mds.m

best routing protocol

% MDS based on distance matrix ALGORITHM
%
% function [Y,eigenvals] = dist_pca(D, dim)
%
% D = distance as N x N matrix ( N = #points)
% dim = embedding dimensionality
% y = embedding as  N x dim matrix
function [y,eigenvals] = mds(D,dim)
    S = D.^2; %the squared distance
    N = length(S);
    g = gramMatrix(S);
    [mu, lam] = eig(g);
    eigenvals = dot(lam,eye(N));
    rep_lam = repmat(eigenvals(N-dim+1:N),N,1);
    new_mu = mu(:,N-dim+1:N); % last d col of  mu
    y = sqrt(rep_lam).*new_mu;
    
function g = gramMatrix(s)
%s is the squared distance matrix
    N = length(s);
    over_i = sum(s);
    total = sum(over_i);
    Gjj = (over_i - total/N/2) / N;
    rep_Gjj = repmat(Gjj,N,1);
    rep_Gii = rep_Gjj';
    g = (rep_Gjj+rep_Gii-s)./2;