Description of slisomap

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slisomap

PURPOSE

SLISOMAP Performs ISOMAP manifold embedding

SYNOPSIS

function [X, spectrum] = slisomap(G, d)

DESCRIPTION

SLISOMAP Performs ISOMAP manifold embedding

 $ Syntax $
   - X = slisomap(G, d)
   - [X, spectrum] = slisomap(G, d)

 $ Arguments $
   - G:            The distance graph for neighbors
   - d:            The dimension of embedded space
   - X:            The embedded coordinates of the samples
   - spectrum:     The eigenvalues of the embedded dimensions

 $ Description $
   - X = slisomap(G, d) performs ISOMAP manifold embedding to pursue 
     an embedding which best preserves the geodesic distances between
     samples.

   - [X, spectrum] = slisomap(G, d) additionally outputs the
     eigen-spectrum of the embedded space.

 $ Remarks $
   - In current implementation, the third-party toolbox: Matlab BGL is
     required for computing the geodesics.

 $ History $
   - Created by Dahua Lin, on Sep 8, 2006

CROSS-REFERENCE INFORMATION

This function calls:

• slsymgraph SLSYMGRAPH Forces symmetry of the adjacency matrix of a graph
• slcmds SLMDS Performs Classical Multidimensional scaling
• raise_lackinput RAISE_LACKINPUT Raises an error indicating lack of input argument

This function is called by:

SOURCE CODE

0001 function [X, spectrum] = slisomap(G, d)
0002 %SLISOMAP Performs ISOMAP manifold embedding
0003 %
0004 % $ Syntax $
0005 %   - X = slisomap(G, d)
0006 %   - [X, spectrum] = slisomap(G, d)
0007 %
0008 % $ Arguments $
0009 %   - G:            The distance graph for neighbors
0010 %   - d:            The dimension of embedded space
0011 %   - X:            The embedded coordinates of the samples
0012 %   - spectrum:     The eigenvalues of the embedded dimensions
0013 %
0014 % $ Description $
0015 %   - X = slisomap(G, d) performs ISOMAP manifold embedding to pursue
0016 %     an embedding which best preserves the geodesic distances between
0017 %     samples.
0018 %
0019 %   - [X, spectrum] = slisomap(G, d) additionally outputs the
0020 %     eigen-spectrum of the embedded space.
0021 %
0022 % $ Remarks $
0023 %   - In current implementation, the third-party toolbox: Matlab BGL is
0024 %     required for computing the geodesics.
0025 %
0026 % $ History $
0027 %   - Created by Dahua Lin, on Sep 8, 2006
0028 %
0029 
0030 %% parse and verify input
0031 
0032 if nargin < 2
0033     raise_lackinput('slisomap', 2);
0034 end
0035 
0036 G = slgraphmat(G, 'sparse', true);
0037 n = size(G, 1);
0038 if d >= n
0039     error('sltoolbox:exceedbound', ...
0040         'The embedded dimension d should be less than the number of samples');
0041 end
0042 
0043 
0044 %% compute
0045 
0046 % compute geodesics
0047 G = slsymgraph(G);
0048 D = all_shortest_paths(G);
0049 
0050 is_inf_dists = isinf(D);
0051 is_inf_dists = is_inf_dists(:);
0052 if any(is_inf_dists)
0053     error('sltoolbox:rterror', ...
0054         'The graph has multiple disconnected components');
0055 end
0056 clear is_inf_dists;
0057 
0058 % perform MDS on D
0059 [X, spectrum] = slcmds(D, d);
0060

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