%LPBALL_DIST Compute Lp distance to a mean%%     [F,G,H] = LPBALL_DIST(M,X,P,FRAC)%% Compute the maximum distance of objects X to the mean M, using Lp% distances with P. To make the distance a bit more robust, just a% fraction FRAC of the data is taken into account. The distance is% returned in F, the derivative in G and the Hessian in H.% 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 Netherlandsfunction [f,g,h] = lpball_dist(m,x,p,frac)if nargin<4	frac = [];end[n,d] = size(x);d = sum( abs(x - repmat(m,n,1)).^p ,2);if isempty(frac)	[f,I] = max(d);else	[f,I] = dd_threshold(d,1-frac);endif nargout>1	d = x(I,:) - m;	g =p*sign(d).*(abs(d).^(p-1));	if nargout>2		h = diag(p*(p-1)*sign(d).*(abs(d).^(p-2)));	endendreturn