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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 slhistmetric_pw
Home > sltoolbox > discrete > slhistmetric_pw.m

slhistmetric_pw

PURPOSE ^

SLHISTMETRIC_PW Computes distance metrics between histograms pairwisely

SYNOPSIS ^

function D = slhistmetric_pw(H1, H2, mtype, varargin)

DESCRIPTION ^

SLHISTMETRIC_PW Computes distance metrics between histograms pairwisely

 $ Syntax $
   - D = slhistmetric_pw(H1, H2, mtype, ...)

 $ Arguments $
   - H1, H2:       The matrices of histogram sets (d1 x n1, d2 x n2)
   - mtype:        The metric type
   - D:            The resulting pairwise metric matrix (n1 x n2)

 $ Description $
   - D = slhistmetric_cp(H1, H2, mtype, ...) computes the distance metrics
     between all histograms in H1 and H2 pairwisely. If H1 and H2 have
     n1 and n2 bins respectively, then D will be an n1 x n2 matrix.
     The function support following types of histogram distances:
     \*
     \t   Table.  The Histogram Metrics
     \h      name     &          description
          'L1dist'    &  The sum of absolute differences: 
                         d = sum |h1(i) - h2(i)|               \\
          'L2dist'    &  Euclidean distance: 
                         d = sqrt(sum( (h1(i) - h2(i))^2 ))    \\
          'quaddist'  &  Quadratic-Form distance: 
                         d = sqrt((h1 - h2)^T * Q * (h1 - h2)) \\
                         use Q (d x d matrix) as the first extra param.
          'hamming'   &  Hamming distance with threshold
                         ht1 = h1 > t
                         ht2 = h2 > t
                         d = sum(ht1 ~= ht2)                  
                         use threshold t as the first extra param.\\
          'intersect' &  Histogram Intersection: 
                         d = 1 - 
                         sum min(h1(i), h2(i))) / sum h2(i) \\
          'chisq'     &  Chi-Square Distance:
                         d = sum (h1(i) - h2(i))^2 / (2 * (h1(i)+h2(i)) \\
          'kolsm'     &  Kolmogorov-Smirnov distance: 
                         d = max |F1(i) - F2(i)| 
                         only suitable for scalar histogram.   \\
          'kramvon'   &  Kramer/Von Mises:
                         d = sum (F1(i) - F2(i))^2              \\
          'kldiv'     &  Kull-back Leibler divergence
                         d = sum h1(i) log h1(i) / h2(i)        \\
          'jeffrey'   &  Jeffrey divergence
                         d = KL(h1, (h1+h2)/2) + KL(h2, (h1+h2)/2) \\
     \*     
          
 $ History $
   - Created by Dahua Lin, on Sep 18, 2006

CROSS-REFERENCE INFORMATION ^

This function calls:
  • sladdvec SLADDVEC adds a vector to columns or rows of a matrix
  • sldiff_pw SLDIFF_PW Measures the pair-wise difference
  • slmetric_pw SLMETRIC_PW Compute the metric between column vectors pairwisely
  • raise_lackinput RAISE_LACKINPUT Raises an error indicating lack of input argument
This function is called by:

