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Statistical Learning Toolbox

from Statistical Learning Toolbox by Dahua Lin
Functions for statistical learning, pattern recognition and computer vision, covering many topics.

Description of sldistmean
Home > sltoolbox > core > sldistmean.m

sldistmean

PURPOSE ^

SLDISTMEAN Uses fast method to compute means of pairwise distances

SYNOPSIS ^

function m = sldistmean(X1, X2, varargin)

DESCRIPTION ^

SLDISTMEAN Uses fast method to compute means of pairwise distances

 $ Syntax $
   - m = sldistmean(X1, X2, mtype, ...)
   - m = sldistmean(X1, X2, w1, w2, mtype, ...)
 
 $ Arguments $
   - X1, X2:       The samples to compute the mean of pairwise distances
   - mtype:        The distance metric type
   - w1, w2:       The weights of samples in X1 and X2
   - m:            The mean value of all pairwise distances

 $ Description $
   - m = sldistmean(X1, X2, mtype, ...) computes the average value of 
     a specified type of distances by using a mathematical equivalent
     and fast way. It would be much faster than computing all pairwise
     distances and calculating their average.
     \*
     \t      Table. Supported Distance Types
     \h       name      &             description 
             'sqdist'   &  square distances d = ||x1 - x2||^2
             'wsqdist'  &  weighted square distances:
                           d = sum_k w_k (x1(k) - x2(k))^2 
                           the first extra parameter it a column vector
                           of weights on all components
             'quaddiff' &  distance in quadratic form:
                           d = (x1 - x2)^T Q (x1 - x2)
                           the first extra parameter is a quadratic form
                           matrix
     \*
     Please not that, if X1 and X2 have n1 an n2 samples respectively, then
     m = 1 /(n1 * n2) * sum_i sum_j d(X1(:,i), X2(:,j)).

   - m = sldistmean(X1, X2, w1, w2, mtype, ...) computes the weighted
     average value of the distances. The w1 and w2 assign weights to
     samples in X1 and X2 respectively. They should be row vectors of
     size 1 x n1 and 1 x n2.

 $ History $
   - Created by Dahua Lin, on Sep 20, 2006

CROSS-REFERENCE INFORMATION ^

This function calls:
  • sladdvec SLADDVEC adds a vector to columns or rows of a matrix
  • slcov SLCOV Compute the covariance matrix
  • slmean SLMEAN Compute the mean vector of samples
  • raise_lackinput RAISE_LACKINPUT Raises an error indicating lack of input argument
This function is called by:

