Daniel@0: function P = sammon(D, P, varargin)
Daniel@0: 
Daniel@0: %SAMMON Computes Sammon's mapping of a data set.
Daniel@0: %
Daniel@0: % P = sammon(D, P, [value], [mode], [alpha], [Mdist])
Daniel@0: %
Daniel@0: %  P = sammon(D,2);            % projection to 2-dim space
Daniel@0: %  P = sammon(sMap,3);         % projects the codebook vectors
Daniel@0: %  P = sammon(sMap,3,[],[],[],Md) % uses distance matrix Md
Daniel@0: %  som_grid(sMap,'Coord',P)    % visualization of map projection
Daniel@0: %
Daniel@0: %  Input and output arguments ([]'s are optional):
Daniel@0: %   D        (matrix) size dlen x dim, data to be projected
Daniel@0: %            (struct) data or map struct            
Daniel@0: %   P        (scalar) output dimension
Daniel@0: %            (matrix) size dlen x odim, initial projection matrix
Daniel@0: %   [value]  (scalar) all different modes (the next argument) require 
Daniel@0: %                     a value, default = 100
Daniel@0: %   [mode]   (string) 'steps' or 'errlimit' or 'errchange' or 'seconds',
Daniel@0: %                     see below, default is 'steps'
Daniel@0: %   [alpha]  (scalar) iteration step size, default = 0.2
Daniel@0: %   [Dist]   (matrix) pairwise distance matrix, size dlen x dlen.
Daniel@0: %                     If the distances in the input space should
Daniel@0: %                     be calculated otherwise than as euclidian
Daniel@0: %                     distances, the distance from each vector
Daniel@0: %                     to each other vector can be given here,
Daniel@0: %                     size dlen x dlen. For example PDIST
Daniel@0: %                     function can be used to calculate the
Daniel@0: %                     distances: Dist = squareform(pdist(D,'mahal'));
Daniel@0: %
Daniel@0: %   P        (matrix) size dlen x odim, the projections
Daniel@0: %
Daniel@0: % The output dimension must be 2 or higher but (naturally) lower 
Daniel@0: % than data set dimension.
Daniel@0: %
Daniel@0: % The mode argument determines the end condition for iteration. If 
Daniel@0: % the mode argument is used, also the value argument has to be 
Daniel@0: % specified. Different mode possibilities are:
Daniel@0: % 'steps'      the iteration is terminated when it is run <value> 
Daniel@0: % 'errlimit'   steps, the iteration is terminated when projection error 
Daniel@0: %              is lower than <value>,
Daniel@0: % 'errchange'  the iteration is terminated when change between 
Daniel@0: %              projection error on two successive iteration rounds
Daniel@0: %	       is less than <value> percent of total error, and
Daniel@0: % 'seconds'    the iteration is terminated after <value> seconds 
Daniel@0: %              of iteration.
Daniel@0: %
Daniel@0: % See also CCA, PCAPROJ, SOM_GRID.
Daniel@0: 
Daniel@0: % Reference: Sammon, J.W. Jr., "A nonlinear mapping for data
Daniel@0: %   structure analysis", IEEE Transactions on Computers, vol. C-18,
Daniel@0: %   no. 5, 1969, pp. 401-409.