SUBFUNCTIONS ^

SOURCE CODE ^

0001 function D = slhistmetric_pw(H1, H2, mtype, varargin)
0002 %SLHISTMETRIC_PW Computes distance metrics between histograms pairwisely
0003 %
0004 % $ Syntax $
0005 %   - D = slhistmetric_pw(H1, H2, mtype, ...)
0006 %
0007 % $ Arguments $
0008 %   - H1, H2:       The matrices of histogram sets (d1 x n1, d2 x n2)
0009 %   - mtype:        The metric type
0010 %   - D:            The resulting pairwise metric matrix (n1 x n2)
0011 %
0012 % $ Description $
0013 %   - D = slhistmetric_cp(H1, H2, mtype, ...) computes the distance metrics
0014 %     between all histograms in H1 and H2 pairwisely. If H1 and H2 have
0015 %     n1 and n2 bins respectively, then D will be an n1 x n2 matrix.
0016 %     The function support following types of histogram distances:
0017 %     \*
0018 %     \t   Table.  The Histogram Metrics
0019 %     \h      name     &          description
0020 %          'L1dist'    &  The sum of absolute differences:
0021 %                         d = sum |h1(i) - h2(i)|               \\
0022 %          'L2dist'    &  Euclidean distance:
0023 %                         d = sqrt(sum( (h1(i) - h2(i))^2 ))    \\
0024 %          'quaddist'  &  Quadratic-Form distance:
0025 %                         d = sqrt((h1 - h2)^T * Q * (h1 - h2)) \\
0026 %                         use Q (d x d matrix) as the first extra param.
0027 %          'hamming'   &  Hamming distance with threshold
0028 %                         ht1 = h1 > t
0029 %                         ht2 = h2 > t
0030 %                         d = sum(ht1 ~= ht2)
0031 %                         use threshold t as the first extra param.\\
0032 %          'intersect' &  Histogram Intersection:
0033 %                         d = 1 -
0034 %                         sum min(h1(i), h2(i))) / sum h2(i) \\
0035 %          'chisq'     &  Chi-Square Distance:
0036 %                         d = sum (h1(i) - h2(i))^2 / (2 * (h1(i)+h2(i)) \\
0037 %          'kolsm'     &  Kolmogorov-Smirnov distance:
0038 %                         d = max |F1(i) - F2(i)|
0039 %                         only suitable for scalar histogram.   \\
0040 %          'kramvon'   &  Kramer/Von Mises:
0041 %                         d = sum (F1(i) - F2(i))^2              \\
0042 %          'kldiv'     &  Kull-back Leibler divergence
0043 %                         d = sum h1(i) log h1(i) / h2(i)        \\
0044 %          'jeffrey'   &  Jeffrey divergence
0045 %                         d = KL(h1, (h1+h2)/2) + KL(h2, (h1+h2)/2) \\
0046 %     \*
0047 %
0048 % $ History $
0049 %   - Created by Dahua Lin, on Sep 18, 2006
0050 %
0051 
0052 %% parse and verify input arguments
0053 
0054 if nargin < 3
0055     raise_lackinput('slhistmetric_cp', 3);
0056 end
0057 if ~isnumeric(H1) || ~isnumeric(H2) || ndims(H1) ~= 2 || ndims(H2) ~= 2
0058     error('sltoolbox:invalidarg', ...
0059         'H1 and H2 should be 2D numeric matrices');
0060 end
0061 
0062 
0063 %% main delegation
0064 
0065 switch mtype
0066     case 'L1dist'
0067         checkhistdim(H1, H2);
0068         D = slmetric_pw(H1, H2, 'cityblk');
0069         
0070     case 'L2dist'
0071         checkhistdim(H1, H2);
0072         D = slmetric_pw(H1, H2, 'eucdist');
0073                 
0074     case 'quaddist'
0075         if length(varargin) ~= 1
0076             error('sltoolbox:invalidarg', ...
0077                 'quaddist has one extra parameter Q');
0078         end
0079         checkhistdim(H1, H2);
0080         D = slmetric_pw(H1, H2, 'quaddiff', varargin{1});
0081         D = sqrt(D);
0082         
0083     case 'hamming'
0084         checkhistdim(H1, H2);
0085         if length(varargin) ~= 1
0086             error('sltoolbox:invalidarg', ...
0087                 'quaddist has one extra parameter t');
0088         end
0089         t = varargin{1};
0090         D = sldiff_pw(double(H1 > t), double(H2 > t), 'abssum');
0091         
0092     case 'intersect'
0093         checkhistdim(H1, H2);
0094         D = histmetricpw_core(H1, H2, 1);
0095                 
0096     case 'chisq'
0097         checkhistdim(H1, H2);
0098         D = histmetricpw_core(H1, H2, 2);        
0099         
0100     case 'kolsm'
0101         checkhistdim(H1, H2);
0102         F1 = cumsum(H1, 1);
0103         F2 = cumsum(H2, 1);
0104         D = sldiff_pw(F1, F2, 'maxdiff');
0105         
0106     case 'kramvon'
0107         checkhistdim(H1, H2);
0108         F1 = cumsum(H1, 1);
0109         F2 = cumsum(H2, 1);
0110         D = slmetric_pw(F1, F2, 'sqdist');        
0111         
0112     case 'kldiv'
0113         checkhistdim(H1, H2);
0114         D = kldivergence(H1, H2);
0115         
0116     case 'jeffrey'
0117         checkhistdim(H1, H2);
0118         D = histmetricpw_core(H1, H2, 3);
0119                       
0120     otherwise
0121         error('sltoolbox:invalidarg', ...
0122             'Invalid histogram metric type: %s', mtype);
0123 end
0124         
0125 
0126 %% Auxiliary functions
0127 
0128 function d = checkhistdim(H1, H2)
0129 
0130 d = size(H1, 1);
0131 if size(H2, 1) ~= d
0132     error('sltoolbox:sizmismatch', 'H1 and H2 have different dimensions.');
0133 end
0134 
0135 function D = kldivergence(H1, H2)
0136 
0137 V = zeros(size(H1));
0138 not_zero = H1 > 0;
0139 V(not_zero) = H1(not_zero) .* log(H1(not_zero));
0140 v1 = sum(V, 1)';
0141 clear V;
0142 
0143 H2(~not_zero) = 1;
0144 L2 = log(H2);
0145 D = -H1' * L2;
0146 D = sladdvec(D, v1, 1);
0147 
0148 
0149 
0150
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