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function sTopol = som_topol_struct(varargin)
%SOM_TOPOL_STRUCT Default values for SOM topology.
%
% sT = som_topol_struct([[argID,] value, ...])
%
% sTopol = som_topol_struct('data',D);
% sTopol = som_topol_struct('data',D,'munits',200);
% sTopol = som_topol_struct(sTopol);
% sTopol = som_topol_struct;
%
% Input and output arguments ([]'s are optional):
% [argID, (string) Default map topology depends on a number of
% value] (varies) factors (see below). These are given as a
% argument ID - argument value pairs, listed below.
%
% sT (struct) The ready topology struct.
%
% Topology struct contains values for map size, lattice (default is 'hexa')
% and shape (default is 'sheet'). Map size depends on training data and the
% number of map units. The number of map units depends on number of training
% samples.
%
% 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) incomplete topology struct: its empty fields
% will be given values
% 'som_topol','sTopol' = 'topol'
%
% For more help, try 'type som_topol_struct' or check out online documentation.
% See also SOM_SET, SOM_TRAIN_STRUCT, SOM_MAKE.
%%%%%%%%%%%%% DETAILED DESCRIPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% som_topol_struct
%
% PURPOSE
%
% Default values for map topology and training parameters.
%
% SYNTAX
%
% sT = som_topol_struct('argID',value,...);
% sT = som_topol_struct(value,...);
%
% DESCRIPTION
%
% This function is used to give sensible values for map topology (ie. map
% size). The topology struct is returned.
%
% The topology struct has three fields: '.msize', '.lattice' and
% '.shape'. Of these, default value for '.lattice' is 'hexa' and for
% '.shape' 'sheet'. Only the '.msize' field depends on the optional
% arguments: 'dlen', 'munits' and 'data'. The value for '.msize' field is
% determined as follows.
%
% First, the number of map units is determined (unless it is given). A
% heuristic formula of 'munits = 5*sqrt(dlen)' is used to calculate
% it. After this, the map size is determined. Basically, the two biggest
% eigenvalues of the training data are calculated and the ratio between
% sidelengths of the map grid is set to the square root of this ratio. The
% actual sidelengths are then set so that their product is as close to the
% desired number of map units as possible. If the lattice of the grid is
% 'hexa', the ratio is modified a bit to take it into account. If the
% lattice is 'hexa' and shape is 'toroid', the map size along the first axis
% must be even.
%
% 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. The valid IDs and corresponding values are listed below. 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) incomplete topology struct: its empty fields
% will be given values
% 'som_topol','sTopol' = 'topol'
%
% OUTPUT ARGUMENTS
%
% sT (struct) The topology struct.
%
% EXAMPLES
%
% The most important optional argument for the default topology is 'data'.
% To get a default topology (given data) use:
%
% sTopol = som_topol_struct('data',D);
%
% This sets lattice to its default value 'hexa'. If you want to have a
% 'rect' lattice instead:
%
% sTopol = som_topol_struct('data',D,'lattice','rect');
% or
% sTopol = som_topol_struct('data',D,'rect');
%
% If you want to have (close to) a specific number of map units, e.g. 100:
%
% sTopol = som_topol_struct('data',D,'munits',100);
%
% SEE ALSO
%
% som_make Initialize and train a map using default parameters.
% som_train_struct Default training parameters.
% som_randinint Random initialization algorithm.
% som_lininit Linear initialization algorithm.
% som_seqtrain Sequential training algorithm.
% som_batchtrain Batch training algorithm.
% Copyright (c) 1999-2000 by the SOM toolbox programming team.
