# ITE / code / IPA / demos / demo_uMA_IPA_LPA.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 %function [] = demo_uMA_IPA_LPA() %uMA-IPA (undercomplete Moving Average Independent Process Analysis; MA-IPA = BSSD = Blind Subspace Deconvolution) illustration. Method: LPA, see 'estimate_uMA_IPA_LPA.m'. % %Model (uMA-IPA): % x(t) = \sum_{i=0}^L H_i e(t-i), e: ISA source, dim(x) > dim(e), and H[z] = \sum_{i=0}^L H_i z^{-i} has a polynomial matrix left inverse (such inverse exists under quite mild conditions in the undercomplete case). %or in short % x = H[z]e. %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 = 'Aw';%see 'sample_subspaces.m' num_of_comps = 3;%number of components/subspaces in sampling num_of_samples = 5*1000;%number of samples undercompleteness = 1; %dim(x) = ceil((undercompleteness+1) x dim(s)) MAparameters.type = 'randn'; %type of the convolution, see 'MA_polynomial.m'. MAparameters.L = 1;%length of the convolution; H_0,...,H_{L}: L+1 H_j matrices %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' %ARfit: ARmethod_parameters.L = [1:2*(MAparameters.L+1)];%AR order; %maximal order of the ARfit is 2*(L+1), this choice was robust for undercompleteness=1 ARmethod_parameters.method = 'stepwiseLS';%AR estimation method, see 'estimate_AR.m' %data generation (x,H,e,de,num_of_comps): [x,H,e,de,num_of_comps] = generate_MA_IPA(data_type,num_of_comps,num_of_samples,undercompleteness,MAparameters); %estimation via the LPA method (e_hat,W_hat,de_hat): De = sum(de); %dimension of the source(e) [e_hat,W_hat,de_hat] = estimate_uMA_IPA_LPA(x,ARmethod_parameters,ICA_method,opt_type,cost_type,cost_name,unknown_dimensions,de,De); %result: %global matrix(G): A = H(:,1:De); 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');