Description of sldists2kernels

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sldists2kernels

PURPOSE

SLDISTS2KERNELS Computes the inner products from distances

SYNOPSIS

function K = sldists2kernels(D, ty)

DESCRIPTION

SLDISTS2KERNELS Computes the inner products from distances

 $ Syntax $
   - K = sldists2kernels(D)
   - K = sldists2kernels(D, 'sqr')

 $ Arguments $
   - D:        The pairwise distance matrix
   - K:        The pairwise inner product matrix (kernel matrix)
   
 $ Description $
   - K = sldists2kernels(D) computes the inner products between samples
     pairwisely with the pairwise norms given. Assume that the samples 
     are in an Euclidean linear space, and are centralized.

   - K = sldists2kernels(D, 'sqr') performs the calculation with the 
     input D matrix containing the square distances.

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

CROSS-REFERENCE INFORMATION

This function calls:

This function is called by:

• slcmds SLMDS Performs Classical Multidimensional scaling

SOURCE CODE

0001 function K = sldists2kernels(D, ty)
0002 %SLDISTS2KERNELS Computes the inner products from distances
0003 %
0004 % $ Syntax $
0005 %   - K = sldists2kernels(D)
0006 %   - K = sldists2kernels(D, 'sqr')
0007 %
0008 % $ Arguments $
0009 %   - D:        The pairwise distance matrix
0010 %   - K:        The pairwise inner product matrix (kernel matrix)
0011 %
0012 % $ Description $
0013 %   - K = sldists2kernels(D) computes the inner products between samples
0014 %     pairwisely with the pairwise norms given. Assume that the samples
0015 %     are in an Euclidean linear space, and are centralized.
0016 %
0017 %   - K = sldists2kernels(D, 'sqr') performs the calculation with the
0018 %     input D matrix containing the square distances.
0019 %
0020 % $ History $
0021 %   - Created by Dahua Lin, on Sep 8th, 2006
0022 %
0023 
0024 %% parse and verify input
0025 
0026 if isempty(D) 
0027     K = [];
0028     return;
0029 end
0030 
0031 if ~isnumeric(D) || ndims(D) ~= 2 || size(D,1) ~= size(D,2)
0032     error('sltoolbox:invalidarg', ...
0033         'D should be a square matrix');
0034 end
0035 
0036 if nargin >= 2 && strcmpi(ty, 'sqr')
0037     is_sqr = true;
0038 else
0039     is_sqr = false;
0040 end
0041 
0042 %% compute
0043 
0044 % preprocess
0045 
0046 if ~is_sqr
0047     K = D .* D;     % make squares
0048 else
0049     K = D;
0050 end
0051 K = 0.5 * (K + K'); % enforce symmetry
0052 
0053 % compute
0054 n = size(K, 1);
0055 
0056 s = sum(K, 1);
0057 t = sum(s);
0058 
0059 s = s / n;
0060 t = t / (n*n);
0061 
0062 for i = 1 : n
0063     K(i,:) = K(i,:) - s(i);
0064 end
0065 for i = 1 : n
0066     K(:,i) = K(:,i) - s(i);
0067 end
0068 K = K + t;
0069 
0070 K = (-0.5) * K;
0071     
0072 
0073 
0074 
0075     
0076     
0077     
0078     
0079     
0080

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