function k = knn_optk(D,d)%KNN_OPTK Optimization of k for the knndd%% k = knn_optk(D,d)%% Optimize the k for the knndd using leave-one-out density% estimation. D is the distance matrix of the original data,% d is the dimensionality of the data.% Copyright: D.M.J. Tax, D.M.J.Tax@prtools.org% Faculty EWI, Delft University of Technology% P.O. Box 5031, 2600 GA Delft, The Netherlands% avoid zero distances:smallD = 1e-20;% find the nearest neighbors in the training set:n = size(D,1);D = sort(+D,2);D(:,1) = []; % smallest distance is always 0: so remove that% find the volume of the k-nn hypersphere:logVsph = volsphere(d,1,1);s = warning('off');  % log of zero is no disaster here...	logDr = logVsph + d*log(D)/2;warning(s);Dr = exp(logDr);% the density becomes:Dr(Dr==0) = smallD;vol = repmat((1:n-1),n,1) ./ Dr;% And the loglikelihood:s = warning('off');  % again log of zero is no disaster here...	vol  = sum(log(vol),1);warning(s);% take the maximum:[maxvol,k] = max(vol);%vol  = std(log(vol),1)%[maxvol,k] = min(vol);return