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function [sMap,sTrain] = som_batchtrain(sMap, D, varargin)
%SOM_BATCHTRAIN Use batch algorithm to train the Self-Organizing Map.
%
% [sM,sT] = som_batchtrain(sM, D, [argID, value, ...])
%
% sM = som_batchtrain(sM,D);
% sM = som_batchtrain(sM,sD,'radius',[10 3 2 1 0.1],'tracking',3);
% [M,sT] = som_batchtrain(M,D,'ep','msize',[10 3],'hexa');
%
% Input and output arguments ([]'s are optional):
% sM (struct) map struct, the trained and updated map is returned
% (matrix) codebook matrix of a self-organizing map
% size munits x dim or msize(1) x ... x msize(k) x dim
% The trained map codebook is returned.
% D (struct) training data; data struct
% (matrix) training data, size dlen x dim
% [argID, (string) See below. The values which are unambiguous can
% value] (varies) be given without the preceeding argID.
%
% sT (struct) learning parameters used during the training
%
% 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) BMU search mask, size dim x 1
% 'msize' (vector) map size
% 'radius' (vector) neighborhood radiuses, length 1, 2 or trainlen
% 'radius_ini' (scalar) initial training radius
% 'radius_fin' (scalar) final training radius
% 'tracking' (scalar) tracking level, 0-3
% 'trainlen' (scalar) training length in epochs
% 'train' *(struct) train struct, parameters for training
% 'sTrain','som_train' = 'train'
% 'neigh' *(string) neighborhood function, 'gaussian', 'cutgauss',
% 'ep' or 'bubble'
% 'topol' *(struct) topology struct
% 'som_topol','sTopol' = 'topol'
% 'lattice' *(string) map lattice, 'hexa' or 'rect'
% 'shape' *(string) map shape, 'sheet', 'cyl' or 'toroid'
% 'weights' (vector) sample weights: each sample is weighted
%
% For more help, try 'type som_batchtrain' or check out online documentation.
% See also SOM_MAKE, SOM_SEQTRAIN, SOM_TRAIN_STRUCT.
%%%%%%%%%%%%% DETAILED DESCRIPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% som_batchtrain
%
% PURPOSE
%
% Trains a Self-Organizing Map using the batch algorithm.
%
% SYNTAX
%
% sM = som_batchtrain(sM,D);
% sM = som_batchtrain(sM,sD);
% sM = som_batchtrain(...,'argID',value,...);
% sM = som_batchtrain(...,value,...);
% [sM,sT] = som_batchtrain(M,D,...);
%
% DESCRIPTION
%
% Trains the given SOM (sM or M above) with the given training data
% (sD or D) using batch training algorithm. If no optional arguments
% (argID, value) are given, a default training is done. Using optional
% arguments the training parameters can be specified. Returns the
% trained and updated SOM and a train struct which contains
% information on the training.
%
% REFERENCES
%
% Kohonen, T., "Self-Organizing Map", 2nd ed., Springer-Verlag,
% Berlin, 1995, pp. 127-128.
% Kohonen, T., "Things you haven't heard about the Self-Organizing
% Map", In proceedings of International Conference
% on Neural Networks (ICNN), San Francisco, 1993, pp. 1147-1156.
%
% KNOWN BUGS
%
% Batchtrain does not work correctly for a map with a single unit.
% This is because of the way 'min'-function works.
%
% REQUIRED INPUT ARGUMENTS
%
% sM The map to be trained.
% (struct) map struct
% (matrix) codebook matrix (field .data of map struct)
% Size is either [munits dim], in which case the map grid
% dimensions (msize) should be specified with optional arguments,
% or [msize(1) ... msize(k) dim] in which case the map
% grid dimensions are taken from the size of the matrix.
% Lattice, by default, is 'rect' and shape 'sheet'.
% D Training data.
% (struct) data struct
% (matrix) data matrix, size [dlen 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. The valid IDs and corresponding values are listed below. The values
% which are unambiguous (marked with '*') can be given without the
% preceeding argID.
