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% initializeif issparse(Ne1), Ne = full(Ne1); else Ne = Ne1; endclear 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 N1ik=1; if n>1,   fprintf(1,'Calculating neighborhood: 1 ');   N1 = Ne;   N1(find(N1~=1)) = 0;   endwhile 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  endendif n>1, fprintf(1,'\n'); end% finally replace all uncalculated distance values with InfNe(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; endNe([0:l-1]*(l+1)+1) = 0;