function [Bmus,Qerrors] = som_bmus(sMap, sData, which_bmus, mask) %SOM_BMUS Find the best-matching units from the map for the given vectors. % % [Bmus, Qerrors] = som_bmus(sMap, sData, [which], [mask]) % % bmus = som_bmus(sM,sD); % [bmus,qerrs] = som_bmus(sM,D,[1 2 3]); % bmus = som_bmus(sM,D,1,[1 1 0 0 1]); % % Input and output arguments ([]'s are optional): % sMap (struct) map struct % (matrix) codebook matrix, size munits x dim % sData (struct) data struct % (matrix) data matrix, size dlen x dim % [which] (vector) which BMUs are returned, [1] by default % (string) 'all', 'best' or 'worst' meaning [1:munits], % [1] and [munits] respectively % [mask] (vector) mask vector, length=dim, sMap.mask by default % % Bmus (matrix) the requested BMUs for each data vector, % size dlen x length(which) % Qerrors (matrix) the corresponding quantization errors, size as Bmus % % NOTE: for a vector with all components NaN's, bmu=NaN and qerror=NaN % NOTE: the mask also effects the quantization errors % % For more help, try 'type som_bmus' or check out online documentation. % See also SOM_QUALITY. %%%%%%%%%%%%% DETAILED DESCRIPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % som_bmus % % PURPOSE % % Finds Best-Matching Units (BMUs) for given data vector from a given map. % % SYNTAX % % Bmus = som_bmus(sMap, sData) % Bmus = som_bmus(..., which) % Bmus = som_bmus(..., which, mask) % [Bmus, Qerrs] = som_bmus(...) % % DESCRIPTION % % Returns the indexes and corresponding quantization errors of the % vectors in sMap that best matched the vectors in sData. % % By default only the index of the best matching unit (/vector) is % returned, but the 'which' argument can be used to get others as % well. For example it might be desirable to get also second- and % third-best matching units as well (which = [1:3]). % % A mask can be used to weight the search process. The mask is used to % weight the influence of components in the distance calculation, as % follows: % % distance(x,y) = (x-y)' diag(mask) (x-y) % % where x and y are two vectors, and diag(mask) is a diagonal matrix with % the elements of mask vector on the diagonal. % % The vectors in the data set (sData) can contain unknown components % (NaNs), but the map (sMap) cannot. If there are completely empty % vectors (all NaNs), the returned BMUs and quantization errors for those % vectors are NaNs. % % REQUIRED INPUT ARGUMENTS % % sMap The vectors from among which the BMUs are searched % for. These must not have any unknown components (NaNs). % (struct) map struct % (matrix) codebook matrix, size munits x dim % % sData The data vector(s) for which the BMUs are searched. % (struct) data struct % (matrix) data matrix, size dlen x dim % % OPTIONAL INPUT ARGUMENTS % % which (vector) which BMUs are returned, % by default only the best (ie. which = [1]) % (string) 'all', 'best' or 'worst' meaning [1:munits], % [1] and [munits] respectively % mask (vector) mask vector to be used in BMU search, % by default sMap.mask, or ones(dim,1) in case % a matrix was given % % OUTPUT ARGUMENTS % % Bmus (matrix) the requested BMUs for each data vector, % size dlen x length(which) % Qerrors (matrix) the corresponding quantization errors, % size equal to that of Bmus % % EXAMPLES % % Simplest case: % bmu = som_bmus(sM, [0.3 -0.4 1.0]); % % 3-dimensional data, returns BMU for vector [0.3 -0.4 1] % bmu = som_bmus(sM, [0.3 -0.4 1.0], [3 5]); % % as above, except returns the 3rd and 5th BMUs % bmu = som_bmus(sM, [0.3 -0.4 1.0], [], [1 0 1]); % % as above, except ignores second component in searching % [bmus qerrs] = som_bmus(sM, D); % % returns BMUs and corresponding quantization errors % % for each vector in D % bmus = som_bmus(sM, sD); % % returns BMUs for each vector in sD using the mask in sM % % SEE ALSO % % som_quality Measure the quantization and topographic error of a SOM. % Copyright (c) 1997-2000 by the SOM toolbox programming team. % http://www.cis.hut.fi/projects/somtoolbox/ % Version 1.0beta juuso 071197, 101297 % Version 2.0alpha juuso 201198 080200 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% check arguments and initialize error(nargchk(1, 4, nargin)); % check no. of input args is correct % sMap if isstruct(sMap), switch sMap.type, case 'som_map', M = sMap.codebook; case 'som_data', M = sMap.data; otherwise, error('Invalid 1st argument.'); end else M = sMap; end [munits dim] = size(M); if any(any(isnan(M))), error ('Map codebook must not have missing components.'); end % data if isstruct(sData), switch sData.type, case 'som_map', D = sData.codebook; case 'som_data', D = sData.data; otherwise, error('Invalid 2nd argument.'); end else D = sData; end [dlen ddim] = size(D); if dim ~= ddim, error('Data and map dimensions do not match.') end % which_bmus if nargin < 3 | isempty(which_bmus) | any(isnan(which_bmus)), which_bmus = 1; else if ischar(which_bmus), switch which_bmus, case 'best', which_bmus = 1; case 'worst', which_bmus = munits; case 'all', which_bmus = [1:munits]; end end end % mask if nargin < 4 | isempty(mask) | any(isnan(mask)), if isstruct(sMap) & strcmp(sMap.type,'som_map'), mask = sMap.mask; elseif isstruct(sData) & strcmp(sData.type,'som_map'), mask = sData.mask; else mask = ones(dim,1); end end if size(mask,1)==1, mask = mask'; end if all(mask == 0), error('All components masked off. BMU search cannot be done.'); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% action Bmus = zeros(dlen,length(which_bmus)); Qerrors = Bmus; % The BMU search 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' % % In 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. % calculate distances & bmus % This is done a block of data at a time rather than in a % single sweep to save memory consumption. The 'Dist' matrix has % size munits*blen which would be HUGE if you did it in a single-sweep % operation. If you _want_ to use the single-sweep version, just % set blen = dlen. If you're having problems with memory, try to % set the value of blen lower. blen = min(munits,dlen); % handle unknown components Known = ~isnan(D); W1 = (mask*ones(1,dlen)) .* Known'; D(find(~Known)) = 0; unknown = find(sum(Known')==0); % completely unknown vectors % constant matrices WD = 2*diag(mask)*D'; % constant matrix dconst = ((D.^2)*mask); % constant term in the distances i0 = 0; while i0+1<=dlen, % calculate distances inds = [(i0+1):min(dlen,i0+blen)]; i0 = i0+blen; Dist = (M.^2)*W1(:,inds) - M*WD(:,inds); % plus dconst for each sample % find the bmus and the corresponding quantization errors if all(which_bmus==1), [Q B] = min(Dist); else [Q B] = sort(Dist); end if munits==1, Bmus(inds,:) = 1; else Bmus(inds,:) = B(which_bmus,:)'; end Qerrors(inds,:) = Q(which_bmus,:)' + dconst(inds,ones(length(which_bmus),1)); end % completely unknown vectors if ~isempty(unknown), Bmus(unknown,:) = NaN; Qerrors(unknown,:) = NaN; end Qerrors = sqrt(Qerrors); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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