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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 slpwscatter
Home > sltoolbox > stat > slpwscatter.m

slpwscatter

PURPOSE ^

SLPWSCATTER Compute the pairwise scatter matrix

SYNOPSIS ^

function S = slpwscatter(tar, W)

DESCRIPTION ^

SLPWSCATTER Compute the pairwise scatter matrix

 $ Syntax $
   - S = slpwscatter(X)
   - S = slpwscatter({X, Y})
   - S = slpwscatter(X, W)
   - S = slpwscatter({X, Y}, W)

 $ Description $
   - S = slpwscatter(X) computes the pairwise scatter matrix on the
     samples X using the following formula. Suppose X has m samples
     stored as columns, then 
       S = sum_{i=1:m} sum_{j=1:m} X(:,i) * X(:,j)'

   - S = slpwscatter({X, Y}) computes the pairwise scatter matrix on
     samples X and Y using the following formula. Suppose X has m samples
     and Y has n samples, then
       S = sum_{i=1:m} sum_{j=1:n} X(:,i) * X(:,j)'

   - S = slpwscatter(X, W) computes the weighted pairwise scatter matrix
     on the samples X using the following formula. Suppose X has m
     samples, then W should be an m x m matrix,
       S = sum_{i=1:m} sum_{j=1:m} W(i,j) X(:,i) * X(:,j)'

   - S = slpwscatter({X, Y}, W) computes the weighted pairwise scatter
     matrix on the samples X using the following formula. Suppose X has
     m samples and Y has n samples, then W should be an m x n matrix,
       S = sum_{i=1:m} sum_{j=1:n} W(i,j) X(:,i) * Y(:,j)'

 $ Remarks $
   - Instead of using the aforementioned formulas directly in computation,
     it converts the problem into matrix multiplication, thus much more
     efficient implementation can be applied.

 $ History $
   - Created by Dahua Lin on Apr 27, 2006

CROSS-REFERENCE INFORMATION ^

This function calls:
This function is called by:
  • slscatter SLSCATTER Compute the scatter matrix

SOURCE CODE ^

0001 function S = slpwscatter(tar, W)
0002 %SLPWSCATTER Compute the pairwise scatter matrix
0003 %
0004 % $ Syntax $
0005 %   - S = slpwscatter(X)
0006 %   - S = slpwscatter({X, Y})
0007 %   - S = slpwscatter(X, W)
0008 %   - S = slpwscatter({X, Y}, W)
0009 %
0010 % $ Description $
0011 %   - S = slpwscatter(X) computes the pairwise scatter matrix on the
0012 %     samples X using the following formula. Suppose X has m samples
0013 %     stored as columns, then
0014 %       S = sum_{i=1:m} sum_{j=1:m} X(:,i) * X(:,j)'
0015 %
0016 %   - S = slpwscatter({X, Y}) computes the pairwise scatter matrix on
0017 %     samples X and Y using the following formula. Suppose X has m samples
0018 %     and Y has n samples, then
0019 %       S = sum_{i=1:m} sum_{j=1:n} X(:,i) * X(:,j)'
0020 %
0021 %   - S = slpwscatter(X, W) computes the weighted pairwise scatter matrix
0022 %     on the samples X using the following formula. Suppose X has m
0023 %     samples, then W should be an m x m matrix,
0024 %       S = sum_{i=1:m} sum_{j=1:m} W(i,j) X(:,i) * X(:,j)'
0025 %
0026 %   - S = slpwscatter({X, Y}, W) computes the weighted pairwise scatter
0027 %     matrix on the samples X using the following formula. Suppose X has
0028 %     m samples and Y has n samples, then W should be an m x n matrix,
0029 %       S = sum_{i=1:m} sum_{j=1:n} W(i,j) X(:,i) * Y(:,j)'
0030 %
0031 % $ Remarks $
0032 %   - Instead of using the aforementioned formulas directly in computation,
0033 %     it converts the problem into matrix multiplication, thus much more
0034 %     efficient implementation can be applied.
0035 %
0036 % $ History $
0037 %   - Created by Dahua Lin on Apr 27, 2006
0038 %
0039 
0040 %% parse and verify input arguments
0041 
0042 % check target
0043 
0044 if isnumeric(tar)   % X
0045     
0046     X = tar;
0047     if ndims(X) ~= 2
0048         error('sltoolbox:invaliddims', ...
0049             'X should be a 2D matrix');
0050     end
0051     m = size(X, 2);    
0052     
0053     targettype = 1;
0054     
0055 elseif iscell(tar)  % {X, Y}
0056     
0057     if length(tar) ~= 2
0058         error('sltoolbox:invalidarg', ...
0059             'For cell target, it should be in the form {X, Y}');
0060     end
0061     
0062     X = tar{1};
0063     Y = tar{2};
0064     
0065     if ndims(X) ~= 2 || ndims(Y) ~= 2
0066         error('sltoolbox:invaliddims', ...
0067             'X and Y should be a 2D matrices');
0068     end
0069     
0070     if size(X, 1) ~= size(Y, 1)
0071         error('sltoolbox:sizmismatch', ...
0072             'The sample dimensions in X and Y are inconsistent');
0073     end
0074     
0075     m = size(X, 2);
0076     n = size(Y, 2);
0077     
0078     targettype = 2;
0079     
0080 else
0081     
0082     error('sltoolbox:invalidarg', ...
0083         'The tar should be either X or {X, Y}');
0084     
0085 end
0086 
0087 % check weight
0088 
0089 if nargin < 2
0090     W = [];
0091 end
0092 
0093 if ~isempty(W)    
0094     switch targettype        
0095         case 1
0096             if ~isequal(size(W), [m, m])
0097                 error('sltoolbox:sizmismatch', ...
0098                     'The weight matrix W should be an m x m matrix');
0099             end            
0100         case 2
0101             if ~isequal(size(W), [m, n])
0102                 error('sltoolbox:sizmismatch', ...
0103                     'The weight matrix W should be an m x n matrix');
0104             end            
0105     end    
0106 end
0107         
0108         
0109 %% compute
0110 
0111 switch targettype
0112     
0113     case 1          % X
0114    
0115         if isempty(W)   % not weighted
0116             D = diag(m(ones(m, 1)));
0117             W = ones(m, m);            
0118             M = 2 * (D - W);
0119             
0120             clear D W;
0121         else            % weighted
0122             D = diag(sum(W,1)' + sum(W,2));
0123             M = D - (W + W');
0124             
0125             clear D;
0126         end
0127         
0128         S = X * M * X';
0129                                                                                    
0130     case 2          % X, Y
0131         
0132         if isempty(W)   % not weighted
0133             S1 = X * diag(m(ones(m, 1))) * X';
0134             S2 = Y * diag(n(ones(n, 1))) * Y';
0135             S12 = S1 + S2;
0136             clear S1 S2;
0137             
0138             S3 = X * ones(m, n) * Y';
0139             S34 = S3 + S3';
0140             clear S3;
0141             
0142             S = S12 - S34;            
0143         else            % weighted
0144             S1 = X * diag(sum(W, 2)) * X';
0145             S2 = Y * diag(sum(W, 1)) * Y';
0146             S12 = S1 + S2;
0147             clear S1 S2;
0148             
0149             S3 = X * W * Y';
0150             S34 = S3 + S3';
0151             clear S3;
0152             
0153             S = S12 - S34;            
0154         end
0155             
0156                             
0157 end
0158 
0159 
0160 
0161     
0162     
0163     
0164     
0165     
0166
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