Description of slcmds

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slcmds

PURPOSE

SLMDS Performs Classical Multidimensional scaling

SYNOPSIS

function [X, spectrum] = slcmds(D, d, w, ty)

DESCRIPTION

SLMDS Performs Classical Multidimensional scaling

 $ Syntax $
   - X = slcmds(D, d)
   - X = slcmds(D, d, w)
   - X = slcmds(D, d, w, 'sqr')
   - [X, spectrum] = slcmds(...)

 $ Arguments $
   - D:        The pairwise distance matrix (n x n)
   - d:        The dimension of the embedding space
   - w:        The weights of samples (1 x n or [])
   - X:        The embedded samples (d x n)

 $ Description $
   - X = slcmds(D, d) performs classic multidimensional scaling to
     pursue an embedding space of d-dimension and the vector 
     representation in that space of the objects, such that the 
     distances are optimally preserved.

   - X = slcmds(D, d, w) If w is not empty, it performs classic 
     multidimensional scaling on weighted samples. 

   - X = slcmds(D, d, w, 'sqr') indicates that D contains the square
     of distances.

   - [X, spectrum] = slcmds(...) additionally outputs the spectrum of
     the embedded space
     
 $ History $
   - Created by Dahua Lin, on Sep 8th, 2006

CROSS-REFERENCE INFORMATION

This function calls:

• sldists2kernels SLDISTS2KERNELS Computes the inner products from distances
• slkernelembed SLKERNELEMBED Finds an embedding space to preserve inner products
• raise_lackinput RAISE_LACKINPUT Raises an error indicating lack of input argument

This function is called by:

• slisomap SLISOMAP Performs ISOMAP manifold embedding

SOURCE CODE

0001 function [X, spectrum] = slcmds(D, d, w, ty)
0002 %SLMDS Performs Classical Multidimensional scaling
0003 %
0004 % $ Syntax $
0005 %   - X = slcmds(D, d)
0006 %   - X = slcmds(D, d, w)
0007 %   - X = slcmds(D, d, w, 'sqr')
0008 %   - [X, spectrum] = slcmds(...)
0009 %
0010 % $ Arguments $
0011 %   - D:        The pairwise distance matrix (n x n)
0012 %   - d:        The dimension of the embedding space
0013 %   - w:        The weights of samples (1 x n or [])
0014 %   - X:        The embedded samples (d x n)
0015 %
0016 % $ Description $
0017 %   - X = slcmds(D, d) performs classic multidimensional scaling to
0018 %     pursue an embedding space of d-dimension and the vector
0019 %     representation in that space of the objects, such that the
0020 %     distances are optimally preserved.
0021 %
0022 %   - X = slcmds(D, d, w) If w is not empty, it performs classic
0023 %     multidimensional scaling on weighted samples.
0024 %
0025 %   - X = slcmds(D, d, w, 'sqr') indicates that D contains the square
0026 %     of distances.
0027 %
0028 %   - [X, spectrum] = slcmds(...) additionally outputs the spectrum of
0029 %     the embedded space
0030 %
0031 % $ History $
0032 %   - Created by Dahua Lin, on Sep 8th, 2006
0033 %
0034 
0035 %% parse and verify input arguments
0036 
0037 if nargin < 2
0038     raise_lackinput('slcmds', 2);
0039 end
0040 
0041 if ndims(D) ~= 2 || size(D, 1) ~= size(D, 2)
0042     error('sltoolbox:invalidarg', ...
0043         'The D should be a square matrix');
0044 end
0045 n = size(D, 1);
0046 
0047 if d >= n
0048     error('sltoolbox:exceedbound', ...
0049         'The dimension d should be less than the number of samples n');
0050 end
0051 
0052 if nargin < 3
0053     w = [];
0054 else
0055     if ~isempty(w)
0056         if ~isequal(size(w), [1, n])
0057             error('sltoolbox:sizmismatch', ...
0058                 'If w is specified, it should be an 1 x n row vector');
0059         end
0060     end
0061 end
0062 
0063 if nargin >= 4 && strcmpi(ty, 'sqr')
0064     is_sqr = true;
0065 else
0066     is_sqr = false;
0067 end
0068 
0069 
0070 %% compute
0071 
0072 if ~is_sqr
0073     K = sldists2kernels(D);
0074 else
0075     K = sldists2kernels(D, 'sqr');
0076 end
0077 
0078 [X, spectrum] = slkernelembed(K, d, w);
0079 
0080 
0081 
0082 
0083 
0084     
0085     
0086 
0087

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