ITE / code / IPA / demos / demo_fAR_IPA.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 %function [] = demo_fAR_IPA() %fAR-IPA (fAR=Functional AutoRegressive, IPA=Independent Process Analysis) illustration. % %Model (fAR-IPA): % s(t) = f(s(t-1),...,s(t-L)) + e(t), s:hidden source, f:unknown, e:ISA source (see 'demo_ISA.m'). % x(t) = A * s(t), A:invertible. %Task: x -> A (or W=A^{-1}),f,s,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 = 'Aw';%see 'sample_subspaces.m' num_of_comps = 2;%number of components/subspaces in sampling num_of_samples = 10*1000;%number of samples L = 1; %fAR order (tested intensively for L=1 only: 'recursive_Nadaraya_Watson_estimator.m') %ISA: unknown_dimensions = 0;%0: '{d_m}_{m=1}^M: known'; 1: 'M is known' %ICA solver (see 'estimate_ICA.m'): ICA.opt_type = 'fastICA'; %ISA solver (clustering of the ICA elements): ISA.cost_type = 'sumH'; %'I','sumH', 'sum-I','Irecursive', 'Ipairwise', 'Ipairwise1d' ISA.cost_name = 'Renyi_kNN_k'; %example: ISA.cost_type = 'sumH', ISA.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'). ISA.opt_type = 'greedy';%optimization type: 'greedy', 'CE', 'exhaustive', 'NCut', 'SP1', 'SP2', 'SP3' %Many combinations are allowed for ISA.cost_type, ISA.cost_name and ISA.opt_type, see 'clustering_UD0.m', 'clustering_UD1.m' %fAR: fAR.beta_normalized = 1/8; %/in (0,1) fAR.method = 'recursiveNW'; %fAR estimation method, see 'estimate_fAR.m' fAR.L = L; %fAR order %data generation (x,A,s,ds,num_of_comps): [x,A,s,e,de,num_of_comps] = generate_fAR_IPA(data_type,num_of_comps,num_of_samples,L); %estimation (e_hat,W_hat,de_hat,s_hat): [e_hat,W_hat,de_hat,s_hat] = estimate_fAR_IPA(x,ICA,ISA,unknown_dimensions,de,fAR); %result: %global matrix(G): G = W_hat * A; hinton_diagram(G,'global matrix (G=WA)');%ideally: block-scaling matrix %performance of G: Amari_index = Amari_index_ISA(G,de,'subspace-dim-proportional',2), h = plot_subspaces(e_hat,data_type,'estimated subspaces (\hat{e}^m), m=1,...,M');