som.zip_SOM_self organization _self-organising maps_zip

% som a self-organizing-map using a circular network topology. % w = som(m,init_n,dec_n,init_d,Input,File) % returns w, the final weight vector for each node in a circular ring % topology, t: the number of iterations and e the squared average distance % at termination. Given input a p-by-n matrix of input vectors of dimension % n, the network w is a 2-layer net constructed as a m-by-n matrix such % that node i's weight vector is w(i,[1-n]). At each presentation of % an input vector i(l), the winner w(j) is found and the winner and % neighbors (according to the current distance function) are updated. % Uses a circular ring topology such that node i is adjacent to node j if % i = j+1 or i=j-1 and node 1 is adajacent to node m. % % NOTE: this version of som expects input to be of unit length and as % such calculates the winner wj = max(i(l)*w). Furthermore, this som % normalizes the weight vectors after each presentation such that they % lie on a unit circle. % % Additionally, writes in File (binary format) the weight vectors for % each time t=0..termination. The File has the following format: % The header: % - a 1-by-3 matrix [p,n,m] where p is the number of input vectors, n is % the dimenionsion of the input vectors and m is the number of output % nodes. % - a p-by-n matrix defining the input vectors % For each t=0..termination % - a 1-by-5 matrix [t,nt,dt,e,j] where t is the time, nt is the learning % rate, dt is the distance e is the squared euclidean distance of % the selected input from the winner, and j is the winning node % - a m-by-n matrix w, the weight vectors at time t % % Input: % m - the number of nodes (output) % init_n - the learning rate n at time t=0 % dec_n - amount to decrease n after each epoch % init_d - the distance d at time t=0 % Input - the input vectors % File - the name of a file to write the weights at each time to. This % file will be written in binary. % % NOTES: % - Expects a function dt = distance(t) to be defined on the path or % in the local directory that determines the distance dt given the % current time. % - This SOM algorithm has been left as general as possible but for the % problem description, (a unit circle), the function norm_circle expects % 2-dimensional inputs. % - Under the assumption that the number of nodes in the output layer is % relatively small, som uses the following weight update rule: % w = w + nt * (il-w) * nj % where nj is 1 for a neighbor of winner or zero otherwise so that the % effect of the rule can be defined as % wj = wj + nt*(il-wj) if j is a neighbor of winner % wj = wj otherwise % By doing so, neighbors of the winner do not have to removed from w % updated and reinserted. If however, the number of nodes is quite % large, it may be less computationally expensive to only calculate % il-w for neighbor nodes. % % Author: Dale Patterson % $Version: 1.4.3 $ $Date: 3.30.06 $ % function w = som(m,nt,dec_n,dt,Training,File) % attempt to open the output file [fid,msg] = fopen(File,'wb'); if fid == -1 error('project2:cannotOpenReportFile',fmsg); end % generate the initial weight vectors % w is a m-by-n matrix such that w(i,[1-n] is the weight vector of node i % weights are generated randomly in the range [-1,1] and normalized [p,n] = size(Training); % get # of samples and dimension w = norm_circle(-1 + 2.*rand(m,n)); % and generate w % since we're using matrix subtraction, we'll make a multidimensional array % I of size m-by-n-by-p where each I(:,:,p) is a m-by-n matrix A where for % each row i (i=1..m) in A equals Training(p,:), that is, each input vector % is repeated m times I = ones(m,n,p); for i=1:p I(:,:,i) = ones(m,1) * Training(i,:); end % write network parameters, input and initial weight vectors t = 0; % start at time t=0 err = Inf; % and err as infinity fwrite(fid,[p,n,m]); % as a uchar fwrite(fid,Training,'double'); % use double for precision fwrite(fid,[t,nt,dt,err,NaN],'double'); fwrite(fid,w,'double'); % loop till computational bounds are exceeded % we'll terminate after 120 epochs, for this problem, that means 20 epochs % at d=0 and n=0.005 while t < p*120 % permutate the input so that there's a different order for each epoch i = randperm(p); % i is a random permuatation of 1..p, use i to index I err = 0; % loop over the input (an epoch) for l=1:p % update the time t = t + 1; il = I(:,:,i(l)); % select an input sample % calculate distance, from i to each node dist = il-w; % distance from i to each node [v,j] = min(sum(dist.^2,2)); % j: winner index, v: sq. euc. dist. nj = neighbors(j,m,dt) * ones(1,n);% nj: 1s for neighbors, 0s otherwise err = err + v; % tally the error % update weight of winner and neighbors, and normalize w = norm_circle(w + nt * dist .* nj); % write period parameters and weight vectors to file fwrite(fid,[t,nt,dt,v,j],'double'); fwrite(fid,w,'double'); end % calculate the error; err = err / p; % update distance and learning rate if nt - dec_n > 0 nt = nt - dec_n; end dt = distance(t); end % clean up fclose(fid); % and close the file %%%% END som %%%% %%%% BEGIN SUB PROCEDURES %%%% % neighbors calculates the neighbors of a given node in a cirular ring topology. % n = neighbors(index,numNodes,distance) % returns n a column vector of 0 or 1, {0=not a neighbor, 1=neighbor} % for the node at index given a vector of numNodes with the given % distance using a circular ring topology function n = neighbors(i,ns,d) n = zeros(ns,1); % initialize a vector of zeros n(mod((-d:d)+(i-1),ns)+1) = 1; % and set to 1 each neighbor of i (inclusive 1)