%
% Below is the list of valid arguments:
% 'mask' (vector) BMU search mask, size dim x 1. Default is
% the one in sM (field '.mask') or a vector of
% ones if only a codebook matrix was given.
% 'msize' (vector) map grid dimensions. Default is the one
% in sM (field sM.topol.msize) or
% 'si = size(sM); msize = si(1:end-1);'
% if only a codebook matrix was given.
% 'radius' (vector) neighborhood radius
% length = 1: radius_ini = radius
% length = 2: [radius_ini radius_fin] = radius
% length > 2: the vector given neighborhood
% radius for each step separately
% trainlen = length(radius)
% 'radius_ini' (scalar) initial training radius
% 'radius_fin' (scalar) final training radius
% 'tracking' (scalar) tracking level: 0, 1 (default), 2 or 3
% 0 - estimate time
% 1 - track time and quantization error
% 2 - plot quantization error
% 3 - plot quantization error and two first
% components
% 'trainlen' (scalar) training length in epochs
% 'train' *(struct) train struct, parameters for training.
% Default parameters, unless specified,
% are acquired using SOM_TRAIN_STRUCT (this
% also applies for 'trainlen', 'radius_ini'
% and 'radius_fin').
% 'sTrain', 'som_topol' (struct) = 'train'
% 'neigh' *(string) The used neighborhood function. Default is
% the one in sM (field '.neigh') or 'gaussian'
% if only a codebook matrix was given. Other
% possible values is 'cutgauss', 'ep' and 'bubble'.
% 'topol' *(struct) topology of the map. Default is the one
% in sM (field '.topol').
% 'sTopol', 'som_topol' (struct) = 'topol'
% 'lattice' *(string) map lattice. Default is the one in sM
% (field sM.topol.lattice) or 'rect'
% if only a codebook matrix was given.
% 'shape' *(string) map shape. Default is the one in sM
% (field sM.topol.shape) or 'sheet'
% if only a codebook matrix was given.
% 'weights' (vector) weight for each data vector: during training,
% each data sample is weighted with the corresponding
% value, for example giving weights = [1 1 2 1]
% would have the same result as having third sample
% appear 2 times in the data
%
% OUTPUT ARGUMENTS
%
% sM the trained map
% (struct) if a map struct was given as input argument, a
% map struct is also returned. The current training
% is added to the training history (sM.trainhist).
% The 'neigh' and 'mask' fields of the map struct
% are updated to match those of the training.
% (matrix) if a matrix was given as input argument, a matrix
% is also returned with the same size as the input
% argument.
% sT (struct) train struct; information of the accomplished training
%
% EXAMPLES
%
% Simplest case:
% sM = som_batchtrain(sM,D);
% sM = som_batchtrain(sM,sD);
%
% To change the tracking level, 'tracking' argument is specified:
% sM = som_batchtrain(sM,D,'tracking',3);
%
% The change training parameters, the optional arguments 'train','neigh',
% 'mask','trainlen','radius','radius_ini' and 'radius_fin' are used.
% sM = som_batchtrain(sM,D,'neigh','cutgauss','trainlen',10,'radius_fin',0);
%
% Another way to specify training parameters is to create a train struct:
% sTrain = som_train_struct(sM,'dlen',size(D,1));
% sTrain = som_set(sTrain,'neigh','cutgauss');
% sM = som_batchtrain(sM,D,sTrain);
%
% By default the neighborhood radius goes linearly from radius_ini to
% radius_fin. If you want to change this, you can use the 'radius' argument
% to specify the neighborhood radius for each step separately:
% sM = som_batchtrain(sM,D,'radius',[5 3 1 1 1 1 0.5 0.5 0.5]);
%
% You don't necessarily have to use the map struct, but you can operate
% directly with codebook matrices. However, in this case you have to
% specify the topology of the map in the optional arguments. The
% following commads are identical (M is originally a 200 x dim sized matrix):
% M = som_batchtrain(M,D,'msize',[20 10],'lattice','hexa','shape','cyl');
% or
% M = som_batchtrain(M,D,'msize',[20 10],'hexa','cyl');
% or
% sT= som_set('som_topol','msize',[20 10],'lattice','hexa','shape','cyl');
% M = som_batchtrain(M,D,sT);
% or
% M = reshape(M,[20 10 dim]);
% M = som_batchtrain(M,D,'hexa','cyl');
%
% The som_batchtrain also returns a train struct with information on the
% accomplished training. This struct is also added to the end of the
% trainhist field of map struct, in case a map struct was given.
