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function U = som_umat(sMap, varargin)
%SOM_UMAT Compute unified distance matrix of self-organizing map.
%
% U = som_umat(sMap, [argID, value, ...])
%
% U = som_umat(sMap);
% U = som_umat(M,sTopol,'median','mask',[1 1 0 1]);
%
% Input and output arguments ([]'s are optional):
% sMap (struct) map struct or
% (matrix) the codebook matrix of the map
% [argID, (string) See below. The values which are unambiguous can
% value] (varies) be given without the preceeding argID.
%
% U (matrix) u-matrix of the self-organizing map
%
% Here are the valid argument IDs and corresponding values. The values which
% are unambiguous (marked with '*') can be given without the preceeding argID.
% 'mask' (vector) size dim x 1, weighting factors for different
% components (same as BMU search mask)
% 'msize' (vector) map grid size
% 'topol' *(struct) topology struct
% 'som_topol','sTopol' = 'topol'
% 'lattice' *(string) map lattice, 'hexa' or 'rect'
% 'mode' *(string) 'min','mean','median','max', default is 'median'
%
% NOTE! the U-matrix is always calculated for 'sheet'-shaped map and
% the map grid must be at most 2-dimensional.
%
% For more help, try 'type som_umat' or check out online documentation.
% See also SOM_SHOW, SOM_CPLANE.
%%%%%%%%%%%%% DETAILED DESCRIPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% som_umat
%
% PURPOSE
%
% Computes the unified distance matrix of a SOM.
%
% SYNTAX
%
% U = som_umat(sM)
% U = som_umat(...,'argID',value,...)
% U = som_umat(...,value,...)
%
% DESCRIPTION
%
% Compute and return the unified distance matrix of a SOM.
% For example a case of 5x1 -sized map:
% m(1) m(2) m(3) m(4) m(5)
% where m(i) denotes one map unit. The u-matrix is a 9x1 vector:
% u(1) u(1,2) u(2) u(2,3) u(3) u(3,4) u(4) u(4,5) u(5)
% where u(i,j) is the distance between map units m(i) and m(j)
% and u(k) is the mean (or minimum, maximum or median) of the
% surrounding values, e.g. u(3) = (u(2,3) + u(3,4))/2.
%
% Note that the u-matrix is always calculated for 'sheet'-shaped map and
% the map grid must be at most 2-dimensional.
%
% REFERENCES
%
% Ultsch, A., Siemon, H.P., "Kohonen's Self-Organizing Feature Maps
% for Exploratory Data Analysis", in Proc. of INNC'90,
% International Neural Network Conference, Dordrecht,
% Netherlands, 1990, pp. 305-308.
% Kohonen, T., "Self-Organizing Map", 2nd ed., Springer-Verlag,
% Berlin, 1995, pp. 117-119.
% Iivarinen, J., Kohonen, T., Kangas, J., Kaski, S., "Visualizing
% the Clusters on the Self-Organizing Map", in proceedings of
% Conference on Artificial Intelligence Research in Finland,
% Helsinki, Finland, 1994, pp. 122-126.
% Kraaijveld, M.A., Mao, J., Jain, A.K., "A Nonlinear Projection
% Method Based on Kohonen's Topology Preserving Maps", IEEE
% Transactions on Neural Networks, vol. 6, no. 3, 1995, pp. 548-559.
%
% REQUIRED INPUT ARGUMENTS
%
% sM (struct) SOM Toolbox struct or the codebook matrix of the map.
% (matrix) The matrix may be 3-dimensional in which case the first
% two dimensions are taken for the map grid dimensions (msize).
%
% OPTIONAL INPUT ARGUMENTS
%
% argID (string) Argument identifier string (see below).
% value (varies) Value for the argument (see below).
%
% The optional arguments are given as 'argID',value -pairs. If the
% value is unambiguous, it can be given without the preceeding argID.
% If an argument is given value multiple times, the last one is used.
%
% Below is the list of valid arguments:
% 'mask' (vector) mask to be used in calculating
% the interunit distances, size [dim 1]. Default is
% the one in sM (field sM.mask) or a vector of
% ones if only a codebook matrix was given.
% 'topol' (struct) topology of the map. Default is the one
% in sM (field sM.topol).
% 'sTopol','som_topol' (struct) = 'topol'
% 'msize' (vector) map grid dimensions
% 'lattice' (string) map lattice 'rect' or 'hexa'
% 'mode' (string) 'min', 'mean', 'median' or 'max'
% Map unit value computation method. In fact,
% eval-function is used to evaluate this, so
% you can give other computation methods as well.
