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Statistical Learning Toolbox

from Statistical Learning Toolbox by Dahua Lin
Functions for statistical learning, pattern recognition and computer vision, covering many topics.

Description of slpca
Home > sltoolbox > subspace > slpca.m

slpca

PURPOSE ^

SLPCA Learns a PCA model from training samples

SYNOPSIS ^

function S = slpca(X, varargin)

DESCRIPTION ^

SLPCA Learns a PCA model from training samples

 $ Syntax $
   - S = slpca(X)
   - S = slpca(X, ...)

 $ Arguments $
   - X:        the training sample matrix
   - S:        the struct representing the learned PCA

 $ Description $
   - S = slpca(X) learns a PCA model from the samples X by default way.

   - S = slpca(X, ...) learns a PCA model from the samples X according to
     the properties specified:
     \*
     \t   Table 1. The properties of PCA learning
     \h    name       &    description                               \\
          'method'    & The method using in training the PCA model.
                        Currently, there are three methods available:
                        default = 'auto'.
                        1. 'auto': automatically selection of the best;
                        2. 'std':  use standard way based on covariance;
                        3. 'svd':  use SVD-based computation
                        4. 'trans': use a transposed way, it is typically
                           used for small-sample-size and high-dimension
                           cases.                                    \\
          'preserve'  & Determine how many components are preserved, it is
                        given in following form: {sch, ...}, which is used
                        as parameters in sldim_by_eigval.       \\
          'weights'   & The 1 x n row vector of sample weights.  
                        If the weights are not specified, then it 
                        considers that all samples have weights 1. 
                        default = [].   \\
     \*
                           
 $ History $
   - Created by Dahua Lin on Apr 24, 2006
   - Modified by Dahua Lin on Apr 25, 2006
       - Extract the dimension determination part to an independent
         function, in order to offer more flexible preservation process,
         and make it reusable in more functions.
   - Modified by Dahua Lin on Aug 17, 2006
       - Add a field energyratio
   - Modified by Dahua Lin, on Sep 10, 2006
       - replace sladd by sladdvec to increase efficiency

CROSS-REFERENCE INFORMATION ^

This function calls:
  • sladdvec SLADDVEC adds a vector to columns or rows of a matrix
  • slmulvec SLMULVEC multiplies a vector to columns or rows of a matrix
  • slnormalize SLNORMALIZE Normalize the sub-arrays
  • slsymeig SLSYMEIG Compute the eigenvalues and eigenvectors for symmetric matrix
  • slmean SLMEAN Compute the mean vector of samples
  • sldim_by_eigval SLDIM_BY_EIGVAL Determines the dimension of principal subspace by eigenvalues
  • slignorevars SLIGNOREVARS Ignores the input variables
  • slparseprops SLPARSEPROPS Parses input parameters
This function is called by:
  • slfld SLFLD Performs Fisher Linear Discriminant Analysis
  • slnlda SLNLDA Performs Nullspace-based Linear Discriminant Analysis