% [M,sTrain] = som_batchtrain(M,D,'msize',[20 10]);
% [sM,sTrain] = som_batchtrain(sM,D); % sM.trainhist{end}==sTrain
%
% SEE ALSO
%
% som_make Initialize and train a SOM using default parameters.
% som_seqtrain Train SOM with sequential algorithm.
% som_train_struct Determine default training parameters.
% Copyright (c) 1997-2000 by the SOM toolbox programming team.
% http://www.cis.hut.fi/projects/somtoolbox/
% Version 1.0beta juuso 071197 041297
% Version 2.0beta juuso 101199
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Check arguments
error(nargchk(2, Inf, nargin)); % check the number of input arguments
% map
struct_mode = isstruct(sMap);
if struct_mode,
sTopol = sMap.topol;
else
orig_size = size(sMap);
if ndims(sMap) > 2,
si = size(sMap); dim = si(end); msize = si(1:end-1);
M = reshape(sMap,[prod(msize) dim]);
else
msize = [orig_size(1) 1];
dim = orig_size(2);
end
sMap = som_map_struct(dim,'msize',msize);
sTopol = sMap.topol;
end
[munits dim] = size(sMap.codebook);
% data
if isstruct(D),
data_name = D.name;
D = D.data;
else
data_name = inputname(2);
end
nonempty = find(sum(isnan(D),2) < dim);
D = D(nonempty,:); % remove empty vectors from the data
[dlen ddim] = size(D); % check input dimension
if dim ~= ddim,
error('Map and data input space dimensions disagree.');
end
% varargin
sTrain = som_set('som_train','algorithm','batch','neigh', ...
sMap.neigh,'mask',sMap.mask,'data_name',data_name);
radius = [];
tracking = 1;
weights = 1;
i=1;
while i<=length(varargin),
argok = 1;
if ischar(varargin{i}),
switch varargin{i},
% argument IDs
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 'mask', i=i+1; sTrain.mask = varargin{i};
case 'neigh', i=i+1; sTrain.neigh = varargin{i};
case 'trainlen', i=i+1; sTrain.trainlen = varargin{i};
case 'tracking', i=i+1; tracking = varargin{i};
case 'weights', i=i+1; weights = varargin{i};
case 'radius_ini', i=i+1; sTrain.radius_ini = varargin{i};
case 'radius_fin', i=i+1; sTrain.radius_fin = varargin{i};
case 'radius',
i=i+1;
l = length(varargin{i});
if l==1,
sTrain.radius_ini = varargin{i};
else
sTrain.radius_ini = varargin{i}(1);
sTrain.radius_fin = varargin{i}(end);
if l>2, radius = varargin{i}; end
end
case {'sTrain','train','som_train'}, i=i+1; sTrain = varargin{i};
case {'topol','sTopol','som_topol'},
i=i+1;
sTopol = varargin{i};
if prod(sTopol.msize) ~= munits,
error('Given map grid size does not match the codebook size.');
end
% unambiguous values
case {'hexa','rect'}, sTopol.lattice = varargin{i};
case {'sheet','cyl','toroid'}, sTopol.shape = varargin{i};
case {'gaussian','cutgauss','ep','bubble'}, sTrain.neigh = 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};
if prod(sTopol.msize) ~= munits,
error('Given map grid size does not match the codebook size.');
end
case 'som_train', sTrain = varargin{i};
otherwise argok=0;
end
else
argok = 0;
end
if ~argok,
disp(['(som_batchtrain) Ignoring invalid argument #' num2str(i+2)]);
end
i = i+1;
end
% take only weights of non-empty vectors
if length(weights)>dlen, weights = weights(nonempty); end
% trainlen
if ~isempty(radius), sTrain.trainlen = length(radius); end
% check topology
if struct_mode,
if ~strcmp(sTopol.lattice,sMap.topol.lattice) | ...
