function [mqe,tge] = som_quality(sMap, D) %SOM_QUALITY Calculate the mean quantization and topographic error. % % [qe,te] = som_quality(sMap, D) % % qe = som_quality(sMap,D); % [qe,te] = som_quality(sMap,sD); % % Input and output arguments: % sMap (struct) a map struct % D the data % (struct) a data struct % (matrix) a data matrix, size dlen x dim % % qe (scalar) mean quantization error % te (scalar) topographic error % % The issue of SOM quality is a complicated one. Typically two % evaluation criterias are used: resolution and topology preservation. % If the dimension of the data set is higher than the dimension of the % map grid, these usually become contradictory goals. % % The first value returned by this function measures resolution and the % second the topology preservation. % qe : Average distance between each data vector and its BMU. % te : Topographic error, the proportion of all data vectors % for which first and second BMUs are not adjacent units. % % NOTE: when calculating BMUs of data vectors, the mask of the given % map is used. % % For more help, try 'type som_quality' or check out the online documentation. % See also SOM_BMUS. %%%%%%%%%%%%% DETAILED DESCRIPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % som_quality % % PURPOSE % % Calculates two quality measures for the given map. % % SYNTAX % % qe = som_quality(sM,sD); % qe = som_quality(sM,D); % [qe,te] = som_quality(...); % % DESCRIPTION % % This function measures the quality of the given map. The measures are % data-dependent: they measure the map in terms of the given % data. Typically, the quality of the map is measured in terms of the % training data. The returned quality measures are average quantization % error and topographic error. % % The issue of SOM quality is a complicated one. Typically two evaluation % criterias are used: resolution and topology preservation. There are % many ways to measure them. The ones implemented here were chosen for % their simplicity. % % qe : Average distance between each data vector and its BMU. % Measures map resolution. % te : Topographic error, the proportion of all data vectors % for which first and second BMUs are not adjacent units. % Measures topology preservation. % % NOTE: when calculating BMUs of data vectors, the mask of the given % map is used. The mask affects the quantization errors, too. % If you want the quantization errors without the weighting given % by the mask, you can use the following code: % bmus = som_bmus(sMap,D); % this uses the mask in finding the BMUs % for i=1:length(bmus), % dx = sMap.codebook(bmus(i),:)-D(i,:); % m - x % dx(isnan(dx)) = 0; % remove NaNs % qerr(i) = sqrt(sum(dx.^2)); % euclidian distance % end % qe = mean(qerr); % average quantization error % % Please note that you should _not_ trust the measures blindly. Generally, % both measures give the best results when the map has overfitted the % data. This may happen when the number of map units is as large or larger % than the number of training samples. Beware when you have such a case. % % REFERENCES % % Kohonen, T., "Self-Organizing Map", 2nd ed., Springer-Verlag, % Berlin, 1995, pp. 113. % Kiviluoto, K., "Topology Preservation in Self-Organizing Maps", % in the proceeding of International Conference on Neural % Networks (ICNN), 1996, pp. 294-299. % % INPUT ARGUMENTS % % sMap (struct) Map struct. % D The data to be used. % (matrix) A data matrix, size dlen x dim. % (struct) A data struct. % % OUTPUT ARGUMENTS % % qe (scalar) mean quantization error % te (scalar) topographic error % % EXAMPLES % % qe = som_quality(sMap,D); % [qe,te] = som_quality(sMap,sD); % % SEE ALSO % % som_bmus Find BMUs for the given set of data vectors. % Copyright (c) 1997-2000 by the SOM toolbox programming team. % http://www.cis.hut.fi/projects/somtoolbox/ % Version 1.0beta juuso 220997 % Version 2.0beta juuso 151199 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% check arguments % input arguments if nargin < 2, error('Not enough input arguments.'); end % data if isstruct(D), D = D.data; end [dlen dim] = size(D); % calculate topographic error, too? if nargout==1, b=1; else b=[1:2]; end [bmus qerrs]= som_bmus(sMap,D,b); inds = find(~isnan(bmus(:,1))); bmus = bmus(inds,:); qerrs = qerrs(inds,:); l = length(inds); if ~l, error('Empty data set.'); end % mean quantization error mqe = mean(qerrs(:,1)); if length(b)==2, % topographic error Ne = full(som_unit_neighs(sMap.topol)); tge = 0; for i=1:l, tge = tge+(Ne(bmus(i,1),bmus(i,2)) ~= 1); end tge = tge / l; else tge = NaN; end return; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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