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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 sl2dmatcov
Home > sltoolbox > subspace_ex > sl2dmatcov.m

sl2dmatcov

PURPOSE ^

SL2DMATCOV Computes the 2D matrix-covariances

SYNOPSIS ^

function varargout = sl2dmatcov(type, data, matsiz, n, meanmat, PL, PR, w)

DESCRIPTION ^

SL2DMATCOV Computes the 2D matrix-covariances

 $ Syntax $
   - CL = sl2dmatcov('CL', data, matsiz, n, meanmat, PL, PR, w)
   - CR = sl2dmatcov('CR', data, matsiz, n, meanmat, PL, PR, w)
   - [CL, CR] = sl2dmatcov('Both', data, matsiz, n, meanmat, PL, PR, w)

 $ Arguments $
   - data:     the stack of matrices or the cell array of filenames of the
               array files storing the matrices.
   - matsiz:   the size of each matrix
   - n:        the number of samples
   - PL:       the left-projection matrix, default = []
   - PR:       the right-projection matrix, default = []
   - w:        the weights of the matrix samples, default = []

 $ Remarks $
   - The function computes the 2D matrix-covariances according to 
     the following formulas:
       Y_i = PL^T * (X - meanX)* PR 
       CL = ( sum_{i=1}^n w(i) * Y_i * Y_i^T ) / ( sum_{i=1}^n w(i) )
       CR = ( sum_{i=1}^n w(i) * Y_i^T * Y_i ) / ( sum_{i=1}^n w(i) )
     Following special cases are considered:
       If w is empty, then we take w(i) = 1 for all i
       If PL is empty, then we take PL as an identity matrix
       If PR is empty, then we take PR as an identity matrix
       If meanmat is 0, then we take meanmat as a zero matrix

 $ History $
   - Created by Dahua Lin, on Jul 31st, 2006

CROSS-REFERENCE INFORMATION ^

This function calls:
  • slreadarray SLREADARRAY Reads an array from an array file
  • raise_lackinput RAISE_LACKINPUT Raises an error indicating lack of input argument
This function is called by:
  • sl2dpcaex SL2DPCAEX Learns Extended 2D PCA on a set of matrix samples