Daniel@0: 
Daniel@0: % Contributed to SOM Toolbox vs2, February 2nd, 2000 by Juha Vesanto
Daniel@0: % Copyright (c) by Juha Vesanto
Daniel@0: % http://www.cis.hut.fi/projects/somtoolbox/
Daniel@0: 
Daniel@0: % juuso 040100 
Daniel@0: 
Daniel@0: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Daniel@0: %% check arguments
Daniel@0: 
Daniel@0: error(nargchk(2, 6, nargin));  % check no. of input arguments is correct
Daniel@0: 
Daniel@0: % input data
Daniel@0: if isstruct(D),
Daniel@0:   if isfield(D, 'data'),         D = D.data; % data struct
Daniel@0:   elseif isfield(D, 'codebook'), D = D.codebook; % map struct
Daniel@0:   else error('Invalid structure');
Daniel@0:   end
Daniel@0: end
Daniel@0: if any(isnan(D(:))), 
Daniel@0:   error('Cannot make Sammon''s projection for data with unknown components')
Daniel@0: end 
Daniel@0: 
Daniel@0: % compute data dimensions
Daniel@0: orig_si = size(D); 
Daniel@0: dim = orig_si(end); 
Daniel@0: noc = prod(orig_si)/dim;
Daniel@0: if length(orig_si)>2, D = reshape(D,[noc dim]); end
Daniel@0: 
Daniel@0: % output dimension / initial projection matrix
Daniel@0: if prod(size(P))==1, 
Daniel@0:   odim = P; 
Daniel@0:   P = rand(noc,odim)-0.5; 
Daniel@0: else 
Daniel@0:   si = size(P);
Daniel@0:   odim = si(end);
Daniel@0:   if prod(si) ~= noc*odim, 
Daniel@0:     error('Initial projection matrix size does not match data size');
Daniel@0:   end
Daniel@0:   if length(si)>2, P = reshape(P,[noc odim]); end
Daniel@0:   inds = find(isnan(P)); 
Daniel@0:   if length(inds), P(inds) = rand(size(inds)); end
Daniel@0: end
Daniel@0: if odim > dim | odim < 2, 
Daniel@0:   error('Output dimension must be within [2, dimension of data]');
Daniel@0: end
Daniel@0: 
Daniel@0: % determine operating mode
Daniel@0: if nargin < 3 | isempty(varargin{1}) | isnan(varargin{1}), value=100;
Daniel@0: else value = varargin{1}; 
Daniel@0: end
Daniel@0:   
Daniel@0: if nargin < 4 | isempty(varargin{2}) | isnan(varargin{2}), mode='steps';
Daniel@0: else mode = varargin{2}; 
Daniel@0: end  
Daniel@0: switch mode,
Daniel@0: case 'steps',     runlen = value;
Daniel@0: case 'errlimit',  errlimit = value;
Daniel@0: case 'errchange', errchange = value; e_prev = 0;
Daniel@0: case 'seconds',   endtime = value;
Daniel@0: otherwise, error(['Illegal mode: ' mode]);
Daniel@0: end
Daniel@0: 
Daniel@0: % iteration step size
Daniel@0: if nargin > 4, alpha = varargin{3}; else alpha = NaN; end
Daniel@0: if isempty(alpha) | isnan(alpha), alpha = 0.2; end
Daniel@0: 
Daniel@0: % mutual distances
Daniel@0: if nargin > 5, Mdist = varargin{4}; else Mdist = []; end
Daniel@0: 
Daniel@0: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Daniel@0: %% initialization
Daniel@0: 
Daniel@0: % these are used quite frequently
Daniel@0: noc_x_1  = ones(noc, 1); 
Daniel@0: odim_x_1 = ones(odim,1); 
Daniel@0: 
Daniel@0: % compute mutual distances between vectors
Daniel@0: if isempty(Mdist) | all(isnan(Mdist(:))),  
Daniel@0:   fprintf(2, 'computing mutual distances\r');
Daniel@0:   dim_x_1 = ones(dim,1);
Daniel@0:   for i = 1:noc,
Daniel@0:     x = D(i,:); 
Daniel@0:     Diff = D - x(noc_x_1,:);
Daniel@0:     N = isnan(Diff);
Daniel@0:     Diff(find(N)) = 0; 
Daniel@0:     Mdist(:,i) = sqrt((Diff.^2)*dim_x_1);
Daniel@0:     N = find(sum(N')==dim); %mutual distance unknown
Daniel@0:     if ~isempty(N), Mdist(N,i) = NaN; end
Daniel@0:   end
Daniel@0: else
Daniel@0:   % if the distance matrix is output from PDIST function
Daniel@0:   if size(Mdist,1)==1, Mdist = squareform(Mdist); end
Daniel@0:   if size(Mdist,1)~=noc, 