~strcmp(sTopol.shape,sMap.topol.shape) | ...
any(sTopol.msize ~= sMap.topol.msize),
warning('Changing the original map topology.');
end
end
sMap.topol = sTopol;
% complement the training struct
sTrain = som_train_struct(sTrain,sMap,'dlen',dlen);
if isempty(sTrain.mask), sTrain.mask = ones(dim,1); end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% initialize
M = sMap.codebook;
mask = sTrain.mask;
trainlen = sTrain.trainlen;
% neighborhood radius
if trainlen==1,
radius = sTrain.radius_ini;
elseif length(radius)<=2,
r0 = sTrain.radius_ini; r1 = sTrain.radius_fin;
radius = r1 + fliplr((0:(trainlen-1))/(trainlen-1)) * (r0 - r1);
else
% nil
end
% distance between map units in the output space
% Since in the case of gaussian and ep neighborhood functions, the
% equations utilize squares of the unit distances and in bubble case
% it doesn't matter which is used, the unitdistances and neighborhood
% radiuses are squared.
Ud = som_unit_dists(sTopol);
Ud = Ud.^2;
radius = radius.^2;
% zero neighborhood radius may cause div-by-zero error
radius(find(radius==0)) = eps;
% The training algorithm involves calculating weighted Euclidian distances
% to all map units for each data vector. Basically this is done as
% for i=1:dlen,
% for j=1:munits,
% for k=1:dim
% Dist(j,i) = Dist(j,i) + mask(k) * (D(i,k) - M(j,k))^2;
% end
% end
% end
% where mask is the weighting vector for distance calculation. However, taking
% into account that distance between vectors m and v can be expressed as
% |m - v|^2 = sum_i ((m_i - v_i)^2) = sum_i (m_i^2 + v_i^2 - 2*m_i*v_i)
% this can be made much faster by transforming it to a matrix operation:
% Dist = (M.^2)*mask*ones(1,d) + ones(m,1)*mask'*(D'.^2) - 2*M*diag(mask)*D'
% Of the involved matrices, several are constant, as the mask and data do
% not change during training. Therefore they are calculated beforehand.
% For the case where there are unknown components in the data, each data
% vector will have an individual mask vector so that for that unit, the
% unknown components are not taken into account in distance calculation.
% In addition all NaN's are changed to zeros so that they don't screw up
% the matrix multiplications and behave correctly in updating step.
Known = ~isnan(D);
W1 = (mask*ones(1,dlen)) .* Known';
D(find(~Known)) = 0;
% constant matrices
WD = 2*diag(mask)*D'; % constant matrix
dconst = ((D.^2)*mask)'; % constant in distance calculation for each data sample
% W2 = ones(munits,1)*mask'; D2 = (D'.^2);
% initialize tracking
start = clock;
qe = zeros(trainlen,1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Action
% With the 'blen' parameter you can control the memory consumption
% of the algorithm, which is in practive directly proportional
% to munits*blen. If you're having problems with memory, try to
% set the value of blen lower.
blen = min(munits,dlen);
% reserve some space
bmus = zeros(1,dlen);
ddists = zeros(1,dlen);
for t = 1:trainlen,
% batchy train - this is done a block of data (inds) at a time
% rather than in a single sweep to save memory consumption.