% Default is 'median'.
%
% OUTPUT ARGUMENTS
%
% U (matrix) the unified distance matrix of the SOM
% size 2*n1-1 x 2*n2-1, where n1 = msize(1) and n2 = msize(2)
%
% EXAMPLES
%
% U = som_umat(sM);
% U = som_umat(sM.codebook,sM.topol,'median','mask',[1 1 0 1]);
% U = som_umat(rand(10,10,4),'hexa','rect');
%
% SEE ALSO
%
% som_show show the selected component planes and the u-matrix
% som_cplane draw a 2D unified distance matrix
% Copyright (c) 1997-2000 by the SOM toolbox programming team.
% http://www.cis.hut.fi/projects/somtoolbox/
% Version 1.0beta juuso 260997
% Version 2.0beta juuso 151199, 151299, 200900
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% check arguments
error(nargchk(1, Inf, nargin)); % check no. of input arguments is correct
% sMap
if isstruct(sMap),
M = sMap.codebook;
sTopol = sMap.topol;
mask = sMap.mask;
elseif isnumeric(sMap),
M = sMap;
si = size(M);
dim = si(end);
if length(si)>2, msize = si(1:end-1);
else msize = [si(1) 1];
end
munits = prod(msize);
sTopol = som_set('som_topol','msize',msize,'lattice','rect','shape','sheet');
mask = ones(dim,1);
M = reshape(M,[munits,dim]);
end
mode = 'median';
% varargin
i=1;
while i<=length(varargin),
argok = 1;
if ischar(varargin{i}),
switch varargin{i},
% argument IDs
case 'mask', i=i+1; mask = varargin{i};
case 'msize', i=i+1; sTopol.msize = varargin{i};
case 'lattice', i=i+1; sTopol.lattice = varargin{i};
case {'topol','som_topol','sTopol'}, i=i+1; sTopol = varargin{i};
case 'mode', i=i+1; mode = varargin{i};
% unambiguous values
case {'hexa','rect'}, sTopol.lattice = varargin{i};
case {'min','mean','median','max'}, mode = varargin{i};
otherwise argok=0;
end
elseif isstruct(varargin{i}) & isfield(varargin{i},'type'),
switch varargin{i}(1).type,
case 'som_topol', sTopol = varargin{i};
case 'som_map', sTopol = varargin{i}.topol;
otherwise argok=0;
end
else
argok = 0;
end
if ~argok,
disp(['(som_umat) Ignoring invalid argument #' num2str(i+1)]);
end
i = i+1;
end
% check
[munits dim] = size(M);
if prod(sTopol.msize)~=munits,
error('Map grid size does not match the number of map units.')
end
if length(sTopol.msize)>2,
error('Can only handle 1- and 2-dimensional map grids.')
end
if prod(sTopol.msize)==1,
warning('Only one codebook vector.'); U = []; return;
end
if ~strcmp(sTopol.shape,'sheet'),
disp(['The ' sTopol.shape ' shape of the map ignored. Using sheet instead.']);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% initialize variables
y = sTopol.msize(1);
x = sTopol.msize(2);
lattice = sTopol.lattice;
shape = sTopol.shape;
M = reshape(M,[y x dim]);
ux = 2 * x - 1;
uy = 2 * y - 1;
U = zeros(uy, ux);
calc = sprintf('%s(a)',mode);
if size(mask,2)>1, mask = mask'; end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% u-matrix computation
% distances between map units
if strcmp(lattice, 'rect'), % rectangular lattice
for j=1:y, for i=1:x,
if i<x,
dx = (M(j,i,:) - M(j,i+1,:)).^2; % horizontal
U(2*j-1,2*i) = sqrt(mask'*dx(:));
end
if j<y,
dy = (M(j,i,:) - M(j+1,i,:)).^2; % vertical
U(2*j,2*i-1) = sqrt(mask'*dy(:));
end
if j<y & i<x,