Daniel@0:     error('Mutual distance matrix size and data set size do not match'); 
Daniel@0:   end
Daniel@0: end
Daniel@0: 
Daniel@0: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Daniel@0: %% action
Daniel@0: 
Daniel@0: if strcmp(mode, 'seconds'), tic; end;
Daniel@0: fprintf(2, 'iterating                    \r');
Daniel@0: 
Daniel@0: % sammon iteration   
Daniel@0: 
Daniel@0: x  = P ;
Daniel@0: xu = zeros(noc, odim);
Daniel@0: xd = zeros(noc, odim);
Daniel@0: dq = zeros(noc, 1);
Daniel@0: dr = zeros(noc, 1);
Daniel@0: 
Daniel@0: i = 0;
Daniel@0: ready = 0;
Daniel@0: while ~ready
Daniel@0:   for j = 1:noc,
Daniel@0:     xd      = -x + x(j*noc_x_1,:);
Daniel@0:     xd2     = xd.^2;
Daniel@0:     dpj     = sqrt(sum(xd2'))';
Daniel@0:     dq      = Mdist(:,j) - dpj;
Daniel@0:     dr      = Mdist(:,j) .* dpj;
Daniel@0:     ind     = find(dr ~= 0);
Daniel@0:     term    = dq(ind) ./ dr(ind);
Daniel@0:     e1      = sum(xd(ind,:) .* term(:,odim_x_1));
Daniel@0:     term2   = ((1.0 + dq(ind) ./ dpj(ind)) ./ dpj(ind)) ./ dr(ind);
Daniel@0:     e2      = sum(term) - sum(xd2(ind,:) .* term2(:,odim_x_1));
Daniel@0:     xu(j,:) = x(j,:) + alpha * e1 ./ abs(e2);
Daniel@0:   end
Daniel@0: 
Daniel@0:   % move the center of mass to the center 
Daniel@0: 
Daniel@0:   c = sum(xu) / noc;
Daniel@0:   x = xu - c(noc_x_1, :);
Daniel@0: 
Daniel@0:   i = i + 1;
Daniel@0: 
Daniel@0:   % compute mapping error
Daniel@0:   % doing this adds about 25% to computing time  
Daniel@0:   if 0,
Daniel@0:     e = 0; tot = 0;
Daniel@0:     for j = 2:noc, 
Daniel@0:       d   = Mdist(1:(j - 1), j);
Daniel@0:       tot = tot + sum(d);
Daniel@0:       ind = find(d ~= 0);
Daniel@0:       xd  = -x(1:(j - 1), :) + x(j * ones(j - 1, 1), :);
Daniel@0:       ee  = d - sqrt(sum(xd'.^2))';
Daniel@0:       e   = e + sum(ee(ind).^2 ./ d(ind));
Daniel@0:     end
Daniel@0:     e = e/tot; 
Daniel@0:     fprintf(2, '\r%d iterations, error %f', i, e);
Daniel@0:   else
Daniel@0:     fprintf(2, '\r%d iterations', i);
Daniel@0:   end
Daniel@0:   
Daniel@0:   % determine is the iteration ready
Daniel@0:   
Daniel@0:   switch mode
Daniel@0:     case 'steps', 
Daniel@0:       if i == runlen, ready = 1; end;
Daniel@0:     case 'errlimit',
Daniel@0:       if e < errlimit, ready = 1; end;
Daniel@0:     case 'errchange',
Daniel@0:       if i > 1
Daniel@0: 	change = 100 * abs(e - e_prev) / e_prev;
Daniel@0: 	if change < errchange, ready = 1; end;
Daniel@0: 	fprintf(2, ', change of error %f %%    ', change);
Daniel@0:       end
Daniel@0:       e_prev = e;
Daniel@0:     case 'seconds'
Daniel@0:       if toc > endtime, ready = 1; end;
Daniel@0:       fprintf(2, ', elapsed time %f seconds  ', toc);
Daniel@0:   end
Daniel@0:   fprintf(2, '        ');
Daniel@0:   
Daniel@0:   % If you want to see the Sammon's projection plotted (in 2-D and 3-D case),
Daniel@0:   % execute the code below; it is not in use by default to speed up 
Daniel@0:   % computation.  
Daniel@0:   if 0, 
Daniel@0:     clf
Daniel@0:     if odim == 1,     plot(x(:,1), noc_x_1, 'o');
Daniel@0:     elseif odim == 2, plot(x(:,1), x(:,2), 'o');
Daniel@0:     else              plot3(x(:,1), x(:,2), x(:,3), 'o')
Daniel@0:     end
Daniel@0:     drawnow
Daniel@0:   end
Daniel@0: end
Daniel@0: 
Daniel@0: fprintf(2, '\n');
Daniel@0: 
Daniel@0: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Daniel@0: %% clean up
Daniel@0: 
Daniel@0: % reshape
Daniel@0: orig_si(end) = odim; 
Daniel@0: P = reshape(x, orig_si);
Daniel@0: 
Daniel@0: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%