Description of slwhiten_from_cov

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slwhiten_from_cov

PURPOSE

SLWHITEN_FROM_COV Compute the whitening transform from covariance matrix

SYNOPSIS

function W = slwhiten_from_cov(C, method, varargin)

DESCRIPTION

SLWHITEN_FROM_COV Compute the whitening transform from covariance matrix

 $ Syntax $
   - W = slwhiten_from_cov(C)
   - W = slwhiten_from_cov(C, method, ...)

 $ Arguments $
   - C:        the covariance matrix
   - method:   the method for computing the whitening transform
   - W:        the computed whitening transform matrix

 $ Description $
   - W = slwhiten_from_cov(C) computes the whitening matrix from C using 
     default method ('std').
   - W = slwhiten_from_cov(C, method, r) computes the whitening matrix 
     from C using specific method and the extra parameters. Please
     refer to slinvevals for the available methods and corresponding
     parameters.

 $ Remarks $
   - C should be a positive semidefinite matrix.

 $ History $
   - Created by Dahua Lin on Apr 30th, 2006
   - Modified by Dahua Lin on Sep 10, 2006
       - replace slmul by slmulvec to increase efficiency

CROSS-REFERENCE INFORMATION

This function calls:

• slmulvec SLMULVEC multiplies a vector to columns or rows of a matrix
• slsymeig SLSYMEIG Compute the eigenvalues and eigenvectors for symmetric matrix
• slinvevals SLINVEVALS Compute the reciprocals of eigenvalues in a robust way

This function is called by:

• slgembed SLGEMBED Solves the general graph-based embedding
• sldlda SLDLDA Performs Direct Linear Discriminant Analysis
• slfld SLFLD Performs Fisher Linear Discriminant Analysis

SOURCE CODE

0001 function W = slwhiten_from_cov(C, method, varargin)
0002 %SLWHITEN_FROM_COV Compute the whitening transform from covariance matrix
0003 %
0004 % $ Syntax $
0005 %   - W = slwhiten_from_cov(C)
0006 %   - W = slwhiten_from_cov(C, method, ...)
0007 %
0008 % $ Arguments $
0009 %   - C:        the covariance matrix
0010 %   - method:   the method for computing the whitening transform
0011 %   - W:        the computed whitening transform matrix
0012 %
0013 % $ Description $
0014 %   - W = slwhiten_from_cov(C) computes the whitening matrix from C using
0015 %     default method ('std').
0016 %   - W = slwhiten_from_cov(C, method, r) computes the whitening matrix
0017 %     from C using specific method and the extra parameters. Please
0018 %     refer to slinvevals for the available methods and corresponding
0019 %     parameters.
0020 %
0021 % $ Remarks $
0022 %   - C should be a positive semidefinite matrix.
0023 %
0024 % $ History $
0025 %   - Created by Dahua Lin on Apr 30th, 2006
0026 %   - Modified by Dahua Lin on Sep 10, 2006
0027 %       - replace slmul by slmulvec to increase efficiency
0028 %
0029 
0030 %% parse and verify input arguments
0031 
0032 if ndims(C) ~= 2 || size(C, 1) ~= size(C, 2)
0033     error('sltoolbox:invaliddims', 'C should be a square matrix');
0034 end
0035 
0036 if nargin < 2
0037     method = 'std';
0038     params = {};
0039 else
0040     params = varargin;
0041 end
0042 
0043 
0044 %% compute
0045 
0046 [evs, U] = slsymeig(C);
0047 revs = slinvevals(evs, method, params{:})';
0048 
0049 if strcmp(method, 'std') 
0050     si = find(revs > 0);
0051     revs = revs(si);
0052     U = U(:, si);
0053 end
0054 
0055 W = slmulvec(U, sqrt(revs), 2);
0056 
0057

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