dz1 = (M(j,i,:) - M(j+1,i+1,:)).^2; % diagonals
dz2 = (M(j+1,i,:) - M(j,i+1,:)).^2;
U(2*j,2*i) = (sqrt(mask'*dz1(:))+sqrt(mask'*dz2(:)))/(2 * sqrt(2));
end
end
end
elseif strcmp(lattice, 'hexa') % hexagonal lattice
for j=1:y,
for i=1:x,
if i<x,
dx = (M(j,i,:) - M(j,i+1,:)).^2; % horizontal
U(2*j-1,2*i) = sqrt(mask'*dx(:));
end
if j<y, % diagonals
dy = (M(j,i,:) - M(j+1,i,:)).^2;
U(2*j,2*i-1) = sqrt(mask'*dy(:));
if rem(j,2)==0 & i<x,
dz= (M(j,i,:) - M(j+1,i+1,:)).^2;
U(2*j,2*i) = sqrt(mask'*dz(:));
elseif rem(j,2)==1 & i>1,
dz = (M(j,i,:) - M(j+1,i-1,:)).^2;
U(2*j,2*i-2) = sqrt(mask'*dz(:));
end
end
end
end
end
% values on the units
if (uy == 1 | ux == 1),
% in 1-D case, mean is equal to median
ma = max([ux uy]);
for i = 1:2:ma,
if i>1 & i<ma,
a = [U(i-1) U(i+1)];
U(i) = eval(calc);
elseif i==1, U(i) = U(i+1);
else U(i) = U(i-1); % i==ma
end
end
elseif strcmp(lattice, 'rect')
for j=1:2:uy,
for i=1:2:ux,
if i>1 & j>1 & i<ux & j<uy, % middle part of the map
a = [U(j,i-1) U(j,i+1) U(j-1,i) U(j+1,i)];
elseif j==1 & i>1 & i<ux, % upper edge
a = [U(j,i-1) U(j,i+1) U(j+1,i)];
elseif j==uy & i>1 & i<ux, % lower edge
a = [U(j,i-1) U(j,i+1) U(j-1,i)];
elseif i==1 & j>1 & j<uy, % left edge
a = [U(j,i+1) U(j-1,i) U(j+1,i)];
elseif i==ux & j>1 & j<uy, % right edge
a = [U(j,i-1) U(j-1,i) U(j+1,i)];
elseif i==1 & j==1, % top left corner
a = [U(j,i+1) U(j+1,i)];
elseif i==ux & j==1, % top right corner
a = [U(j,i-1) U(j+1,i)];
elseif i==1 & j==uy, % bottom left corner
a = [U(j,i+1) U(j-1,i)];
elseif i==ux & j==uy, % bottom right corner
a = [U(j,i-1) U(j-1,i)];
else
a = 0;
end
U(j,i) = eval(calc);
end
end
elseif strcmp(lattice, 'hexa')
for j=1:2:uy,
for i=1:2:ux,
if i>1 & j>1 & i<ux & j<uy, % middle part of the map
a = [U(j,i-1) U(j,i+1)];
if rem(j-1,4)==0, a = [a, U(j-1,i-1) U(j-1,i) U(j+1,i-1) U(j+1,i)];
else a = [a, U(j-1,i) U(j-1,i+1) U(j+1,i) U(j+1,i+1)]; end
elseif j==1 & i>1 & i<ux, % upper edge
a = [U(j,i-1) U(j,i+1) U(j+1,i-1) U(j+1,i)];
elseif j==uy & i>1 & i<ux, % lower edge
a = [U(j,i-1) U(j,i+1)];
if rem(j-1,4)==0, a = [a, U(j-1,i-1) U(j-1,i)];
else a = [a, U(j-1,i) U(j-1,i+1)]; end
elseif i==1 & j>1 & j<uy, % left edge
a = U(j,i+1);
if rem(j-1,4)==0, a = [a, U(j-1,i) U(j+1,i)];
else a = [a, U(j-1,i) U(j-1,i+1) U(j+1,i) U(j+1,i+1)]; end
elseif i==ux & j>1 & j<uy, % right edge
a = U(j,i-1);
if rem(j-1,4)==0, a=[a, U(j-1,i) U(j-1,i-1) U(j+1,i) U(j+1,i-1)];
else a = [a, U(j-1,i) U(j+1,i)]; end
elseif i==1 & j==1, % top left corner
a = [U(j,i+1) U(j+1,i)];
elseif i==ux & j==1, % top right corner
a = [U(j,i-1) U(j+1,i-1) U(j+1,i)];
elseif i==1 & j==uy, % bottom left corner
if rem(j-1,4)==0, a = [U(j,i+1) U(j-1,i)];
else a = [U(j,i+1) U(j-1,i) U(j-1,i+1)]; end
elseif i==ux & j==uy, % bottom right corner
if rem(j-1,4)==0, a = [U(j,i-1) U(j-1,i) U(j-1,i-1)];
else a = [U(j,i-1) U(j-1,i)]; end
else
a=0;
end
U(j,i) = eval(calc);
end
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% normalization between [0,1]
% U = U - min(min(U));
% ma = max(max(U)); if ma > 0, U = U / ma; end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%