%PLOTGTM Plot a trained GTM mapping in 1D, 2D or 3D
%
% H = PLOTGTM (W)
%
% INPUT
% W Trained GTM mapping
%
% OUTPUT
% H Graphics handles
%
% DESCRIPTION
% Creates a plot of the GTM manifold in the original data space, but at
% most in 3D.
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% GTM, SOM, PRPLOTSOM
% (c) Dick de Ridder, 2003
% Information & Communication Theory Group
% Faculty of Electrical Engineering, Mathematics and Computer Science
% Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands
function ret = plotgtm (w)
global GRIDSIZE;
gs = [ 100 10 5 ]+1;
if (~ismapping(w)) | (~strcmp(get(w,'name'),'GTM'))
error ('can only plot a GTM mapping');
else
data = getdata(w); K = data{1}; M = data{2};
W = data{3}; sigma = data{4}; mapto = data{5};
end;
[d,D] = size(w); KK = prod(K); MM = prod(M);
phi_mu = makegrid(M,D); % Basis function centers.
phi_sigma = 2/(mean(M)-1); % Basis function widths.
% For plotting.
if (D == 1),
Kplot = gs(1); sz = 1/(gs(1)-1);
xplot = 0:sz:1;
elseif (D == 2)
Kplot = gs(2)^2; sz = 1/(gs(2)-1);
[xx,yy] = meshgrid(0:sz:1,0:sz:1);
xplot = [reshape(xx,1,Kplot); reshape(yy,1,Kplot)];
elseif (D >= 3)
Kplot = gs(3)^3; sz = 1/(gs(3)-1);
[xx,yy,zz] = meshgrid(0:sz:1,0:sz:1,0:sz:1);
xplot = [reshape(xx,1,Kplot); reshape(yy,1,Kplot); reshape(zz,1,Kplot)];
D = 3;
end;
% Pre-calculate Phiplot.
for j = 1:Kplot
for i = 1:MM
Phiplot(i,j) = exp(-(xplot(1:D,j)-phi_mu(1:D,i))'*(xplot(1:D,j)-phi_mu(1:D,i))/(phi_sigma^2));
end;
end;
% Plot grid lines.
yplot = W(1:d,:)*Phiplot;
hold on; h = [];
if (D == 1)
h = [h plot(yplot(1,:),yplot(2,:),'k-')];
elseif (D == 2)
for k = 1:gs(2)
h = [h plot(yplot(1,(k-1)*gs(2)+1:k*gs(2)),yplot(2,(k-1)*gs(2)+1:k*gs(2)),'k-')];
h = [h plot(yplot(1,k:gs(2):end),yplot(2,k:gs(2):end),'k-')];
end;
elseif (D >= 3)
for k = 1:gs(3)
for l = 1:gs(3)
h = [h plot3(yplot(1,(k-1)*gs(3)^2+(l-1)*gs(3)+1:(k-1)*gs(3)^2+l*gs(3)),...
yplot(2,(k-1)*gs(3)^2+(l-1)*gs(3)+1:(k-1)*gs(3)^2+l*gs(3)),...
yplot(3,(k-1)*gs(3)^2+(l-1)*gs(3)+1:(k-1)*gs(3)^2+l*gs(3)),'k-')];
h = [h plot3(yplot(1,(k-1)*gs(3)^2+l:gs(3):k*gs(3)^2),...
yplot(2,(k-1)*gs(3)^2+l:gs(3):k*gs(3)^2),...
yplot(3,(k-1)*gs(3)^2+l:gs(3):k*gs(3)^2),'k-')];
h = [h plot3(yplot(1,(k-1)*gs(3)+l:gs(3)^2:end),...
yplot(2,(k-1)*gs(3)+l:gs(3)^2:end),...
yplot(3,(k-1)*gs(3)+l:gs(3)^2:end),'k-')];
end;
end;
view(3);
end;
set (h,'LineWidth',2);
hold off;
if (nargout > 0), ret = h; end;
return
% GRID = MAKEGRID (K,D)
%
% Create a KK = prod(K)-dimensional grid with dimensions K(1), K(2), ... of
% D-dimensional uniformly spaced grid points on [0,1]^prod(K), and store it
% as a D x KK matrix X.
function grid = makegrid (K,D)
KK = prod(K);
for h = 1:D
xx{h} = 0:(1/(K(h)-1)):1; % Support point means
end;
% Do that voodoo / that you do / so well...
if (D==1)
xm = xx;
else
cmd = '[';
for h = 1:D-1, cmd = sprintf ('%sxm{%d}, ', cmd, h); end;
cmd = sprintf ('%sxm{%d}] = ndgrid(', cmd, D);
for h = 1:D-1, cmd = sprintf ('%sxx{%d}, ', cmd, h); end;
cmd = sprintf ('%sxx{%d});', cmd, D); eval(cmd);
end;
cmd = 'mm = zeros(D, ';
for h = 1:D-1, cmd = sprintf ('%s%d, ', cmd, K(h)); end;
cmd = sprintf ('%s%d);', cmd, K(D)); eval (cmd);
for h = 1:D
cmd = sprintf ('mm(%d,', h);
for g = 1:D-1, cmd = sprintf ('%s:,', cmd); end;
cmd = sprintf ('%s:) = xm{%d};', cmd, h); eval (cmd);
end;
grid = reshape(mm,D,KK);
return