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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 slmetric_pw
Home > sltoolbox > core > slmetric_pw.m

slmetric_pw

PURPOSE ^

SLMETRIC_PW Compute the metric between column vectors pairwisely

SYNOPSIS ^

function M = slmetric_pw(X1, X2, mtype, varargin)

DESCRIPTION ^

SLMETRIC_PW Compute the metric between column vectors pairwisely

 $ Syntax $
   - M = slmetric_pw(X1, X2, mtype);
   - M = slmetric_pw(X1, X2, mtype, ...);

 $ Description $
    - M = slmetric_pw(X1, X2, mtype) Computes the metrics between
    column vectors of X1 and X2 pairwisely, using the metric
    specified by mtype. If X1 has n1 columns, X2 has n2 columns, then
    the resultant M would be of size n1 x n2. The entry at i-th row
    and j-th column of M represents the metric between X1(:, i) and
    X2(:, j).

    - M = slmetric_pw(X1, X2, mtype, ...) Some metric types requires
    extra parameters, which should be specified in params.

    - The supported metrics of this function are listed as follows:
      \*
      \t  Table 1. The supported metrics                             \\
      \h     name     &       description                            \\
          'eucdist'   &  Euclidean distance: ||x - y||               \\         
          'sqdist'    &  Square of Euclidean distance: ||x - y||^2   \\
          'dotprod'   &  Canonical dot product: <x,y> = x^T * y      \\
          'nrmcorr'   &  Normalized correlation (cosine angle):
                         (x^T * y ) / (||x|| * ||y||)                \\
          'angle'     &  Angle between two vectors (in radian)       \\
          'quadfrm'   &  Quadratic form:  x^T * Q * y                
                         Q is specified in the 1st extra parameter   \\
          'quaddiff'  &  Quadratic form of difference:
                         (x - y)^T * Q * (x - y),                
                         Q is specified in the 1st extra parameter   \\
          'cityblk'   &  City block distance (abssum of difference)  \\
          'maxdiff'   &  Maximum absolute difference                 \\
          'mindiff'   &  Minimum absolute difference                 \\
          'wsqdist'   &  Weighted square of Euclidean distance       \\
                         \sum_i w_i (x_i - y_i)^2,  w = (w_1, ..., w_d)                     
                         the weights w is specified in 1st extra parameter 
                         as a length-d column vector                  \\
      \*

 $ Remarks $
   - X1 and X2 are both matrices with n1 column vectors and n2 column 
     vectors respectively. Then the resultant matrix M will be a n1 * n2
     matrix. The entry at i-th row and j-th column of M is the metric between
     the i-th column vector in X1 and the j-th column vector in X2.

 $ History $
   - Created by Dahua Lin on Dec 06th, 2005
   - Modified by Dahua Lin on Apr 21st, 2005
       - regularize the error reporting
   - Modified by Dahua Lin on Sep 11st, 2005
       - completely rewrite the core codes based on new mex computation 
         cores, and the runtime efficiency in both time and space is 
         significantly increased.

CROSS-REFERENCE INFORMATION ^

This function calls:
  • sladdrowcols SLADDROWCOLS Adds the vectors to all rows and all columns
  • sldiff_pw SLDIFF_PW Measures the pair-wise difference
  • slmulrowcols SLMULROWCOLS Multiplies the vectors to all rows and all columns
  • slmulvec SLMULVEC multiplies a vector to columns or rows of a matrix
  • raise_lackinput RAISE_LACKINPUT Raises an error indicating lack of input argument
This function is called by:
  • slkmeans SLKMEANS Performs K-Means Clustering on samples
  • slclassify_eucnn SLCLASSIFY_EUCNN Classifies samples using Euclidena-based NN
  • slhistmetric_pw SLHISTMETRIC_PW Computes distance metrics between histograms pairwisely
  • slvechist SLVECHIST Makes the histogram on prototype vectors by voting
  • slfindnn SLFINDNN Finds the nearest neighbors using specified strategy
  • slpwmetricgraph SLPWMETRICGRAPH Constructs a graph based on pairwise metrics
  • slkernel SLKERNEL Computes the kernel for samples
  • slgaussmdist SLGAUSSMDIST Computes the Malanobis distance between samples and centers
  • slscatter SLSCATTER Compute the scatter matrix