SUBFUNCTIONS ^

SOURCE CODE ^

0001 function m = sldistmean(X1, X2, varargin)
0002 %SLDISTMEAN Uses fast method to compute means of pairwise distances
0003 %
0004 % $ Syntax $
0005 %   - m = sldistmean(X1, X2, mtype, ...)
0006 %   - m = sldistmean(X1, X2, w1, w2, mtype, ...)
0007 %
0008 % $ Arguments $
0009 %   - X1, X2:       The samples to compute the mean of pairwise distances
0010 %   - mtype:        The distance metric type
0011 %   - w1, w2:       The weights of samples in X1 and X2
0012 %   - m:            The mean value of all pairwise distances
0013 %
0014 % $ Description $
0015 %   - m = sldistmean(X1, X2, mtype, ...) computes the average value of
0016 %     a specified type of distances by using a mathematical equivalent
0017 %     and fast way. It would be much faster than computing all pairwise
0018 %     distances and calculating their average.
0019 %     \*
0020 %     \t      Table. Supported Distance Types
0021 %     \h       name      &             description
0022 %             'sqdist'   &  square distances d = ||x1 - x2||^2
0023 %             'wsqdist'  &  weighted square distances:
0024 %                           d = sum_k w_k (x1(k) - x2(k))^2
0025 %                           the first extra parameter it a column vector
0026 %                           of weights on all components
0027 %             'quaddiff' &  distance in quadratic form:
0028 %                           d = (x1 - x2)^T Q (x1 - x2)
0029 %                           the first extra parameter is a quadratic form
0030 %                           matrix
0031 %     \*
0032 %     Please not that, if X1 and X2 have n1 an n2 samples respectively, then
0033 %     m = 1 /(n1 * n2) * sum_i sum_j d(X1(:,i), X2(:,j)).
0034 %
0035 %   - m = sldistmean(X1, X2, w1, w2, mtype, ...) computes the weighted
0036 %     average value of the distances. The w1 and w2 assign weights to
0037 %     samples in X1 and X2 respectively. They should be row vectors of
0038 %     size 1 x n1 and 1 x n2.
0039 %
0040 % $ History $
0041 %   - Created by Dahua Lin, on Sep 20, 2006
0042 %
0043 
0044 %% parse and verify input arguments
0045 
0046 if nargin < 3
0047     raise_lackinput('sldistmean', 3);
0048 end
0049 
0050 if ~isnumeric(X1) || ~isnumeric(X2) || ndims(X1) ~= 2 || ndims(X2) ~= 2
0051     error('sltoolbox:invalidarg', ...
0052         'X1 and X2 should be numeric 2D matrices');
0053 end
0054 
0055 if ischar(varargin{1})
0056     mtype = varargin{1};
0057     if nargin == 3
0058         params = {};
0059     else
0060         params = varargin(2:end);
0061     end
0062     w1 = [];
0063     w2 = [];
0064 else
0065     w1 = varargin{1};
0066     w2 = varargin{2};
0067     
0068     n1 = size(X1, 2);
0069     n2 = size(X2, 2);
0070     if ~isequal(size(w1), [1 n1]) || ~isequal(size(w2), [1, n2])
0071         error('sltoolbox:invalidarg', ...
0072             'The size of w1 or w2 is illegal');
0073     end
0074     
0075     mtype = varargin{3};
0076     if nargin == 5
0077         params = {};
0078     else
0079         params = varargin(4:end);
0080     end
0081 end
0082 
0083 
0084 %% main skeleton
0085 
0086 switch mtype
0087     case {'sqdist', 'wsqdist'}
0088         d = check_samedim(X1, X2);
0089         if strcmp(mtype, 'sqdist')
0090             wc = [];
0091         else
0092             check_paramsnum(mtype, params, 1);
0093             wc = params{1};
0094             if ~isequal(size(wc), [d, 1])
0095                 error('sltoolbox:sizmismatch', ...
0096                     'The weights on components should be d x 1 vector');
0097             end
0098         end                
0099         
0100         vm1 = slmean(X1, w1, true);
0101         vm2 = slmean(X2, w2, true);
0102         vs1 = compute_vars(X1, vm1, w1);
0103         vs2 = compute_vars(X2, vm2, w2);
0104         vmd = vm1 - vm2;
0105         vsm = vmd .* vmd;
0106         
0107         if isempty(wc)
0108             m = sum(vsm + vs1 + vs2);
0109         else
0110             m = sum((vsm + vs1 + vs2) .* wc);
0111         end
0112                        
0113     case 'quaddiff'
0114         d = check_samedim(X1, X2);
0115         check_paramsnum(mtype, params, 1);
0116         Q = params{1};
0117         if ~isequal(size(Q), [d d])
0118             error('sltoolbox:sizmismatch', ...
0119                 'The Q matrix should be a d x d square matrix');
0120         end
0121         
0122         vm1 = slmean(X1, w1, true);
0123         vm2 = slmean(X2, w2, true);
0124         C1 = slcov(X1, w1, vm1, true);
0125         C2 = slcov(X2, w2, vm2, true);
0126         vmd = vm1 - vm2;
0127         
0128         m = vmd' * Q * vmd + sum(sum(Q .* (C1 + C2)));
0129                 
0130     otherwise
0131         error('sltoolbox:invalidarg', ...
0132             'Invalid metric type: %s', mtype);
0133 end
0134 
0135         
0136 %% Auxiliary functions
0137 
0138 function d = check_samedim(X1, X2)
0139 
0140 d = size(X1, 1);
0141 if d ~= size(X2, 1)
0142     error('sltoolbox:sizmismatch', ...
0143         'X1 and X2 have different sample dimensions');
0144 end
0145 
0146 function check_paramsnum(name, params, n)
0147 
0148 if length(params) ~= n
0149     error('sltoolbox:invalidarg', ...
0150         'For metric %s, it has %d extra parameters.', name, n);
0151 end
0152 
0153 function vs = compute_vars(X, vmean, w)
0154 
0155 DX = sladdvec(X, -vmean);
0156 vs = slmean(DX .* DX, w);
0157 
0158 
0159 
0160 
0161 
0162 
0163 
0164
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