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

first hg version after svn

+function P = sammon(D, P, varargin)
+
+%SAMMON Computes Sammon's mapping of a data set.
+%
+% P = sammon(D, P, [value], [mode], [alpha], [Mdist])
+%
+%  P = sammon(D,2);            % projection to 2-dim space
+%  P = sammon(sMap,3);         % projects the codebook vectors
+%  P = sammon(sMap,3,[],[],[],Md) % uses distance matrix Md
+%  som_grid(sMap,'Coord',P)    % visualization of map projection
+%
+%  Input and output arguments ([]'s are optional):
+%   D        (matrix) size dlen x dim, data to be projected
+%            (struct) data or map struct            
+%   P        (scalar) output dimension
+%            (matrix) size dlen x odim, initial projection matrix
+%   [value]  (scalar) all different modes (the next argument) require 
+%                     a value, default = 100
+%   [mode]   (string) 'steps' or 'errlimit' or 'errchange' or 'seconds',
+%                     see below, default is 'steps'
+%   [alpha]  (scalar) iteration step size, default = 0.2
+%   [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'));
+%
+%   P        (matrix) size dlen x odim, the projections
+%
+% The output dimension must be 2 or higher but (naturally) lower 
+% than data set dimension.
+%
+% The mode argument determines the end condition for iteration. If 
+% the mode argument is used, also the value argument has to be 
+% specified. Different mode possibilities are:
+% 'steps'      the iteration is terminated when it is run <value> 
+% 'errlimit'   steps, the iteration is terminated when projection error 
+%              is lower than <value>,
+% 'errchange'  the iteration is terminated when change between 
+%              projection error on two successive iteration rounds
+%	       is less than <value> percent of total error, and
+% 'seconds'    the iteration is terminated after <value> seconds 
+%              of iteration.
+%
+% See also CCA, PCAPROJ, SOM_GRID.
+
+% Reference: Sammon, J.W. Jr., "A nonlinear mapping for data
+%   structure analysis", IEEE Transactions on Computers, vol. C-18,
+%   no. 5, 1969, pp. 401-409.
+
+% Contributed to SOM Toolbox vs2, February 2nd, 2000 by Juha Vesanto
+% Copyright (c) by Juha Vesanto
+% http://www.cis.hut.fi/projects/somtoolbox/
+
+% juuso 040100 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% check arguments
+
+error(nargchk(2, 6, nargin));  % check no. of input arguments is correct
+
+% input data
+if isstruct(D),
+  if isfield(D, 'data'),         D = D.data; % data struct
+  elseif isfield(D, 'codebook'), D = D.codebook; % map struct
+  else error('Invalid structure');
+  end
+end
+if any(isnan(D(:))), 
+  error('Cannot make Sammon''s projection for data with unknown components')
+end 
+
+% compute data dimensions
+orig_si = size(D); 
+dim = orig_si(end); 
+noc = prod(orig_si)/dim;
+if length(orig_si)>2, D = reshape(D,[noc dim]); end
+
+% output dimension / initial projection matrix
+if prod(size(P))==1, 
+  odim = P; 
+  P = rand(noc,odim)-0.5; 
+else 
+  si = size(P);
+  odim = si(end);
+  if prod(si) ~= noc*odim, 
+    error('Initial projection matrix size does not match data size');
+  end
+  if length(si)>2, P = reshape(P,[noc odim]); end
+  inds = find(isnan(P)); 
+  if length(inds), P(inds) = rand(size(inds)); end
+end
+if odim > dim | odim < 2, 
+  error('Output dimension must be within [2, dimension of data]');
+end
+
+% determine operating mode