SUBFUNCTIONS ^

SOURCE CODE ^

0001 function M = slmetric_pw(X1, X2, mtype, varargin)
0002 %SLMETRIC_PW Compute the metric between column vectors pairwisely
0003 %
0004 % $ Syntax $
0005 %   - M = slmetric_pw(X1, X2, mtype);
0006 %   - M = slmetric_pw(X1, X2, mtype, ...);
0007 %
0008 % $ Description $
0009 %    - M = slmetric_pw(X1, X2, mtype) Computes the metrics between
0010 %    column vectors of X1 and X2 pairwisely, using the metric
0011 %    specified by mtype. If X1 has n1 columns, X2 has n2 columns, then
0012 %    the resultant M would be of size n1 x n2. The entry at i-th row
0013 %    and j-th column of M represents the metric between X1(:, i) and
0014 %    X2(:, j).
0015 %
0016 %    - M = slmetric_pw(X1, X2, mtype, ...) Some metric types requires
0017 %    extra parameters, which should be specified in params.
0018 %
0019 %    - The supported metrics of this function are listed as follows:
0020 %      \*
0021 %      \t  Table 1. The supported metrics                             \\
0022 %      \h     name     &       description                            \\
0023 %          'eucdist'   &  Euclidean distance: ||x - y||               \\
0024 %          'sqdist'    &  Square of Euclidean distance: ||x - y||^2   \\
0025 %          'dotprod'   &  Canonical dot product: <x,y> = x^T * y      \\
0026 %          'nrmcorr'   &  Normalized correlation (cosine angle):
0027 %                         (x^T * y ) / (||x|| * ||y||)                \\
0028 %          'angle'     &  Angle between two vectors (in radian)       \\
0029 %          'quadfrm'   &  Quadratic form:  x^T * Q * y
0030 %                         Q is specified in the 1st extra parameter   \\
0031 %          'quaddiff'  &  Quadratic form of difference:
0032 %                         (x - y)^T * Q * (x - y),
0033 %                         Q is specified in the 1st extra parameter   \\
0034 %          'cityblk'   &  City block distance (abssum of difference)  \\
0035 %          'maxdiff'   &  Maximum absolute difference                 \\
0036 %          'mindiff'   &  Minimum absolute difference                 \\
0037 %          'wsqdist'   &  Weighted square of Euclidean distance       \\
0038 %                         \sum_i w_i (x_i - y_i)^2,  w = (w_1, ..., w_d)
0039 %                         the weights w is specified in 1st extra parameter
0040 %                         as a length-d column vector                  \\
0041 %      \*
0042 %
0043 % $ Remarks $
0044 %   - X1 and X2 are both matrices with n1 column vectors and n2 column
0045 %     vectors respectively. Then the resultant matrix M will be a n1 * n2
0046 %     matrix. The entry at i-th row and j-th column of M is the metric between
0047 %     the i-th column vector in X1 and the j-th column vector in X2.
0048 %
0049 % $ History $
0050 %   - Created by Dahua Lin on Dec 06th, 2005
0051 %   - Modified by Dahua Lin on Apr 21st, 2005
0052 %       - regularize the error reporting
0053 %   - Modified by Dahua Lin on Sep 11st, 2005
0054 %       - completely rewrite the core codes based on new mex computation
0055 %         cores, and the runtime efficiency in both time and space is
0056 %         significantly increased.
0057 %
0058 
0059 
0060 %% parse and verify input arguments
0061 if nargin < 3
0062     raise_lackinput('slmetric_pw', 3);
