Description of sllocaltancoords

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sllocaltancoords

PURPOSE

SLLOCALTANCOORDS Computes the local tangent coordinates

SYNOPSIS

function [Y, GM] = sllocaltancoords(LM, LP, X, G, ga)

DESCRIPTION

SLLOCALTANCOORDS Computes the local tangent coordinates

 $ Syntax $
   - [Y, GM] = sllocaltancoords(LM, LP, X, G)
   - [Y, GM] = sllocaltancoords(LM, LP, X, G, ga);

 $ Arguments $
   - LM:       The local means (d0 x m)
   - LP:       The local space basis (d0 x dl x m)
   - X:        The input samples (d0 x n)
   - G:        The graph indicating which sample is managed by which model
               (1 x n)
   - ga:       The graph arrangement (default = 'N')
                   - 'N': m x n, models as sources, samples as targets
                   - 'T': n x m, samples as sources, models as targets
   - Y:        The computed local coordinates (dl x nnz)

 $ Description $
   - [Y, GM] = sllocaltancoords(LM, LP, X, G) computes the local tangent
     coordinates using the default graph arrangement. For each non-zero
     entry in G, there is a pairs of a space model characterized by 
     a mean vector vm and space basis P and a sample x. Then the local
     tangent coordinates are computed by
           y = P^T * (x - vm)
     If there are nnz non-zero entries in G, then Y has nnz columns. The 
     output graph GM is a sparse matrix, with the values in GM telling 
     the index of the corresponding column in Y.

   - [Y, GM] = sllocaltancoords(LM, LP, X, G, ga) computes the local tangent
     coordinates using the specified graph arrangement. There are two
     arrangements to choose:
       - 'N': G is m x n, models as sources, samples as targets
              the edge connecting the i-th source and the j-th target
              refers to the pair of the i-th model and the j-th sample
       - 'T': G is n x m, samples as sources, models as targets
              the edge connecting the i-th source and the j-th target
              refers to the pair of the i-th sample and the j-th model

 $ Remarks $
   - When map is not specified, the number of models should be equal to
     the number of samples. (m = n)

 $ History $
   - Created by Dahua Lin, on Sep 13rd, 2006

CROSS-REFERENCE INFORMATION

This function calls:

• sladdvec SLADDVEC adds a vector to columns or rows of a matrix
• sladjmat SLADJMAT Constructs the adjacency matrix representation of a graph
• slgraphinfo SLGRAPHINFO Extracts basic information of a given graph representation
• raise_lackinput RAISE_LACKINPUT Raises an error indicating lack of input argument

This function is called by:

