%MDS_INIT Initialization for MDS (variants of Sammon) mapping
%
% Y = MDS_INIT (D,N,INIT)
%
% INPUT
% D Square dissimilarity matrix of the size M x M
% N Desired output dimensionality (optional; default: 2)
% INIT Initialization method (optional; default: 'randnp')
%
% OUTPUT
% Y Initial configuration for the MDS method
%
% DESCRIPTION
% Finds a configuration of points Y in an N-dimensional space, used as
% a starting configuration for an MDS mapping based on the distance matrix D.
% The parameter INIT is a string standing for the initialization method:
%
% 'randp' - linear mapping of D on n randomly (uniform distribution) chosen vectors
% 'randnp' - linear mapping of D on n randomly (normal distribution) chosen vectors
% 'randv' - randomly (uniform distribution) chosen vectors from D
% 'maxv' - n columns of D with the largest variances
% 'kl' - Karhunen Loeve projection (linear mapping) of D (first n eigenvectors)
% 'cs' - Classical Scaling
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% MAPPINGS, MDS_CS, MDS
%
% Undocumented use: if W is an already trained MDS, then for adding new points Dnew
% W = mds_init(W,Ystart)
% would assign Ystart as an initial configuration for he new MDS.
%
%
% Copyright: Elzbieta Pekalska, ela@ph.tn.tudelft.nl, 2000-2003
% Faculty of Applied Sciences, Delft University of Technology
%
function [Y,w] = mds_init(D,n,initm)
w = [];
if isa(D,'prmapping') % assign an initial configuration for the new MDS
ww = getdata(D);
if size(n,2) ~= size(ww{1},2),
error('The dimensionality of the MDS map and the initial configuration does not match.')
end
if nargin < 3,
;
end
ww{6} = n;
Y = setdata(D,ww);
return
else
if nargin < 2, n = 2; end
if nargin < 3, initm = 'randnp'; end
if isa(D,'prdataset'),
lab = getlab(D);
D=+D;
end
D = remove_nan(D);
[m,mm] = size(D);
w = [];
switch initm
case 'randp',
Y = D * rand(mm,n)/10;
case 'randnp',
Y = D * randn(mm,n)/10;
case 'randv',
Y = rand(m,n);
case 'maxv',
U = std(D);
[V,I] = sort(-U);
Y = D(:,I(1:n));
case 'kl',
options.disp = 0;
[E,L] = eigs(prcov(+D),n,'lm',options);
Y = D * E/100;
case 'cs',
if length(n) == 1 & m == mm,
w = mds_cs(D,n);
Y = D*w;
else
error('The CS initialization is not possible');
end
otherwise,
error('The possible initializations are: randp, randnp, randv, maxv, cs or kl.');
end
end
return;
function D = remove_nan(D)
% Remove all appearing NaN's by replacing them by the nearest neighbors.
%
[m,mm] = size(D);
nanindex = find(isnan(D(:)));
if ~isempty(nanindex),
for i=1:m
K = find(isnan(D(i,:)));
I = 1:mm;
[md,kk] = min(D(i,:));
if md < eps,
I(kk) = [];
end
D(i,K) = min(D(i,I));
end
% check whether D has a zero diagonal
if length(intersect(find(D(:) < eps), 1:m+1:(m*m))) >= m,
D = (D+D')/2;
end
end