SUBFUNCTIONS ^

SOURCE CODE ^

0001 function S = slpca(X, varargin)
0002 %SLPCA Learns a PCA model from training samples
0003 %
0004 % $ Syntax $
0005 %   - S = slpca(X)
0006 %   - S = slpca(X, ...)
0007 %
0008 % $ Arguments $
0009 %   - X:        the training sample matrix
0010 %   - S:        the struct representing the learned PCA
0011 %
0012 % $ Description $
0013 %   - S = slpca(X) learns a PCA model from the samples X by default way.
0014 %
0015 %   - S = slpca(X, ...) learns a PCA model from the samples X according to
0016 %     the properties specified:
0017 %     \*
0018 %     \t   Table 1. The properties of PCA learning
0019 %     \h    name       &    description                               \\
0020 %          'method'    & The method using in training the PCA model.
0021 %                        Currently, there are three methods available:
0022 %                        default = 'auto'.
0023 %                        1. 'auto': automatically selection of the best;
0024 %                        2. 'std':  use standard way based on covariance;
0025 %                        3. 'svd':  use SVD-based computation
0026 %                        4. 'trans': use a transposed way, it is typically
0027 %                           used for small-sample-size and high-dimension
0028 %                           cases.                                    \\
0029 %          'preserve'  & Determine how many components are preserved, it is
0030 %                        given in following form: {sch, ...}, which is used
0031 %                        as parameters in sldim_by_eigval.       \\
0032 %          'weights'   & The 1 x n row vector of sample weights.
0033 %                        If the weights are not specified, then it
0034 %                        considers that all samples have weights 1.
0035 %                        default = [].   \\
0036 %     \*
0037 %
0038 % $ History $
0039 %   - Created by Dahua Lin on Apr 24, 2006
0040 %   - Modified by Dahua Lin on Apr 25, 2006
0041 %       - Extract the dimension determination part to an independent
0042 %         function, in order to offer more flexible preservation process,
0043 %         and make it reusable in more functions.
0044 %   - Modified by Dahua Lin on Aug 17, 2006
0045 %       - Add a field energyratio
0046 %   - Modified by Dahua Lin, on Sep 10, 2006
0047 %       - replace sladd by sladdvec to increase efficiency
0048 %
0049 
0050 %% parse and verify input arguments
0051 
0052 % for size
0053 if ndims(X) ~= 2
0054     error('sltoolbox:invaliddims', 'X should be a 2D sample matrix');
0055 end
0056 [d, n] = size(X);
0057 
0058 % for options
0059 opts.method = 'auto';
0060 opts.preserve = {'rank'};
0061 opts.weights = [];
0062 opts = slparseprops(opts, varargin{:});
0063 
0064 % check options
0065 
0066 switch opts.method
0067     case 'auto'
0068         fh_learnpca = @pca_auto;
0069     case 'std'
0070         fh_learnpca = @pca_std;
0071     case 'svd'
0072         fh_learnpca = @pca_svd;
0073     case 'trans'
0074         fh_learnpca = @pca_trans;
0075     otherwise
0076         error('sltoolbox:invalidarg', ...
0077             'Invalid PCA learning method %s', opts.method);
0078 end
0079 
0080 
0081 if ~isempty(opts.weights)
0082     if ~isequal(size(opts.weights), [1, n])
0083         error('sltoolbox:sizmismatch', ...
0084             'The sample weights should be a 1 x n row vector');
0085     end
0086 end
0087 
0088 
0089 %% Compute
0090 
0091 % data centralization
0092 vmean = slmean(X, opts.weights);
0093 X = sladdvec(X, -vmean, 1);
0094 
0095 % sample scaling
0096 % in order to normalize the energy per unit sample weight
0097 if isempty(opts.weights)
0098     X = sqrt(1 / n) * X;
0099 else
0100     w = max(opts.weights, 0);
0101     tw = sum(w);
0102     sf = sqrt(w / tw);
0103     X = slmulvec(X, sf, 2);
0104     clear sf;
0105 end
0106     
0107 % learn full size PCA
0108 
0109 [P, evals] = fh_learnpca(X);
0110 
0111 
0112 % preserve principal components
0113 
0114 evals = max(evals, 0);
0115 kmax = min([size(P, 2), d, n-1]);
0116 if kmax < size(P, 2)
0117     P = P(:, 1:kmax);
0118     evals = evals(1:kmax);
0119 end
0120 k = sldim_by_eigval(evals, opts.preserve{:});
0121 
0122 
0123 %% Output the PCA struct
0124 
0125 S.sampledim = d;
0126 S.feadim    = k;
0127 
0128 if isempty(opts.weights)
0129     S.support = n;
0130 else
0131     S.support = tw;
0132 end
0133 
0134 S.vmean = vmean;
0135 if k < kmax
0136     S.P = P(:, 1:k);
0137     S.eigvals = evals(1:k);
0138     S.residue = sum(evals(k+1:kmax));
0139 else
0140     S.P = P;
0141     S.eigvals = evals;
0142     S.residue = 0;
0143 end
0144 
0145 prinenergy = sum(S.eigvals);
0146 S.energyratio = prinenergy / (prinenergy + S.residue);
0147 
0148 
0149 %% Sub functions for Learning PCA from centralized samples
0150 
0151 function [P, evals] = pca_auto(X)
0152 
0153 [d, n] = size(X);
0154 if d <= n
0155     [P, evals] = pca_std(X);
0156 else
0157     [P, evals] = pca_trans(X);
0158 end
0159 
0160 
0161 function [P, evals] = pca_std(X)
0162 
0163 C = X * X';
0164 [evals, P] = slsymeig(C);
0165 
0166 
0167 function [P, evals] = pca_svd(X)
0168 
0169 [P, D, V] = svd(X, 0);
0170 clear V;
0171 evals = diag(D) .^ 2;
0172 
0173 slignorevars(V);
0174 
0175 function [P, evals] = pca_trans(X)
0176 
0177 Ct = X' * X;
0178 [evals, P] = slsymeig(Ct);
0179 P = slnormalize(X * P);
0180 
0181 
0182 
0183
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