somtoolbox2/som_distortion.m
 4dbef185 ``` function [adm,admu,tdmu] = som_distortion(sM, D, arg1, arg2) %SOM_DISTORTION Calculate distortion measure for the map. % % [adm,admu,tdmu] = som_distortion(sMap, D, [radius], ['prob']) % % adm = som_distortion(sMap,D); % [adm,admu] = som_distortion(sMap,D); % som_show(sMap,'color',admu); % % Input and output arguments: % sMap (struct) a map struct % D (struct) a data struct % (matrix) size dlen x dim, a data matrix % [radius] (scalar) neighborhood function radius to be used. % Defaults to the last radius_fin in the % trainhist field of the map struct, or 1 if % that is missing. % ['prob'] (string) If given, this argument forces the % neigborhood function values for each map % unit to be normalized so that they sum to 1. % % adm (scalar) average distortion measure (sum(dm)/dlen) % admu (vector) size munits x 1, average distortion in each unit % tdmu (vector) size munits x 1, total distortion for each unit % % The distortion measure is defined as: % 2 % E = sum sum h(bmu(i),j) ||m(j) - x(i)|| % i j % % where m(i) is the ith prototype vector of SOM, x(j) is the jth data % vector, and h(.,.) is the neighborhood function. In case of fixed % neighborhood and discreet data, the distortion measure can be % interpreted as the energy function of the SOM. Note, though, that % the learning rule that follows from the distortion measure is % different from the SOM training rule, so SOM only minimizes the % distortion measure approximately. % % If the 'prob' argument is given, the distortion measure can be % interpreted as an expected quantization error when the neighborhood % function values give the likelyhoods of accidentally assigning % vector j to unit i. The normal quantization error is a special case % of this with zero incorrect assignement likelihood. % % NOTE: when calculating BMUs and distances, the mask of the given % map is used. % % See also SOM_QUALITY, SOM_BMUS, SOM_HITS. % Reference: Kohonen, T., "Self-Organizing Map", 2nd ed., % Springer-Verlag, Berlin, 1995, pp. 120-121. % % Graepel, T., Burger, M. and Obermayer, K., % "Phase Transitions in Stochastic Self-Organizing Maps", % Physical Review E, Vol 56, No 4, pp. 3876-3890 (1997). % Contributed to SOM Toolbox vs2, Feb 3rd, 2000 by Juha Vesanto % Copyright (c) by Juha Vesanto % http://www.cis.hut.fi/projects/somtoolbox/ % Version 2.0beta juuso 030200 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% check arguments % input arguments if nargin < 2, error('Not enough input arguments.'); end % map M = sM.codebook; munits = prod(sM.topol.msize); % data if isstruct(D), D = D.data; end [dlen dim] = size(D); % arg1, arg2 rad = NaN; normalize = 0; if nargin>2, if isnumeric(arg1), rad = arg1; elseif ischar(arg1) & strcmp(arg1,'prob'), normalize = 0; end end if nargin>3, if isnumeric(arg2), rad = arg2; elseif ischar(arg2) & strcmp(arg2,'prob'), normalize = 0; end end % neighborhood radius if isempty(rad) | isnan(rad), if ~isempty(sM.trainhist), rad = sM.trainhist(end).radius_fin; else rad = 1; end end if rad0); admu(ind) = admu(ind) ./ hits(ind); % average distortion measure adm = sum(tdmu)/dlen; return; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ```