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private/dtw.m

+function y=dtw(a,b)
+% DTW   Calculates the dynamic time warping distance.
+%     D=DTW(A,B) calculates the dynamic time warping (DTW) 
+%     distance between row vectors A and B. If A and B are 
+%     arrays, DTW distances are calculated for all rows in
+%     these array, thus D is a column vector of length(A).
+%     The size(A,1) has to match size(B,1).
+%
+%     Reference:
+%     Myers, C. S, Rabiner, L. R.:
+%     A comparative study of several dynamic time-warping algorithms 
+%     for connected word recognition, The Bell System Technical 
+%     Journal, 60(7), 1982, 1389-1409.
+%     FastDTW: Toward Accurate Dynamic Time Warping in Linear Time 
+%     and Space, Stan Salvador and Philip Chan. Intelligent 
+%     Data Analysis, 2007.
+
+% Copyright (c) 2008 by AMRON
+% Norbert Marwan, Potsdam University, Germany
+% http://www.agnld.uni-potsdam.de
+%
+% $Date$
+% $Revision$
+
+
+if size(a,1) ~= size(b,1)
+    error('Array''s dimension 1 does not match.')
+end
+
+
+Na = size(a,2); Nb = size(b,2);
+
+y = zeros(size(a,1),1);
+%h = waitbar(0, 'Calculation DTW distance');
+for k = 1:size(a,1), %if k/100 == fix(k/100), waitbar(k/size(a,1)), end
+    aa = a(k,:)'; bb = b(k,:)';
+    eucDis = (repmat(aa,1,Nb) - repmat(bb',Na,1)).^2; 
+
+    D = zeros(size(eucDis));
+    D(1,1) = eucDis(1,1);
+    D(2:Na,1) = eucDis(2:Na,1) + D((2:Na)-1,1);
+    D(1,2:Nb) = eucDis(1,2:Nb) + D(1,(2:Nb)-1);
+    for n = 2:Na
+        for m = 2:Nb
+            D(n,m) = eucDis(n,m) + min([D(n-1,m), D(n-1,m-1), D(n,m-1)]);
+        end
+    end
+
+    y(k) = D(Na,Nb);
+end
+%delete(h)

private/levenshtein.m

+function y=levenshtein(a,b)
+% LEVENSHTEIN   Calculates the Levenshtein distance.
+%     D=LEVENSHTEIN(A,B) calculates the Levenshtein distance
+%     between row vectors A and B. If A and B are arrays,
+%     Levenshtein distances are calculated for all rows in
+%     these array, thus D is a column vector of length(A).
+%     The size(A,1) has to match size(B,1).
+%
+%     Reference:
+%     Levenshtein, V. I.: 
+%     Binary codes capable of correcting deletions, insertions, 
+%     and reversals, Doklady Akademii Nauk SSSR, 163(4), 1965, 
+%     845-848, 1965 (Russian). 
+%     English in: Soviet Physics Doklady, 10(8), 1966, 707-710.
+
+% Copyright (c) 2008 by AMRON
+% Norbert Marwan, Potsdam University, Germany
+% http://www.agnld.uni-potsdam.de
+%
+% $Date$
+% $Revision$
+
+if size(a,1) ~= size(b,1)
+    error('Array''s dimension 1 does not match.')
+end
+
+
+Na = size(a,2); Nb = size(b,2);
+
+y = zeros(size(a,1),1);
+
+for k = 1:size(a,1)
+    D = zeros([Na+1, Nb+1]);
+    D(1,:) = 0:Nb; D(:,1) = 0:Na;
+
+    for i = 2:Na + 1
+       for j = 2:Nb + 1
+          cost = (b(k, j-1) ~= a(k, i-1));
+          D(i,j)=min([D(i-1,j-1) + cost, D(i-1,j)+1, D(i,j-1)+1]);
+       end
+    end
+    y(k) = D(end,end);
+end