• slltsa SLLTSA Performs Local Tangent Space Alignment Learning

SOURCE CODE

0001 function [Y, GM] = sllocaltancoords(LM, LP, X, G, ga)
0002 %SLLOCALTANCOORDS Computes the local tangent coordinates
0003 %
0004 % $ Syntax $
0005 %   - [Y, GM] = sllocaltancoords(LM, LP, X, G)
0006 %   - [Y, GM] = sllocaltancoords(LM, LP, X, G, ga);
0007 %
0008 % $ Arguments $
0009 %   - LM:       The local means (d0 x m)
0010 %   - LP:       The local space basis (d0 x dl x m)
0011 %   - X:        The input samples (d0 x n)
0012 %   - G:        The graph indicating which sample is managed by which model
0013 %               (1 x n)
0014 %   - ga:       The graph arrangement (default = 'N')
0015 %                   - 'N': m x n, models as sources, samples as targets
0016 %                   - 'T': n x m, samples as sources, models as targets
0017 %   - Y:        The computed local coordinates (dl x nnz)
0018 %
0019 % $ Description $
0020 %   - [Y, GM] = sllocaltancoords(LM, LP, X, G) computes the local tangent
0021 %     coordinates using the default graph arrangement. For each non-zero
0022 %     entry in G, there is a pairs of a space model characterized by
0023 %     a mean vector vm and space basis P and a sample x. Then the local
0024 %     tangent coordinates are computed by
0025 %           y = P^T * (x - vm)
0026 %     If there are nnz non-zero entries in G, then Y has nnz columns. The
0027 %     output graph GM is a sparse matrix, with the values in GM telling
0028 %     the index of the corresponding column in Y.
0029 %
0030 %   - [Y, GM] = sllocaltancoords(LM, LP, X, G, ga) computes the local tangent
0031 %     coordinates using the specified graph arrangement. There are two
0032 %     arrangements to choose:
0033 %       - 'N': G is m x n, models as sources, samples as targets
0034 %              the edge connecting the i-th source and the j-th target
0035 %              refers to the pair of the i-th model and the j-th sample
0036 %       - 'T': G is n x m, samples as sources, models as targets
0037 %              the edge connecting the i-th source and the j-th target
0038 %              refers to the pair of the i-th sample and the j-th model
0039 %
0040 % $ Remarks $
0041 %   - When map is not specified, the number of models should be equal to
0042 %     the number of samples. (m = n)
0043 %
0044 % $ History $
0045 %   - Created by Dahua Lin, on Sep 13rd, 2006
0046 %
0047 
0048 %% parse and verify input arguments
0049 
0050 if nargin < 4
0051     raise_lackinput('sllocaltancoords', 4);
0052 end
0053 
0054 [d, m] = size(LM);
0055 [dP, dl, m2] = size(LP);
0056 [dX, n] = size(X);
0057 
0058 if d ~= dP || d ~= dX
0059     error('sltoolbox:sizmismatch', ...
0060         'The sample dimensions are inconsistent among LM, LP and X');
0061 end
0062 if m~= m2
0063     error('sltoolbox:sizmismatch', ...
0064         'The space numbers in LM and LP are inconsistent');
0065 end
0066 
0067 gi = slgraphinfo(G);
0068 
0069 if nargin < 5
0070     ga = 'N';
0071 end
0072 switch ga
0073     case 'N'
0074         if ~isequal([gi.n, gi.nt], [m, n])
0075             error('sltoolbox:sizmismatch', ...
0076                 'The size of the graph does not match the samples and models');
0077         end
0078     case 'T'
0079         if ~isequal([gi.n, gi.nt], [n, m])
0080             error('sltoolbox:sizmismatch', ...
0081                 'The size of the graph does not match the samples and models');
0082         end
0083     otherwise
0084         error('sltoolbox:invalidarg', ...
0085             'Invalid graph arrangement: %s', ga);
0086 end
0087 
0088 
0089 %% main
0090 
0091 % prepare indices
0092 if ~strcmp(gi.form, 'adjmat')
0093     G = sladjmat(G, 'valtype', 'logical', 'sparse', true);
0094 end
0095         
0096 % prepare storage
0097 ny = nnz(G);
0098 Y = zeros(dl, ny);
0099 GM = spalloc(gi.n, gi.nt, ny);
0100 
0101 % main loop
0102 cp = 0;
0103 switch ga
0104     case 'N'
0105         for k = 1 : m
0106             vm = LM(:,k);
0107             P = LP(:,:,k);
0108             ci = find(G(k,:));
0109             curX = X(:, ci);
0110             cn = length(ci);
0111             curY = P' * sladdvec(curX, -vm, 1);
0112             Y(:, cp+1:cp+cn) = curY;
0113             GM(k, ci) = cp+1:cp+cn;
0114             cp = cp + cn;
0115         end
0116     case 'T'
0117         for k = 1 : m
0118             vm = LM(:,k);
0119             P = LP(:,:,k);
0120             ci = find(G(:,k));
0121             curX = X(:, ci);
0122             cn = length(ci);
0123             curY = P' * sladdvec(curX, -vm, 1);
0124             Y(:, cp+1:cp+cn) = curY;
0125             GM(ci, k) = (cp+1:cp+cn)';
0126             cp = cp + cn;
0127         end                        
0128 end
0129 
0130 
0131

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