# ITE / code / IPA / demos / demo_complex_ISA.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 %function [] = demo_complex_ISA() %Complex ISA (Independent Subspace Analysis) illustration. Method: complex -> real transformation, +real ISA. % %Model (complex ISA): % x = Ae, A:invertible, e=[e^1,...,e^M] (e^m:d_m-dimensional, i.e., e^m in C^{d_m}), I(C2R_vector(e)^1,...,C2R_vector(e)^M)=0, e_t: i.i.d. in time t, at most one of the C2R_vector(e^m)-s is Gaussian. %Task: x -> e. % %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 . %clear start: clear all; close all; %parameters: %dataset: data_type = 'multi4-geom';%see 'sample_subspaces.m' num_of_comps = 2;%number of components/subspaces in sampling num_of_samples = 5*1000;%number of samples %(real) ISA: unknown_dimensions = 0;%0: '{d_m}_{m=1}^M: known'; 1: 'M is known' ICA_method = 'fastICA'; %see 'estimate_ICA.m' %ISA cost (during the clustering of the ICA elements): cost_type = 'sumH'; %'I','sumH', 'sum-I','Irecursive', 'Ipairwise', 'Ipairwise1d' cost_name = 'Renyi_kNN_k'; %example: cost_type = 'sumH', cost_name = 'Renyi_kNN_1tok' means that we use an entropy sum ISA formulation ('sumH'), where the entropies are Renyi entropies estimated via kNN methods ('Renyi_kNN_1tok'). opt_type = 'greedy';%optimization type: 'greedy', 'CE', 'exhaustive', 'NCut', 'SP1', 'SP2', 'SP3' %A wide variety of combinations are allowed for cost_type, cost_name and opt_type, see 'clustering_UD0.m', 'clustering_UD1.m' %data generation (x,A,e,de,num_of_comps): [x,A,e,de,num_of_comps] = generate_complex_ISA(data_type,num_of_comps,num_of_samples); %estimation (e_real_hat,W_real_hat,de_real_hat,e_hat): [e_real_hat,W_real_hat,de_real_hat,e_hat] = estimate_complex_ISA(x,ICA_method,opt_type,cost_type,cost_name,unknown_dimensions,de,size(x,1)); %result: %global matrix(G): A_real = C2R_matrix(A); G = W_real_hat * A_real; hinton_diagram(G,'global matrix (G=W\phi_M(A))');%ideally: block-scaling matrix with (2d_m) x (2d_m) sized blocks. %performance of G: de_real = 2 * de; Amari_index = Amari_index_ISA(G,de_real,'subspace-dim-proportional',2),