Description of slltsa

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slltsa

PURPOSE

SLLTSA Performs Local Tangent Space Alignment Learning

SYNOPSIS

function [GC, spectrum, CTS] = slltsa(X, G, dl, dg)

DESCRIPTION

SLLTSA Performs Local Tangent Space Alignment Learning

 $ Syntax $
   - [GC, spectrum] = slltsa(X, G, dl)
   - [GC, spectrum] = slltsa(X, G, dl, dg)
   - [GC, spectrum, CTS] = slltsa(...)

 $ Arguments $
   - X:        The input sample matrix
   - G:        The neighborhood graph
   - dl:       The local dimension
   - dg:       The global embedding dimension
   - GC:       The global embedding coordinates
   - spectrum: The eigenvalue spectrum of the embedding space
   - CTS:      The struct of the coordinate transform system
               it has the following fields:
                   - means:   d0 x n
                   - bases:   d0 x dl x n
                   - ftrans:  dl x dg x n
                      the forward transforms: local coord -> global coord

 $ Description $
   - [GC, spectrum] = slltsa(X, G, dl) performs the local tangent space
     alignment learning based on the samples in X and the neighborhood
     graph in G. By default the global embedding dimension is set to the
     same as the local dimension.

   - [GC, spectrum] = slltsa(X, G, dl, dg) performs the LTSA with the 
     local and global embeding dimension respectively given.

   - [GC, spectrum, CTS] = slltsa(...) additionally returns the coordinate
     transform system.

 $ Remarks $
   - The implementation wraps the three major components:
       - sllocaltanspace:   learns the local tangent spaces
       - sllocaltancoords:  produces the local coordinates
       - sllocalcoordalign: pursues the global embedding by aligning the
                            local coordinates

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

CROSS-REFERENCE INFORMATION

This function calls:

• sladjmat SLADJMAT Constructs the adjacency matrix representation of a graph
• slgraphinfo SLGRAPHINFO Extracts basic information of a given graph representation
• sllocalcoordalign SLLOCALCOORDALIGN Performs optimal local coordinate alignment
• sllocaltancoords SLLOCALTANCOORDS Computes the local tangent coordinates
• sllocaltanspace SLLOCALTANSPACE Solves the local tangent spaces

This function is called by:

SOURCE CODE

0001 function [GC, spectrum, CTS] = slltsa(X, G, dl, dg)
0002 %SLLTSA Performs Local Tangent Space Alignment Learning
0003 %
0004 % $ Syntax $
0005 %   - [GC, spectrum] = slltsa(X, G, dl)
0006 %   - [GC, spectrum] = slltsa(X, G, dl, dg)
0007 %   - [GC, spectrum, CTS] = slltsa(...)
0008 %
0009 % $ Arguments $
0010 %   - X:        The input sample matrix
0011 %   - G:        The neighborhood graph
0012 %   - dl:       The local dimension
0013 %   - dg:       The global embedding dimension
0014 %   - GC:       The global embedding coordinates
0015 %   - spectrum: The eigenvalue spectrum of the embedding space
0016 %   - CTS:      The struct of the coordinate transform system
0017 %               it has the following fields:
0018 %                   - means:   d0 x n
0019 %                   - bases:   d0 x dl x n
0020 %                   - ftrans:  dl x dg x n
0021 %                      the forward transforms: local coord -> global coord
0022 %
0023 % $ Description $
0024 %   - [GC, spectrum] = slltsa(X, G, dl) performs the local tangent space
0025 %     alignment learning based on the samples in X and the neighborhood
0026 %     graph in G. By default the global embedding dimension is set to the
0027 %     same as the local dimension.
0028 %
0029 %   - [GC, spectrum] = slltsa(X, G, dl, dg) performs the LTSA with the
0030 %     local and global embeding dimension respectively given.
0031 %
0032 %   - [GC, spectrum, CTS] = slltsa(...) additionally returns the coordinate
0033 %     transform system.
0034 %
0035 % $ Remarks $
0036 %   - The implementation wraps the three major components:
0037 %       - sllocaltanspace:   learns the local tangent spaces
0038 %       - sllocaltancoords:  produces the local coordinates
0039 %       - sllocalcoordalign: pursues the global embedding by aligning the
0040 %                            local coordinates
0041 %
0042 % $ History $
0043 %   - Created by Dahua Lin, on Sep 13rd, 2006
0044 %
0045 
0046 %% parse and verify input arguments
0047 
0048 if ~isnumeric(X) || ndims(X) ~= 2
0049     error('X should be a 2D numeric matrix');
0050 end
0051 n = size(X, 2);
0052 
0053 gi = slgraphinfo(G, {[n, n]});
0054 
0055 if nargin < 4
0056     dg = dl;
0057 end
0058 
0059 if ~strcmp(gi.form, 'adjmat')
0060     G = sladjmat(G, 'sparse', true);
0061 end
0062 
0063 out_cts = (nargout >= 3);
0064 
0065 
0066 %% main skeleton
0067 
0068 % learn local tangent spaces
0069 [LM, LP] = sllocaltanspace(X, G, dl);
0070 
0071 % compute local coordinates
0072 [Y, GM] = sllocaltancoords(LM, LP, X, G, 'T');
0073 if ~out_cts
0074     clear LM LP;
0075 end
0076 
0077 % align local systems to global embedding
0078 if out_cts
0079     [GC, spectrum, LT] = sllocalcoordalign(GM, Y, dg);
0080 else
0081     [GC, spectrum] = sllocalcoordalign(GM, Y, dg);
0082 end
0083 
0084 % organize output
0085 if out_cts
0086     CTS.means = LM;
0087     CTS.bases = LP;
0088     CTS.ftrans = LT;
0089 end
0090

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