%CONDENTROPY conditional entropy between two categorical variables%   given (X,Y), the conditional entropy H(Y|X) quantifies the remaining entropy (i.e. uncertainty) %   of a random variable Y given that the value of a second random variable%   X is known [1]%%   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%%   h = condentropy(x,y) for x,y being column vectors with categorical measures, it%   computes the conditional entropy [1][2] H(Y|X) found on Y given X.%   %   x,y variables must be column vectors with categorical data. The number%   of categories per variable can be different.%%   Example:%%       x=[1;2;2;2;0;0;1;0;1;2];%       y=[1;2;2;2;2;1;0;2;1;0];%       h = condentropy(x,y) returns H(y|x)%%   References%   [1] C. E. Shannon, A mathematical theory of communication, Bell System Technical Journal, vol. 27, pp. 379-423 and 623-656, July and October, 1948.%   [2] http://en.wikipedia.org/wiki/Conditional_entropyfunction h = condentropy(x,y)if ~(isvector(x) && isvector(y))    %x,y must be one-dimensional vectors    disp('Error: input data must be one dimensional vectors')    h = nan;elseif size(x)~=size(y) %vectors must have the same size    disp('Error: input vectors must have the same size')    h = nan;else    valuesX = unique(x);    %different values found in vector x    valuesY = unique(y);    %different values found in vector y        numValues = numel(x);   %number of elements contained on each vector    h = 0;  %initial value of conditional entropy        for i = valuesX'  %for each different value found in x                iOcurrences = find(x==i);   %ocurrences in x being i        numOcurrences = numel(iOcurrences); %number of ocurrences in x being i        pi = numOcurrences / numValues;  %probability p(i)                for j = valuesY'   %for each different value found in y            jOcurrences = numel(find(y(iOcurrences)==j));   %ocurrences in subset of y being j            if jOcurrences > 0  %if there where at at least one ocurrence                pjcondi = jOcurrences / numOcurrences;  %partial conditional entropy for specific values of x and y                h = h - pi*pjcondi*log2(pjcondi);   %cumulative of partial cont            end        end     endend