SUBFUNCTIONS ^

SOURCE CODE ^

0001 function varargout = sl2dmatcov(type, data, matsiz, n, meanmat, PL, PR, w)
0002 %SL2DMATCOV Computes the 2D matrix-covariances
0003 %
0004 % $ Syntax $
0005 %   - CL = sl2dmatcov('CL', data, matsiz, n, meanmat, PL, PR, w)
0006 %   - CR = sl2dmatcov('CR', data, matsiz, n, meanmat, PL, PR, w)
0007 %   - [CL, CR] = sl2dmatcov('Both', data, matsiz, n, meanmat, PL, PR, w)
0008 %
0009 % $ Arguments $
0010 %   - data:     the stack of matrices or the cell array of filenames of the
0011 %               array files storing the matrices.
0012 %   - matsiz:   the size of each matrix
0013 %   - n:        the number of samples
0014 %   - PL:       the left-projection matrix, default = []
0015 %   - PR:       the right-projection matrix, default = []
0016 %   - w:        the weights of the matrix samples, default = []
0017 %
0018 % $ Remarks $
0019 %   - The function computes the 2D matrix-covariances according to
0020 %     the following formulas:
0021 %       Y_i = PL^T * (X - meanX)* PR
0022 %       CL = ( sum_{i=1}^n w(i) * Y_i * Y_i^T ) / ( sum_{i=1}^n w(i) )
0023 %       CR = ( sum_{i=1}^n w(i) * Y_i^T * Y_i ) / ( sum_{i=1}^n w(i) )
0024 %     Following special cases are considered:
0025 %       If w is empty, then we take w(i) = 1 for all i
0026 %       If PL is empty, then we take PL as an identity matrix
0027 %       If PR is empty, then we take PR as an identity matrix
0028 %       If meanmat is 0, then we take meanmat as a zero matrix
0029 %
0030 % $ History $
0031 %   - Created by Dahua Lin, on Jul 31st, 2006
0032 %
0033 
0034 %% parse and verify input arguments
0035 
0036 if nargin < 5
0037     raise_lackinput('sl2dmatcov', 5);
0038 end
0039 if nargin < 6
0040     PL = [];
0041 end
0042 if nargin < 7
0043     PR = [];
0044 end
0045 if nargin < 8
0046     w = [];
0047 end
0048 
0049 matsiz = matsiz(:)';
0050 if length(matsiz) ~= 2
0051     error('sltoolbox:invalidarg', ...
0052         'matsiz shoudl be a 2-elem vector');
0053 end
0054 if ~isequal(size(meanmat), matsiz)
0055     error('sltoolbox:invalidarg', ...
0056         'The size of mean matrix is not as specified');
0057 end
0058 
0059 d1 = matsiz(1);
0060 d2 = matsiz(2);
0061 if ~isempty(PL) && size(PL, 1) ~= d1
0062     error('sltoolbox:invalidarg', ...
0063         'The size of PL is inconsistent with the matrix dimension');
0064 end
0065 if ~isempty(PR) && size(PR, 1) ~= d2
0066     error('sltoolbox:invalidarg', ...
0067         'The size of PR is inconsistent with the matrix dimension');
0068 end
0069 
0070 if ~isempty(w)
0071     if length(w) ~= n
0072         error('The weights length is inconsistent with the number of samples');
0073     end
0074     tw = sum(w);
0075 else
0076     tw = n;
0077 end
0078 
0079 
0080 %% Main body
0081 
0082 if isnumeric(data)
0083 
0084     if ~isequal(size(data), [matsiz, n])
0085         error('sltoolbox:invalidarg', ...
0086             'The size of data is inconsistent with specified');
0087     end
0088     
0089     Y = compute_Y(data, meanmat, PL, PR);
0090     
0091     switch type
0092         case 'CL'
0093             CL = compute_SL(Y, w);
0094             CL = CL / tw;
0095             varargout = {CL};
0096         case 'CR'
0097             CR = compute_SR(Y, w);
0098             CR = CR / tw;
0099             varargout = {CR};
0100         case 'Both'
0101             [CL, CR] = compute_SLSR(Y, w);
0102             CL = CL / tw;
0103             CR = CR / tw;
0104             varargout = {CL, CR};
0105         otherwise
0106             error('sltoolbox:invalidarg', ...
0107                 'invalid type: %s', type);
0108     end            
0109     
0110     
0111 elseif iscell(data)
0112     
0113     nfiles = length(data);
0114     cf = 0;
0115     
0116     switch type
0117         case 'CL'
0118             for i = 1 : nfiles
0119                 curarr = slreadarray(data{i});
0120                 curn = size(curarr, 3);
0121                 Y = compute_Y(curarr, meanmat, PL, PR);
0122                 curCL = compute_SL(Y, w); 
0123                 if i == 1
0124                     CL = curCL;
0125                 else
0126                     CL = CL + curCL;
0127                 end
0128                 clear Y curCL;
0129                 cf = cf + curn;
0130             end
0131             CL = CL / tw;
0132             varargout = {CL};
0133             
0134         case 'CR'
0135             for i = 1 : nfiles
