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