comparison toolboxes/MIRtoolbox1.3.2/somtoolbox/cca.m @ 0:e9a9cd732c1e tip

first hg version after svn

+function [P] = cca(D, P, epochs, Mdist, alpha0, lambda0)
+
+%CCA Projects data vectors using Curvilinear Component Analysis.
+%
+% P = cca(D, P, epochs, [Dist], [alpha0], [lambda0])
+%
+%  P = cca(D,2,10);           % projects the given data to a plane
+%  P = cca(D,pcaproj(D,2),5); % same, but with PCA initialization
+%  P = cca(D, 2, 10, Dist);   % same, but the given distance matrix is used
+%  
+%  Input and output arguments ([]'s are optional):
+%   D          (matrix) the data matrix, size dlen x dim
+%              (struct) data or map struct            
+%   P          (scalar) output dimension
+%              (matrix) size dlen x odim, the initial projection
+%   epochs     (scalar) training length
+%   [Dist]     (matrix) pairwise distance matrix, size dlen x dlen.
+%                       If the distances in the input space should
+%                       be calculated otherwise than as euclidian
+%                       distances, the distance from each vector
+%                       to each other vector can be given here,
+%                       size dlen x dlen. For example PDIST
+%                       function can be used to calculate the
+%                       distances: Dist = squareform(pdist(D,'mahal'));
+%   [alpha0]   (scalar) initial step size, 0.5 by default
+%   [lambda0]  (scalar) initial radius of influence, 3*max(std(D)) by default
+%  
+%   P          (matrix) size dlen x odim, the projections
+%
+% Unknown values (NaN's) in the data: projections of vectors with
+% unknown components tend to drift towards the center of the
+% projection distribution. Projections of totally unknown vectors are
+% set to unknown (NaN).
+%
+% See also SAMMON, PCAPROJ. 
+
+% Reference: Demartines, P., Herault, J., "Curvilinear Component
+%   Analysis: a Self-Organizing Neural Network for Nonlinear
+%   Mapping of Data Sets", IEEE Transactions on Neural Networks, 
+%   vol 8, no 1, 1997, pp. 148-154.
+
+% Contributed to SOM Toolbox 2.0, February 2nd, 2000 by Juha Vesanto
+% Copyright (c) by Juha Vesanto
+% http://www.cis.hut.fi/projects/somtoolbox/
+
+% juuso 171297 040100
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Check arguments 
+
+error(nargchk(3, 6, nargin)); % check the number of input arguments
+
+% input data
+if isstruct(D), 
+  if strcmp(D.type,'som_map'), D = D.codebook; else D = D.data; end
+end
+[noc dim] = size(D);
+noc_x_1  = ones(noc, 1); % used frequently
+me = zeros(1,dim); st = zeros(1,dim);
+for i=1:dim,
+  me(i) = mean(D(find(isfinite(D(:,i))),i));
+  st(i) = std(D(find(isfinite(D(:,i))),i));
+end
+
+% initial projection
+if prod(size(P))==1, 
+  P = (2*rand(noc,P)-1).*st(noc_x_1,1:P) + me(noc_x_1,1:P); 
+else
+  % replace unknown projections with known values
+  inds = find(isnan(P)); P(inds) = rand(size(inds));
+end
+[dummy odim] = size(P);
+odim_x_1  = ones(odim, 1); % this is used frequently
+
+% training length
+train_len = epochs*noc;
+
+% random sample order
+rand('state',sum(100*clock));
+sample_inds = ceil(noc*rand(train_len,1));
+
+% mutual distances
+if nargin<4 | isempty(Mdist) | all(isnan(Mdist(:))),
+  fprintf(2, 'computing mutual distances\r');
+  dim_x_1 = ones(dim,1);
+  for i = 1:noc,
+    x = D(i,:); 
+    Diff = D - x(noc_x_1,:);
+    N = isnan(Diff);
+    Diff(find(N)) = 0; 
+    Mdist(:,i) = sqrt((Diff.^2)*dim_x_1);
+    N = find(sum(N')==dim); %mutual distance unknown
+    if ~isempty(N), Mdist(N,i) = NaN; end
+  end
+else
+  % if the distance matrix is output from PDIST function
+  if size(Mdist,1)==1, Mdist = squareform(Mdist); end
+  if size(Mdist,1)~=noc, 
+    error('Mutual distance matrix size and data set size do not match'); 
+  end
+end
+
+% alpha and lambda
+if nargin<5 | isempty(alpha0) | isnan(alpha0), alpha0 = 0.5; end
+alpha = potency_curve(alpha0,alpha0/100,train_len);
+
+if nargin<6 | isempty(lambda0) | isnan(lambda0), lambda0 = max(st)*3; end
+lambda = potency_curve(lambda0,0.01,train_len);
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Action
+
+k=0; fprintf(2, 'iterating: %d / %d epochs\r',k,epochs);
+
+for i=1:train_len, 
+  
+  ind = sample_inds(i);     % sample index
+  dx = Mdist(:,ind);        % mutual distances in input space
+  known = find(~isnan(dx)); % known distances
+
+  if ~isempty(known),
+    % sample vector's projection
+    y = P(ind,:);                 
+
+    % distances in output space
+    Dy = P(known,:) - y(noc_x_1(known),:); 
+    dy = sqrt((Dy.^2)*odim_x_1);           
+  
+    % relative effect
+    dy(find(dy==0)) = 1;        % to get rid of div-by-zero's
+    fy = exp(-dy/lambda(i)) .* (dx(known) ./ dy - 1);
+
+    % Note that the function F here is e^(-dy/lambda)) 
+    % instead of the bubble function 1(lambda-dy) used in the 
+    % paper.