+if nargin < 3 | isempty(varargin{1}) | isnan(varargin{1}), value=100;
+else value = varargin{1}; 
+end
+  
+if nargin < 4 | isempty(varargin{2}) | isnan(varargin{2}), mode='steps';
+else mode = varargin{2}; 
+end  
+switch mode,
+case 'steps',     runlen = value;
+case 'errlimit',  errlimit = value;
+case 'errchange', errchange = value; e_prev = 0;
+case 'seconds',   endtime = value;
+otherwise, error(['Illegal mode: ' mode]);
+end
+
+% iteration step size
+if nargin > 4, alpha = varargin{3}; else alpha = NaN; end
+if isempty(alpha) | isnan(alpha), alpha = 0.2; end
+
+% mutual distances
+if nargin > 5, Mdist = varargin{4}; else Mdist = []; end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% initialization
+
+% these are used quite frequently
+noc_x_1  = ones(noc, 1); 
+odim_x_1 = ones(odim,1); 
+
+% compute mutual distances between vectors
+if 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
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% action
+
+if strcmp(mode, 'seconds'), tic; end;
+fprintf(2, 'iterating                    \r');
+
+% sammon iteration   
+
+x  = P ;
+xu = zeros(noc, odim);
+xd = zeros(noc, odim);
+dq = zeros(noc, 1);
+dr = zeros(noc, 1);
+
+i = 0;
+ready = 0;
+while ~ready
+  for j = 1:noc,
+    xd      = -x + x(j*noc_x_1,:);
+    xd2     = xd.^2;
+    dpj     = sqrt(sum(xd2'))';
+    dq      = Mdist(:,j) - dpj;
+    dr      = Mdist(:,j) .* dpj;
+    ind     = find(dr ~= 0);
+    term    = dq(ind) ./ dr(ind);
+    e1      = sum(xd(ind,:) .* term(:,odim_x_1));
+    term2   = ((1.0 + dq(ind) ./ dpj(ind)) ./ dpj(ind)) ./ dr(ind);
+    e2      = sum(term) - sum(xd2(ind,:) .* term2(:,odim_x_1));
+    xu(j,:) = x(j,:) + alpha * e1 ./ abs(e2);
+  end
+
+  % move the center of mass to the center 
+
+  c = sum(xu) / noc;
+  x = xu - c(noc_x_1, :);
+
+  i = i + 1;
+
+  % compute mapping error
+  % doing this adds about 25% to computing time  
+  if 0,
+    e = 0; tot = 0;
+    for j = 2:noc, 
+      d   = Mdist(1:(j - 1), j);
+      tot = tot + sum(d);
+      ind = find(d ~= 0);
+      xd  = -x(1:(j - 1), :) + x(j * ones(j - 1, 1), :);
+      ee  = d - sqrt(sum(xd'.^2))';
+      e   = e + sum(ee(ind).^2 ./ d(ind));
+    end
+    e = e/tot; 
+    fprintf(2, '\r%d iterations, error %f', i, e);
+  else
+    fprintf(2, '\r%d iterations', i);
+  end
+  
+  % determine is the iteration ready
+  
+  switch mode
+    case 'steps', 
+      if i == runlen, ready = 1; end;
+    case 'errlimit',
+      if e < errlimit, ready = 1; end;
+    case 'errchange',
+      if i > 1
+	change = 100 * abs(e - e_prev) / e_prev;
+	if change < errchange, ready = 1; end;
+	fprintf(2, ', change of error %f %%    ', change);
+      end
+      e_prev = e;
+    case 'seconds'
+      if toc > endtime, ready = 1; end;
+      fprintf(2, ', elapsed time %f seconds  ', toc);
+  end
+  fprintf(2, '        ');
+  
+  % If you want to see the Sammon's projection plotted (in 2-D and 3-D case),
+  % execute the code below; it is not in use by default to speed up 
+  % computation.  
+  if 0, 
+    clf
+    if odim == 1,     plot(x(:,1), noc_x_1, 'o');
+    elseif odim == 2, plot(x(:,1), x(:,2), 'o');
+    else              plot3(x(:,1), x(:,2), x(:,3), 'o')
+    end
+    drawnow
+  end
+end
+
+fprintf(2, '\n');
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% clean up
+
+% reshape
+orig_si(end) = odim; 
+P = reshape(x, orig_si);
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%