0063 end
0064 mtype = lower(mtype);
0065 
0066 %% compute
0067 switch mtype        
0068     case {'eucdist', 'sqdist'}
0069         checkdim(X1, X2);
0070         sqs1 = sum(X1 .* X1, 1)';
0071         sqs2 = sum(X2 .* X2, 1);
0072         M = (-2) * X1' * X2;
0073         M = sladdrowcols(M, sqs2, sqs1);
0074         M(M < 0) = 0;                        
0075         if strcmp(mtype, 'eucdist')
0076             M = sqrt(M);
0077         end 
0078         
0079     case 'dotprod'
0080         checkdim(X1, X2);
0081         M = X1' * X2;
0082                 
0083     case {'nrmcorr', 'angle'}
0084         checkdim(X1, X2);
0085         M = X1' * X2;
0086         f1 = sqrt(sum(X1 .* X1, 1))';
0087         f2 = sqrt(sum(X2 .* X2, 1));
0088         f1(f1 < eps) = eps;  % prevent from being zeros
0089         f2(f2 < eps) = eps;
0090         f1 = 1 ./ f1;
0091         f2 = 1 ./ f2;
0092         M = slmulrowcols(M, f2, f1);        
0093         if strcmp(mtype, 'angle0')
0094             M = real(acos(M));
0095         end 
0096         
0097     case 'quadfrm'
0098         % parse parameters
0099         Q = varargin{1};
0100         [d1, d2] = size(Q);
0101         if size(X1, 1) ~= d1 || size(X2, 1) ~= d2
0102             error('sltoolbox:sizmismatch', ...
0103                 'The dimensions of X1 and X2 are not consistent with Q');
0104         end
0105         
0106         % compute
0107         M = X1' * Q * X2;
0108         
0109     case 'quaddiff'
0110         % parse parameters
0111         d = checkdim(X1, X2);
0112         Q = varargin{1};
0113         if ~isequal(size(Q), [d, d])
0114             error('sltoolbox:dimmismatch', ...
0115                 'The dimensions of X1 and X2 are not consistent with Q');
0116         end
0117         
0118         % compute
0119         qs1 = sum(X1 .* (Q * X1), 1)';
0120         qs2 = sum(X2 .* (Q * X2), 1);
0121         M = X1' * (-(Q + Q')) * X2;        
0122         M = sladdrowcols(M, qs2, qs1);
0123                 
0124     case 'cityblk'
0125         M = sldiff_pw(X1, X2, 'abssum');
0126         
0127     case 'maxdiff'
0128         M = sldiff_pw(X1, X2, 'maxdiff');
0129         
0130     case 'mindiff'
0131         M = sldiff_pw(X1, X2, 'mindiff');
0132                 
0133     case 'wsqdist'
0134         % parse parameters
0135         d = checkdim(X1, X2);
0136         w = varargin{1};
0137         if ~isequal(size(w), [d, 1])
0138             error('sltoolbox:sizmismatch', ...
0139                 'w is not a proper size column vector');
0140         end
0141 
0142         % compute
0143        wX1 = slmulvec(X1, w, 1);
0144        qs1 = sum(wX1 .* X1, 1)';
0145        clear wX1;
0146        wX2 = slmulvec(X2, w, 1);
0147        qs2 = sum(wX2 .* X2, 1);
0148        M = (-2) * X1' * wX2;
0149        clear wX2;
0150        M = sladdrowcols(M, qs2, qs1);
0151         
0152     otherwise
0153         error('sltoolbox:invalid_type', 'Unknown metric type %s', mtype);
0154         
0155 end
0156         
0157 %% Auxiliary function
0158 
0159 function d = checkdim(X1, X2)
0160 
0161 d = size(X1, 1);
0162 if d ~= size(X2, 1)
0163     error('sltoolbox:sizmismatch', ...
0164         'X1 and X2 have different sample dimensions');
0165 end
0166 
0167 
0168 
0169 
0170
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