0136                 curarr = slreadarray(data{i});
0137                 curn = size(curarr, 3);
0138                 Y = compute_Y(curarr, meanmat, PL, PR);
0139                 curCR = compute_SR(Y, w); 
0140                 if i == 1
0141                     CR = curCR;
0142                 else
0143                     CR = CR + curCR;
0144                 end
0145                 clear Y curCR;
0146                 cf = cf + curn;
0147             end
0148             CR = CR / tw;
0149             varargout = {CR};
0150             
0151         case 'Both'
0152             for i = 1 : nfiles
0153                 curarr = slreadarray(data{i});
0154                 curn = size(curarr, 3);
0155                 Y = compute_Y(curarr, meanmat, PL, PR);
0156                 [curCL, curCR] = compute_SLSR(Y, w); 
0157                 if i == 1
0158                     CL = curCL;
0159                     CR = curCR;
0160                 else
0161                     CL = CL + curCL;
0162                     CR = CR + curCR;
0163                 end
0164                 clear Y curCL curCR;
0165                 cf = cf + curn;
0166             end
0167             CL = CL / tw;
0168             CR = CR / tw;
0169             varargout = {CL, CR};
0170             
0171         otherwise
0172             error('sltoolbox:invalidarg', ...
0173                 'invalid type: %s', type);        
0174     end
0175     
0176     if cf ~= n
0177         error('sltoolbox:sizmismatch', ...
0178             'The total number of samples is not n');
0179     end
0180             
0181 else
0182     error('sltoolbox:invalidarg', ...
0183         'data should be a numeric array or a cell array of filenames');    
0184 end
0185 
0186 
0187 
0188 %% Core routine
0189 
0190 function Y = compute_Y(X, M, PL, PR)
0191 
0192 n = size(X, 3);
0193 if isempty(PL)
0194     if isempty(PR)
0195         if isequal(M, 0)
0196             Y = X;
0197         else
0198             Y = zeros(size(X, 1), size(X, 2), n);
0199             for i = 1 : n
0200                 Y(:,:,i) = X(:,:,i) - M;
0201             end
0202         end
0203     else
0204         Y = zeros(size(X, 1), size(PR, 2), n);
0205         if isequal(M, 0)           
0206             for i = 1 : n
0207                 Y(:,:,i) = X(:,:,i) * PR;
0208             end
0209         else
0210             for i = 1 : n
0211                 Y(:,:,i) = (X(:,:,i) - M) * PR;
0212             end
0213         end
0214     end
0215 else
0216     PLT = PL';
0217     if isempty(PR)
0218         Y = zeros(size(PL, 2), size(X, 2), n);
0219         if isequal(M, 0)
0220             for i = 1 : n
0221                 Y(:,:,i) = PLT * X(:,:,i);
0222             end
0223         else
0224             for i = 1 : n
0225                 Y(:,:,i) = PLT * (X(:,:,i) - M);
0226             end
0227         end
0228     else
0229         Y = zeros(size(PL, 2), size(PR, 2), n);
0230         if isequal(M, 0)
0231             for i = 1 : n
0232                 Y(:,:,i) = PLT * X(:,:,i) * PR;
0233             end
0234         else
0235             for i = 1 : n
0236                 Y(:,:,i) = PLT * (X(:,:,i) - M) * PR;
0237             end
0238         end
0239     end
0240 end
0241 
0242 
0243 function SL = compute_SL(Y, w)
0244 
0245 SL = zeros(size(Y, 1));
0246 n = size(Y, 3);
0247 if isempty(w)
0248     for i = 1 : n
0249         curY = Y(:, :, i);
0250         SL = SL + curY * curY';
0251     end
0252 else
0253     for i = 1 : n
0254         curY = Y(:, :, i);
0255         SL = SL + w(i) * curY * curY';
0256     end
0257 end
0258 
0259 function SR = compute_SR(Y, w)
0260 
0261 SR = zeros(size(Y, 2));
0262 n = size(Y, 3);
0263 if isempty(w)
0264     for i = 1 : n
0265         curY = Y(:, :, i);
0266         SR = SR + curY' * curY;
0267     end
0268 else
0269     for i = 1 : n
0270         curY = Y(:, :, i);
0271         SR = SR + w(i) * curY' * curY;
0272     end
0273 end    
0274 
0275 function [SL, SR] = compute_SLSR(Y, w)
0276 
0277 SL = zeros(size(Y, 1));
0278 SR = zeros(size(Y, 2));
0279 n = size(Y, 3);
0280 if isempty(w)
0281     for i = 1 : n
0282         curY = Y(:, :, i);
0283         SL = SL + curY * curY';
0284         SR = SR + curY' * curY;
0285     end
0286 else
0287     for i = 1 : n
0288         curY = Y(:, :, i);
0289         SL = SL + w(i) * curY * curY';
0290         SR = SR + w(i) * curY' * curY;
0291     end
0292 end
0293     
0294
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