+    
+    % Note that here a simplification has been made: the derivatives of the
+    % F function have been ignored in calculating the gradient of error
+    % function w.r.t. to changes in dy.
+    
+    % update
+    P(known,:) = P(known,:) + alpha(i)*fy(:,odim_x_1).*Dy;
+  end
+
+  % track
+  if rem(i,noc)==0, 
+    k=k+1; fprintf(2, 'iterating: %d / %d epochs\r',k,epochs);
+  end
+
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% clear up
+
+% calculate error
+error = cca_error(P,Mdist,lambda(train_len));
+fprintf(2,'%d iterations, error %f          \n', epochs, error);
+
+% set projections of totally unknown vectors as unknown
+unknown = find(sum(isnan(D)')==dim);
+P(unknown,:) = NaN;
+
+return;
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% tips
+
+% to plot the results, use the code below
+
+%subplot(2,1,1), 
+%switch(odim), 
+%  case 1, plot(P(:,1),ones(dlen,1),'x')
+%  case 2, plot(P(:,1),P(:,2),'x'); 
+%  otherwise, plot3(P(:,1),P(:,2),P(:,3),'x'); rotate3d on
+%end
+%subplot(2,1,2), dydxplot(P,Mdist);
+
+% to a project a new point x in the input space to the output space
+% do the following:
+
+% Diff = D - x(noc_x_1,:); Diff(find(isnan(Diff))) = 0; 
+% dx = sqrt((Diff.^2)*dim_x_1);
+% p = project_point(P,x,dx); % this function can be found from below
+% tlen = size(p,1);
+% plot(P(:,1),P(:,2),'bx',p(tlen,1),p(tlen,2),'ro',p(:,1),p(:,2),'r-')
+
+% similar trick can be made to the other direction
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% subfunctions
+
+function vals = potency_curve(v0,vn,l)
+
+  % curve that decreases from v0 to vn with a rate that is 
+  % somewhere between linear and 1/t
+  vals = v0 * (vn/v0).^([0:(l-1)]/(l-1));
+
+
+function error = cca_error(P,Mdist,lambda)
+
+  [noc odim] = size(P);
+  noc_x_1 = ones(noc,1);
+  odim_x_1 = ones(odim,1);
+
+  error = 0;
+  for i=1:noc,
+    known = find(~isnan(Mdist(:,i)));
+    if ~isempty(known),   
+      y = P(i,:);                 
+      Dy = P(known,:) - y(noc_x_1(known),:);
+      dy = sqrt((Dy.^2)*odim_x_1);
+      fy = exp(-dy/lambda);
+      error = error + sum(((Mdist(known,i) - dy).^2).*fy);
+    end
+  end
+  error = error/2;
+
+
+function [] = dydxplot(P,Mdist)
+
+  [noc odim] = size(P);
+  noc_x_1 = ones(noc,1);
+  odim_x_1 = ones(odim,1);
+  Pdist = zeros(noc,noc);
+    
+  for i=1:noc,
+    y = P(i,:);                 
+    Dy = P - y(noc_x_1,:);
+    Pdist(:,i) = sqrt((Dy.^2)*odim_x_1);
+  end
+
+  Pdist = tril(Pdist,-1); 
+  inds = find(Pdist > 0); 
+  n = length(inds);
+  plot(Pdist(inds),Mdist(inds),'.');
+  xlabel('dy'), ylabel('dx')
+
+
+function p = project_point(P,x,dx)
+
+  [noc odim] = size(P);
+  noc_x_1 = ones(noc,1);
+  odim_x_1 = ones(odim,1);
+
+  % initial projection
+  [dummy,i] = min(dx);
+  y = P(i,:)+rand(1,odim)*norm(P(i,:))/20;
+ 
+  % lambda 
+  lambda = norm(std(P));
+
+  % termination
+  eps = 1e-3; i_max = noc*10;
+  
+  i=1; p(i,:) = y; 
+  ready = 0;
+  while ~ready,
+
+    % mutual distances
+    Dy = P - y(noc_x_1,:);        % differences in output space
+    dy = sqrt((Dy.^2)*odim_x_1);  % distances in output space
+    f = exp(-dy/lambda);
+  
+    fprintf(2,'iteration %d, error %g \r',i,sum(((dx - dy).^2).*f));
+
+    % all the other vectors push the projected one
+    fy = f .* (dx ./ dy - 1) / sum(f);
+  
+    % update    
+    step = - sum(fy(:,odim_x_1).*Dy);
+    y = y + step;
+  
+    i=i+1;
+    p(i,:) = y;   
+    ready = (norm(step)/norm(y) < eps | i > i_max);
+
+  end
+  fprintf(2,'\n');
+     
+