Daniel@0: function sMap = som_lininit(D, varargin)
Daniel@0: 
Daniel@0: %SOM_LININIT Initialize a Self-Organizing Map linearly.
Daniel@0: %
Daniel@0: % sMap = som_lininit(D, [[argID,] value, ...])
Daniel@0: %
Daniel@0: %  sMap = som_lininit(D);
Daniel@0: %  sMap = som_lininit(D,sMap);
Daniel@0: %  sMap = som_lininit(D,'munits',100,'hexa');
Daniel@0: % 
Daniel@0: %  Input and output arguments ([]'s are optional): 
Daniel@0: %   D                 The training data.
Daniel@0: %            (struct) data struct
Daniel@0: %            (matrix) data matrix, size dlen x dim
Daniel@0: %   [argID,  (string) Parameters affecting the map topology are given 
Daniel@0: %    value]  (varies) as argument ID - argument value pairs, listed below.
Daniel@0: %   sMap     (struct) map struct
Daniel@0: %
Daniel@0: % Here are the valid argument IDs and corresponding values. The values 
Daniel@0: % which are unambiguous (marked with '*') can be given without the
Daniel@0: % preceeding argID.
Daniel@0: %  'munits'       (scalar) number of map units
Daniel@0: %  'msize'        (vector) map size
Daniel@0: %  'lattice'     *(string) map lattice: 'hexa' or 'rect'
Daniel@0: %  'shape'       *(string) map shape: 'sheet', 'cyl' or 'toroid'
Daniel@0: %  'topol'       *(struct) topology struct
Daniel@0: %  'som_topol','sTopol'    = 'topol'
Daniel@0: %  'map'         *(struct) map struct
Daniel@0: %  'som_map','sMap'        = 'map'
Daniel@0: %
Daniel@0: % For more help, try 'type som_lininit' or check out online documentation.
Daniel@0: % See also SOM_MAP_STRUCT, SOM_RANDINIT, SOM_MAKE.
Daniel@0: 
Daniel@0: %%%%%%%%%%%%% DETAILED DESCRIPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Daniel@0: %
Daniel@0: % som_lininit
Daniel@0: %
Daniel@0: % PURPOSE
Daniel@0: %
Daniel@0: % Initializes a SOM linearly along its greatest eigenvectors.
Daniel@0: %
Daniel@0: % SYNTAX
Daniel@0: %
Daniel@0: %  sMap = som_lininit(D);
Daniel@0: %  sMap = som_lininit(D,sMap);
Daniel@0: %  sMap = som_lininit(D,'munits',100,'hexa');
Daniel@0: %
Daniel@0: % DESCRIPTION
Daniel@0: %
Daniel@0: % Initializes a SOM linearly. If necessary, a map struct is created
Daniel@0: % first. The initialization is made by first calculating the eigenvalues
Daniel@0: % and eigenvectors of the training data. Then, the map is initialized
Daniel@0: % along the mdim greatest eigenvectors of the training data, where
Daniel@0: % mdim is the dimension of the map grid.
Daniel@0: %
Daniel@0: % REFERENCES
Daniel@0: %
Daniel@0: % Kohonen, T., "Self-Organizing Map", 2nd ed., Springer-Verlag, 
Daniel@0: %    Berlin, 1995, pp. 106-107.
Daniel@0: %
Daniel@0: % REQUIRED INPUT ARGUMENTS
Daniel@0: %
Daniel@0: %  D                 The training data.
Daniel@0: %           (struct) Data struct. If this is given, its '.comp_names' and 
Daniel@0: %                    '.comp_norm' fields are copied to the map struct.
Daniel@0: %           (matrix) data matrix, size dlen x dim
Daniel@0: %  
Daniel@0: % OPTIONAL INPUT ARGUMENTS 
Daniel@0: %
Daniel@0: %  argID (string) Argument identifier string (see below).
Daniel@0: %  value (varies) Value for the argument (see below).
Daniel@0: %
Daniel@0: %  The optional arguments can be given as 'argID',value -pairs. If an
Daniel@0: %  argument is given value multiple times, the last one is used. 
Daniel@0: %
Daniel@0: %  Here are the valid argument IDs and corresponding values. The values 
Daniel@0: %  which are unambiguous (marked with '*') can be given without the 
Daniel@0: %  preceeding argID.
Daniel@0: %  'dlen'         (scalar) length of the training data
Daniel@0: %  'data'         (matrix) the training data
Daniel@0: %                *(struct) the training data
Daniel@0: %  'munits'       (scalar) number of map units
Daniel@0: %  'msize'        (vector) map size
Daniel@0: %  'lattice'     *(string) map lattice: 'hexa' or 'rect'
Daniel@0: %  'shape'       *(string) map shape: 'sheet', 'cyl' or 'toroid'
Daniel@0: %  'topol'       *(struct) topology struct
Daniel@0: %  'som_topol','sTopol'    = 'topol'
Daniel@0: %  'map'         *(struct) map struct
Daniel@0: %  'som_map','sMap'        = 'map'
Daniel@0: %
Daniel@0: % OUTPUT ARGUMENTS
Daniel@0: % 
Daniel@0: %  sMap     (struct) The initialized map struct.
