%KLSYMDIVERGENCE symmetric Jensen-Shannon redundancy measure for %categorical-discrete data based on Kullback-Leibler divergence.%   KL = KLSYMDIVERGENCE(X,Y) returns the Jensen-Shannon divergence between %   the two column vectors X and Y containing categorical measures.%%   The Jensen-Shannon divergence [1] also known as symmetric %   Kullback-Leibler divergence, is a measure that averages%   Kullback-Leibler divergence [2][3] of both (X,Y) and (Y,X);%%   It is important to remark that the implementation introduced in this %   script allows to compute the Jensen-Shannon divergence directly on two %   column vectors containing categorical data instead of requiring their %   probability distributions as inputs. The number of categories (distinct%   values) per vector must be the same.%%   Joaquin Go?i <jgoni@unav.es> & %   I?igo Martincorena <imartincore@alumni.unav.es>%   University of Navarra - Dpt. of Physics and Applied Mathematics &%   Centre for Applied Medical Research. Pamplona (Spain).%%   December 13th, 2007. Information Theory Toolbox v1.0%%   Example:%   %    x = [1;2;2;2;0;0;1;0;1;2];%    y = [1;2;2;2;2;1;0;2;1;0];%    klsym = klsymdivergence(x,y);%%   Citation:%%   If you use them for your academic research work,please kindly cite this %   toolbox as: %   Joaquin Go?i, I?igo Martincorena. Information Theory Toolbox v1.0.  %   University of Navarra - Dpt. of Physics and Applied Mathematics & %   Centre for Applied Medical Research. Pamplona (Spain).%%   References%   [1] Jensen-Shannon Divergence and Hilbert space embedding, Bent Fuglede %   and Flemming Tops?e University of Copenhagen, Department of Mathematics%   [2] Kullback, S., and Leibler, R. A., 1951, On information and %   sufficiency, Annals of Mathematical Statistics 22: 79-86.%   [3] http://en.wikipedia.org/wiki/Kullback-Leibler_divergencefunction klsym = klsymdivergence (x,y)lambda = 0.5;klsym = lambda*kldivergence(x,y) + (1-lambda)*kldivergence(y,x);    %average of the two possible KL divergences for vectors x and y