function Ne = som_neighborhood(Ne1,n) %SOM_NEIGHBORHOOD Calculate neighborhood matrix. % % Ne = som_neighborhood(Ne1,n) % % Ne = som_neighborhood(Ne1); % Ne = som_neighborhood(som_unit_neighs(topol),2); % % Input and output arguments ([]'s are optional): % Ne1 (matrix, size [munits m]) a sparse matrix indicating % the units in 1-neighborhood for each map unit % [n] (scalar) maximum neighborhood which is calculated, default=Inf % % Ne (matrix, size [munits munits]) neighborhood matrix, % each row (and column) contains neighborhood % values from the specific map unit to all other % map units, or Inf if the value is unknown. % % For more help, try 'type som_neighborhood' or check out online documentation. % See also SOM_UNIT_NEIGHS, SOM_UNIT_DISTS, SOM_UNIT_COORDS, SOM_CONNECTION. %%%%%%%%%%%%% DETAILED DESCRIPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % som_neighborhood % % PURPOSE % % Calculate to which neighborhood each map unit belongs to relative to % each other map unit, given the units in 1-neighborhood of each unit. % % SYNTAX % % Ne = som_neighborhood(Ne1); % Ne = som_neighborhood(Ne1,n); % % DESCRIPTION % % For each map unit, finds the minimum neighborhood to which it belongs % to relative to each other map unit. Or, equivalently, for each map % unit, finds which units form its k-neighborhood, where k goes from % 0 to n. % % The neighborhood is calculated iteratively using the reflexivity of % neighborhood. % let N1i be the 1-neighborhood set a unit i % and let N11i be the set of units in the 1-neighborhood of any unit j in N1i % then N2i (the 2-neighborhood set of unit i) is N11i \ N1i % % Consider, for example, the case of a 5x5 map. The neighborhood in case of % 'rect' and 'hexa' lattices (and 'sheet' shape) for the unit at the % center of the map are depicted below: % % 'rect' lattice 'hexa' lattice % -------------- -------------- % 4 3 2 3 4 3 2 2 2 3 % 3 2 1 2 3 2 1 1 2 3 % 2 1 0 1 2 2 1 0 1 2 % 3 2 1 2 3 2 1 1 2 3 % 4 3 2 3 4 3 2 2 2 3 % % Because the iterative procedure is rather slow, the neighborhoods % are calculated upto given maximal value. The uncalculated values % in the returned matrix are Inf:s. % % REQUIRED INPUT ARGUMENTS % % Ne1 (matrix) Each row contains 1, if the corresponding unit is adjacent % for that map unit, 0 otherwise. This can be calculated % using SOM_UNIT_NEIGHS. The matrix can be sparse. % Size munits x munits. % % OPTIONAL INPUT ARGUMENTS % % n (scalar) Maximal neighborhood value which is calculated, % Inf by default (all neighborhoods). % % OUTPUT ARGUMENTS % % Ne (matrix) neighborhood values for each map unit, size is % [munits, munits]. The matrix contains the minimum % neighborhood of unit i, to which unit j belongs, % or Inf, if the neighborhood was bigger than n. % % EXAMPLES % % Ne = som_neighborhood(Ne1,1); % upto 1-neighborhood % Ne = som_neighborhood(Ne1,Inf); % all neighborhoods % Ne = som_neighborhood(som_unit_neighs(topol),4); % % SEE ALSO % % som_unit_neighs Calculate units in 1-neighborhood for each map unit. % som_unit_coords Calculate grid coordinates. % som_unit_dists Calculate interunit distances. % som_connection Connection matrix. % Copyright (c) 1999-2000 by the SOM toolbox programming team. % http://www.cis.hut.fi/projects/somtoolbox/ % Version 1.0beta juuso 141097 % Version 2.0beta juuso 101199 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Check arguments error(nargchk(1, 2, nargin)); if nargin<2, n=Inf; end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Action % initialize if issparse(Ne1), Ne = full(Ne1); else Ne = Ne1; end clear Ne1 [munits dummy] = size(Ne); Ne(find(Ne==0)) = NaN; for i=1:munits, Ne(i,i)=0; end % Calculate neighborhood distance for each unit using reflexsivity % of neighborhood: % let N1i be the 1-neighborhood set a unit i % then N2i is the union of all map units, belonging to the % 1-neighborhood of any unit j in N1i, not already in N1i k=1; if n>1, fprintf(1,'Calculating neighborhood: 1 '); N1 = Ne; N1(find(N1~=1)) = 0; end while k<n & any(isnan(Ne(:))), k=k+1; fprintf(1,'%d ',k); for i=1:munits, candidates = isnan(Ne(i,:)); % units not in any neighborhood yet if any(candidates), prevneigh = find(Ne(i,:)==k-1); % neighborhood (k-1) N1_of_prevneigh = any(N1(prevneigh,:)); % union of their N1:s Nn = find(N1_of_prevneigh & candidates); if length(Nn), Ne(i,Nn) = k; Ne(Nn,i) = k; end end end end if n>1, fprintf(1,'\n'); end % finally replace all uncalculated distance values with Inf Ne(find(isnan(Ne))) = Inf; return; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% faster version? l = size(Ne1,1); Ne1([0:l-1]*(l+1)+1) = 1; Ne = full(Ne1); M0 = Ne1; k = 2; while any(Ne(:)==0), M1=(M0*Ne1>0); Ne(find(M1-M0))=k; M0=M1; k=k+1; end Ne([0:l-1]*(l+1)+1) = 0;

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