

fn apply_1( &mut self, data: &impl ToInputArray, mean: &impl ToInputArray, flags: i32, retained_variance: f64, ) -> Result<PCA>

performs %PCA

fn read(&mut self, fn_: &impl FileNodeTraitConst) -> Result<()>

load PCA objects

impl PCATraitConst for PCA

fn as_raw_PCA(&self) -> *const c_void

fn eigenvectors(&self) -> Mat

eigenvectors of the covariation matrix

fn eigenvalues(&self) -> Mat

eigenvalues of the covariation matrix

fn mean(&self) -> Mat

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

fn project(&self, vec: &impl ToInputArray) -> Result<Mat>

Projects vector(s) to the principal component subspace.

fn project_to( &self, vec: &impl ToInputArray, result: &mut impl ToOutputArray, ) -> Result<()>

Projects vector(s) to the principal component subspace.

fn back_project(&self, vec: &impl ToInputArray) -> Result<Mat>

Reconstructs vectors from their PC projections.

fn back_project_to( &self, vec: &impl ToInputArray, result: &mut impl ToOutputArray, ) -> Result<()>

Reconstructs vectors from their PC projections.

fn write(&self, fs: &mut impl FileStorageTrait) -> Result<()>

write PCA objects

impl Send for PCA