Daniel@0: %
Daniel@0: % EXAMPLES
Daniel@0: %
Daniel@0: %  sMap = som_lininit(D);
Daniel@0: %  sMap = som_lininit(D,sMap);
Daniel@0: %  sMap = som_lininit(D,'msize',[10 10]);
Daniel@0: %  sMap = som_lininit(D,'munits',100,'rect');
Daniel@0: %
Daniel@0: % SEE ALSO
Daniel@0: % 
Daniel@0: %  som_map_struct   Create a map struct.
Daniel@0: %  som_randinit     Initialize a map with random values.
Daniel@0: %  som_make         Initialize and train self-organizing map.
Daniel@0: 
Daniel@0: % Copyright (c) 1997-2000 by the SOM toolbox programming team.
Daniel@0: % http://www.cis.hut.fi/projects/somtoolbox/
Daniel@0: 
Daniel@0: % Version 1.0beta ecco 100997
Daniel@0: % Version 2.0beta 101199
Daniel@0: 
Daniel@0: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Daniel@0: %% check arguments
Daniel@0: 
Daniel@0: % data
Daniel@0: if isstruct(D), 
Daniel@0:   data_name = D.name; 
Daniel@0:   comp_names = D.comp_names; 
Daniel@0:   comp_norm = D.comp_norm; 
Daniel@0:   D = D.data;
Daniel@0:   struct_mode = 1; 
Daniel@0: else 
Daniel@0:   data_name = inputname(1); 
Daniel@0:   struct_mode = 0;
Daniel@0: end
Daniel@0: [dlen dim] = size(D);
Daniel@0: 
Daniel@0: % varargin
Daniel@0: sMap = [];
Daniel@0: sTopol = som_topol_struct; 
Daniel@0: sTopol.msize = 0; 
Daniel@0: munits = NaN;
Daniel@0: i=1; 
Daniel@0: while i<=length(varargin), 
Daniel@0:   argok = 1; 
Daniel@0:   if ischar(varargin{i}), 
Daniel@0:     switch varargin{i}, 
Daniel@0:      case 'munits',     i=i+1; munits = varargin{i}; sTopol.msize = 0;
Daniel@0:      case 'msize',      i=i+1; sTopol.msize = varargin{i};
Daniel@0:                                munits = prod(sTopol.msize); 
Daniel@0:      case 'lattice',    i=i+1; sTopol.lattice = varargin{i}; 
Daniel@0:      case 'shape',      i=i+1; sTopol.shape = varargin{i}; 
Daniel@0:      case {'som_topol','sTopol','topol'}, i=i+1; sTopol = varargin{i}; 
Daniel@0:      case {'som_map','sMap','map'}, i=i+1; sMap = varargin{i}; sTopol = sMap.topol;
Daniel@0:      case {'hexa','rect'}, sTopol.lattice = varargin{i}; 
Daniel@0:      case {'sheet','cyl','toroid'}, sTopol.shape = varargin{i};
Daniel@0:      otherwise argok=0; 
Daniel@0:     end
Daniel@0:   elseif isstruct(varargin{i}) & isfield(varargin{i},'type'), 
Daniel@0:     switch varargin{i}.type, 
Daniel@0:      case 'som_topol',
Daniel@0:       sTopol = varargin{i}; 
Daniel@0:      case 'som_map', 
Daniel@0:       sMap = varargin{i};
Daniel@0:       sTopol = sMap.topol;
Daniel@0:      otherwise argok=0; 
Daniel@0:     end
Daniel@0:   else
Daniel@0:     argok = 0; 
Daniel@0:   end
Daniel@0:   if ~argok, 
Daniel@0:     disp(['(som_topol_struct) Ignoring invalid argument #' num2str(i)]); 
Daniel@0:   end
Daniel@0:   i = i+1; 
Daniel@0: end
Daniel@0: 
Daniel@0: if length(sTopol.msize)==1, sTopol.msize = [sTopol.msize 1]; end
Daniel@0: 
Daniel@0: if ~isempty(sMap), 
Daniel@0:   [munits dim2] = size(sMap.codebook);
Daniel@0:   if dim2 ~= dim, error('Map and data must have the same dimension.'); end
Daniel@0: end
Daniel@0: 
Daniel@0: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Daniel@0: %% create map
Daniel@0: 
Daniel@0: % map struct
Daniel@0: if ~isempty(sMap), 
Daniel@0:   sMap = som_set(sMap,'topol',sTopol);
Daniel@0: else  
Daniel@0:   if ~prod(sTopol.msize), 
Daniel@0:     if isnan(munits), 
Daniel@0:       sTopol = som_topol_struct('data',D,sTopol);
Daniel@0:     else
Daniel@0:       sTopol = som_topol_struct('data',D,'munits',munits,sTopol);
Daniel@0:     end
Daniel@0:   end  
Daniel@0:   sMap = som_map_struct(dim, sTopol); 
Daniel@0: end
Daniel@0: 
Daniel@0: if struct_mode, 
Daniel@0:   sMap = som_set(sMap,'comp_names',comp_names,'comp_norm',comp_norm);
Daniel@0: end
Daniel@0: 
Daniel@0: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Daniel@0: %% initialization
Daniel@0: 
Daniel@0: % train struct
Daniel@0: sTrain = som_train_struct('algorithm','lininit');
Daniel@0: sTrain = som_set(sTrain,'data_name',data_name);
Daniel@0: 
Daniel@0: msize = sMap.topol.msize;
Daniel@0: mdim = length(msize);
Daniel@0: munits = prod(msize);
Daniel@0: 
Daniel@0: [dlen dim] = size(D);
Daniel@0: if dlen<2,  
Daniel@0:   %if dlen==1, sMap.codebook = (sMap.codebook - 0.5)*diag(D); end
Daniel@0:   error(['Linear map initialization requires at least two NaN-free' ...