% The 'Dist' and 'Hw' matrices have size munits*blen
% which - if you have a lot of data - would be HUGE if you
% calculated it all at once. A single-sweep version would
% look like this:
% Dist = (M.^2)*W1 - M*WD; %+ W2*D2
% [ddists, bmus] = min(Dist);
% (notice that the W2*D2 term can be ignored since it is constant)
% This "batchy" version is the same as single-sweep if blen=dlen.
i0 = 0;
while i0+1<=dlen,
inds = [(i0+1):min(dlen,i0+blen)]; i0 = i0+blen;
Dist = (M.^2)*W1(:,inds) - M*WD(:,inds);
[ddists(inds), bmus(inds)] = min(Dist);
end
% tracking
if tracking > 0,
ddists = ddists+dconst; % add the constant term
ddists(ddists<0) = 0; % rounding errors...
qe(t) = mean(sqrt(ddists));
trackplot(M,D,tracking,start,t,qe);
end
% neighborhood
% notice that the elements Ud and radius have been squared!
% note: 'bubble' matches the original "Batch Map" algorithm
switch sTrain.neigh,
case 'bubble', H = (Ud<=radius(t));
case 'gaussian', H = exp(-Ud/(2*radius(t)));
case 'cutgauss', H = exp(-Ud/(2*radius(t))) .* (Ud<=radius(t));
case 'ep', H = (1-Ud/radius(t)) .* (Ud<=radius(t));
end
% update
% In principle the updating step goes like this: replace each map unit
% by the average of the data vectors that were in its neighborhood.
% The contribution, or activation, of data vectors in the mean can
% be varied with the neighborhood function. This activation is given
% by matrix H. So, for each map unit the new weight vector is
%
% m = sum_i (h_i * d_i) / sum_i (h_i),
%
% where i denotes the index of data vector. Since the values of
% neighborhood function h_i are the same for all data vectors belonging to
% the Voronoi set of the same map unit, the calculation is actually done
% by first calculating a partition matrix P with elements p_ij=1 if the
% BMU of data vector j is i.
P = sparse(bmus,[1:dlen],weights,munits,dlen);
% Then the sum of vectors in each Voronoi set are calculated (P*D) and the
% neighborhood is taken into account by calculating a weighted sum of the
% Voronoi sum (H*). The "activation" matrix A is the denominator of the
% equation above.
S = H*(P*D);
A = H*(P*Known);
% If you'd rather make this without using the Voronoi sets try the following:
% Hi = H(:,bmus);
% S = Hi * D; % "sum_i (h_i * d_i)"
% A = Hi * Known; % "sum_i (h_i)"
% The bad news is that the matrix Hi has size [munits x dlen]...
% only update units for which the "activation" is nonzero
nonzero = find(A > 0);
M(nonzero) = S(nonzero) ./ A(nonzero);
end; % for t = 1:trainlen
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Build / clean up the return arguments
% tracking
if tracking > 0, fprintf(1,'\n'); end
% update structures
sTrain = som_set(sTrain,'time',datestr(now,0));
if struct_mode,
sMap = som_set(sMap,'codebook',M,'mask',sTrain.mask,'neigh',sTrain.neigh);
tl = length(sMap.trainhist);
sMap.trainhist(tl+1) = sTrain;
else
sMap = reshape(M,orig_size);
end
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% subfunctions
%%%%%%%%
function [] = trackplot(M,D,tracking,start,n,qe)
l = length(qe);
elap_t = etime(clock,start);
tot_t = elap_t*l/n;
fprintf(1,'\rTraining: %3.0f/ %3.0f s',elap_t,tot_t)
switch tracking
case 1,
case 2,
plot(1:n,qe(1:n),(n+1):l,qe((n+1):l))
title('Quantization error after each epoch');
drawnow
otherwise,
subplot(2,1,1), plot(1:n,qe(1:n),(n+1):l,qe((n+1):l))
title('Quantization error after each epoch');
subplot(2,1,2), plot(M(:,1),M(:,2),'ro',D(:,1),D(:,2),'b+');
title('First two components of map units (o) and data vectors (+)');
drawnow
end
% end of trackplot