% http://www.cis.hut.fi/projects/somtoolbox/
% Version 2.0alpha juuso 060898 250399 070499 050899 240801
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% check arguments
% initialize
sTopol = som_set('som_topol','lattice','hexa','shape','sheet');
D = [];
dlen = NaN;
dim = 2;
munits = NaN;
% varargin
i=1;
while i<=length(varargin),
argok = 1;
if ischar(varargin{i}),
switch varargin{i},
case 'dlen', i=i+1; dlen = varargin{i};
case 'munits', i=i+1; munits = varargin{i}; sTopol.msize = 0;
case 'msize', i=i+1; sTopol.msize = varargin{i};
case 'lattice', i=i+1; sTopol.lattice = varargin{i};
case 'shape', i=i+1; sTopol.shape = varargin{i};
case 'data',
i=i+1;
if isstruct(varargin{i}), D = varargin{i}.data;
else D = varargin{i};
end
[dlen dim] = size(D);
case {'hexa','rect'}, sTopol.lattice = varargin{i};
case {'sheet','cyl','toroid'}, sTopol.shape = varargin{i};
case {'som_topol','sTopol','topol'},
i=i+1;
if ~isempty(varargin{i}.msize) & prod(varargin{i}.msize),
sTopol.msize = varargin{i}.msize;
end
if ~isempty(varargin{i}.lattice), sTopol.lattice = varargin{i}.lattice; end
if ~isempty(varargin{i}.shape), sTopol.shape = varargin{i}.shape; end
otherwise argok=0;
end
elseif isstruct(varargin{i}) & isfield(varargin{i},'type'),
switch varargin{i}.type,
case 'som_topol',
if ~isempty(varargin{i}.msize) & prod(varargin{i}.msize),
sTopol.msize = varargin{i}.msize;
end
if ~isempty(varargin{i}.lattice), sTopol.lattice = varargin{i}.lattice; end
if ~isempty(varargin{i}.shape), sTopol.shape = varargin{i}.shape; end
case 'som_data',
D = varargin{i}.data;
[dlen dim] = size(D);
otherwise argok=0;
end
else
argok = 0;
end
if ~argok,
disp(['(som_topol_struct) Ignoring invalid argument #' num2str(i)]);
end
i = i+1;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% action - topology struct
% lattice and shape set already, so if msize is also set, there's
% nothing else to do
if prod(sTopol.msize) & ~isempty(sTopol.msize), return; end
% otherwise, decide msize
% first (if necessary) determine the number of map units (munits)
if isnan(munits),
if ~isnan(dlen),
munits = ceil(5 * dlen^0.5); % this is just one way to make a guess...
else
munits = 100; % just a convenient value
end
end
% then determine the map size (msize)
if dim == 1, % 1-D data
sTopol.msize = [1 ceil(munits)];
elseif size(D,1)<2, % eigenvalues cannot be determined since there's no data
sTopol.msize = round(sqrt(munits));
sTopol.msize(2) = round(munits/sTopol.msize(1));
else % determine map size based on eigenvalues
% initialize xdim/ydim ratio using principal components of the input
% space; the ratio is the square root of ratio of two largest eigenvalues
% autocorrelation matrix
A = zeros(dim)+Inf;
for i=1:dim, D(:,i) = D(:,i) - mean(D(isfinite(D(:,i)),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(ind);
%me = mean(D);
%D = D - me(ones(length(ind),1),:); % remove mean from data
%eigval = sort(eig((D'*D)./size(D,1)));
if eigval(end)==0 | eigval(end-1)*munits<eigval(end),
ratio = 1;
else
ratio = sqrt(eigval(end)/eigval(end-1)); % ratio between map sidelengths
end
% in hexagonal lattice, the sidelengths are not directly
% proportional to the number of units since the units on the
% y-axis are squeezed together by a factor of sqrt(0.75)
if strcmp(sTopol.lattice,'hexa'),
sTopol.msize(2) = min(munits, round(sqrt(munits / ratio * sqrt(0.75))));
else
sTopol.msize(2) = min(munits, round(sqrt(munits / ratio)));
end
sTopol.msize(1) = round(munits / sTopol.msize(2));
% if actual dimension of the data is 1, make the map 1-D
if min(sTopol.msize) == 1, sTopol.msize = [1 max(sTopol.msize)]; end;
% a special case: if the map is toroid with hexa lattice,
% size along first axis must be even
if strcmp(sTopol.lattice,'hexa') & strcmp(sTopol.shape,'toroid'),
if mod(sTopol.msize(1),2), sTopol.msize(1) = sTopol.msize(1) + 1; end
end
end
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%