Daniel@0: 	 ' samples.']);
Daniel@0:   return;
Daniel@0: end
Daniel@0: 
Daniel@0: % compute principle components
Daniel@0: if dim > 1 & sum(msize > 1) > 1,
Daniel@0:   % calculate mdim largest eigenvalues and their corresponding
Daniel@0:   % eigenvectors
Daniel@0:     
Daniel@0:   % autocorrelation matrix
Daniel@0:   A = zeros(dim);
Daniel@0:   me = zeros(1,dim);
Daniel@0:   for i=1:dim, 
Daniel@0:     me(i) = mean(D(isfinite(D(:,i)),i)); 
Daniel@0:     D(:,i) = D(:,i) - me(i); 
Daniel@0:   end  
Daniel@0:   for i=1:dim, 
Daniel@0:     for j=i:dim, 
Daniel@0:       c = D(:,i).*D(:,j); c = c(isfinite(c));
Daniel@0:       A(i,j) = sum(c)/length(c); A(j,i) = A(i,j); 
Daniel@0:     end
Daniel@0:   end
Daniel@0:   
Daniel@0:   % take mdim first eigenvectors with the greatest eigenvalues
Daniel@0:   [V,S]   = eig(A);
Daniel@0:   eigval  = diag(S);
Daniel@0:   [y,ind] = sort(eigval); 
Daniel@0:   eigval  = eigval(flipud(ind));
Daniel@0:   V       = V(:,flipud(ind)); 
Daniel@0:   V       = V(:,1:mdim);
Daniel@0:   eigval  = eigval(1:mdim);   
Daniel@0: 
Daniel@0:   % normalize eigenvectors to unit length and multiply them by 
Daniel@0:   % corresponding (square-root-of-)eigenvalues
Daniel@0:   for i=1:mdim, V(:,i) = (V(:,i) / norm(V(:,i))) * sqrt(eigval(i)); end
Daniel@0:   
Daniel@0: else
Daniel@0: 
Daniel@0:   me = zeros(1,dim);
Daniel@0:   V = zeros(1,dim);
Daniel@0:   for i=1:dim, 
Daniel@0:     inds = find(~isnan(D(:,i)));
Daniel@0:     me(i) = mean(D(inds,i),1);
Daniel@0:     V(i) = std(D(inds,i),1);
Daniel@0:   end
Daniel@0:   
Daniel@0: end
Daniel@0: 
Daniel@0: % initialize codebook vectors
Daniel@0: if dim>1, 
Daniel@0:   sMap.codebook = me(ones(munits,1),:); 
Daniel@0:   Coords = som_unit_coords(msize,'rect','sheet');
Daniel@0:   cox = Coords(:,1); Coords(:,1) = Coords(:,2); Coords(:,2) = cox;
Daniel@0:   for i=1:mdim,
Daniel@0:     ma = max(Coords(:,i)); mi = min(Coords(:,i)); 
Daniel@0:     if ma>mi, Coords(:,i) = (Coords(:,i)-mi)/(ma-mi); else Coords(:,i) = 0.5; end
Daniel@0:   end
Daniel@0:   Coords = (Coords-0.5)*2;
Daniel@0:   for n = 1:munits,   
Daniel@0:     for d = 1:mdim,    
Daniel@0:       sMap.codebook(n,:) = sMap.codebook(n,:)+Coords(n,d)*V(:, d)';
Daniel@0:     end
Daniel@0:   end
Daniel@0: else  
Daniel@0:   sMap.codebook = [0:(munits-1)]'/(munits-1)*(max(D)-min(D))+min(D);
Daniel@0: end
Daniel@0: 
Daniel@0: % training struct
Daniel@0: sTrain = som_set(sTrain,'time',datestr(now,0));
Daniel@0: sMap.trainhist = sTrain;
Daniel@0: 
Daniel@0: return;
Daniel@0: 
Daniel@0: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%