# ITE / code / IPA / optimization / clustering_UD0_CE_pairadditive_wrt_coordinates.m

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 function [perm_ICA] = clustering_UD0_CE_pairadditive_wrt_coordinates(S,ds) %Clusters the ICA (s_ICA) elements to subspaces of given dimensions (ds) %using (i) the 'CE' method and (ii) and (ii) similarity matrix S. % %Note: % in case of different ISA formulations, one can use 'clustering_UD0_CE_general.m' to carry out the optimization. % %INPUT: % s_ICA: s_ICA(:,t) is the t^th estimated realization of the ICA sources. % ds: subspace dimensions. %OUTPUT: % perm_ICA: permutation of the ICA elements. %REFERENCE: % This function is a simple adaptation of the works: % Zoltán Szabó, Barnabás Póczos, András Lőrincz: Cross-Entropy Optimization for Independent Process Analysis. ICA 2006, pages 909916. (adaptation to the ISA problem) % Reuven Y. Rubinstein, Dirk P. Kroese. The Cross-Entropy Method. Springer, 2004. (TSP problem; TSP=travelling salesman problem) % to the pairwise similarity (S) based (see cost_type = 'Ipairwise1d') ISA formulation. % %Copyright (C) 2012 Zoltan Szabo ("http://nipg.inf.elte.hu/szzoli", "szzoli (at) cs (dot) elte (dot) hu") % %This file is part of the ITE (Information Theoretical Estimators) Matlab/Octave toolbox. % %ITE is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by %the Free Software Foundation, either version 3 of the License, or (at your option) any later version. % %This software is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of %MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. % %You should have received a copy of the GNU General Public License along with ITE. If not, see . %parameters: alpha = 0.4;%smoothing parameter rho = 1/10;%elite treshold c = 5;%number of CE samples = c x number of parameters to estimate %stopping criteria: tolerance_treshold = 0.005; %stop optimization if the change of P is smaller than tolerance_treshold tolerance_last = 7; %stop optimization if the last tolerance_last gamma values (=elite treshold) were equal %initialization: D = size(S,1);%dim(s) num_of_CE_samples = c * D * (D-1); %c x number of parameters tours = zeros(D,num_of_CE_samples); %preallocation costs = zeros(num_of_CE_samples,1); %preallocation %transition probabilities (uniform): P = ones(D) / (D-1); P = P - diag(diag(P)); P_elite = zeros(D); %preallocation costs_last = zeros(tolerance_last,1); it = 0; const_gammas = false; P_old = inf(D);%P in the last iteration %mask (corresponding to coordinate pairs from different subspaces): mask = ds_mask(ds); disp('Clustering of the ICA elements (CE optimization): started.'); while (max(max(abs(P-P_old))) > tolerance_treshold) && (~const_gammas) %while P changed 'much' and the last gamma values were different in the last tolerance_last iterations %generate num_of_CE_samples samples and compute their costs: for k = 1 : num_of_CE_samples tour = TSP_tour_generation_via_node_transitions(P); tours(:,k) = tour; costs(k) = sum(sum(S(tour,tour).*mask)); end %sort the samples according to their performances: [costs,I] = sort(costs); num_of_elites = floor(rho*num_of_CE_samples); %best \rho percent is the elite %Estimation the transition probabilites via the elite samples: P_elite = TSP_estimate_elite_transition_probabilities(tours,num_of_elites,I); %P update: P_old = P; %last P (see the stopping criterion) P = alpha * P_elite + (1-alpha) * P; %stopping criterion (costs_last, const_gammas): %update the vector of previous costs: costs_last(1:end-1) = costs_last(2:end); costs_last(end) = costs(num_of_elites); const_gammas = (sum(costs_last==costs_last(end)) == tolerance_last); %true if the elite treshold (gamma) has not changed in the last tolerance_last iterations it = it + 1; disp(strcat(['Iteration ', num2str(it),': ready [elite level(=gamma_t)=',num2str(costs_last(end)),'].'])); end disp('Clustering of the ICA elements: ready.'); perm_ICA = tours(:,I(1)); 
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