ITE / code / IPA / demos / estimate_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 52 53 54 55 56 57 58 59 60 61``` ```function [e_hat,W_hat,de_hat] = estimate_ISA(x,ICA_method,opt_type,cost_type,cost_name,unknown_dimensions,de,dim_reduction) %Estimates the ISA model. Method: ICA + clustering of the ICA elements (=ISA separation theorem). % %INPUT: % x: x(:,t) is the observation at time t. % ICA_method: the name of the ICA method applied, see 'estimate_ICA.m'. % cost_type, cost_name, opt_type: cost type, cost name, optimization type. Example: cost_type = 'sumH', cost_name = 'Renyi_kNN_1tok', opt_type = 'greedy' means that we use an entropy sum ISA formulation ('sumH'), where the entropies are estimated Renyi entropies via kNN methods ('Renyi_kNN_1tok') and the optimization is greedy; see also 'demo_ISA.m' % unknown_dimensions: '0' means 'the subspace dimensions are known'; '1' means 'the number of the subspaces are known' (but the individual dimensions are unknown). % de: % 1)in case of 'unknown_dimensions = 0': 'de' contains the subspace dimensions. % 2)in case of 'unknown_dimensions = 1': the length of 'de' must be equal to the number of subspaces, but the coordinates of the vector can be arbitrary. % dim_reduction: dim(x) = size(x,1) >= dim_reduction; if '>' holds, perform dimension reduction to dimension dim_reduction, too. %OUTPUT: % e_hat: e_hat(:,t) is the estimated ISA source at time t. % W_hat: estimated ISA demixing matrix. % de_hat: in case of known subspace dimensions ('unknown_dimensions = 0') de_hat = de; else it contains the estimated subspace dimensions; ordered increasingly. %REFERENCE: % Zoltan Szabo, Barnabas Poczos, Andras Lorincz: Undercomplete Blind Subspace Deconvolution. Journal of Machine Learning Research 8(May):1063-1095, 2007. (proof; sufficient conditions for the ISA separation theorem) % Jean-Francois Cardoso. Multidimensional independent component analysis. International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pages 1941�1944, 1998. (conjecture) % Lieven De Lathauwer, Bart De Moor, and Joos Vandewalle. Fetal electrocardiogram extraction by source subspace separation. In IEEE SP/Athos Workshop on Higher-Order Statistics, pages 134�138, 1995. ('conjecture') % %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 . disp('ISA estimation: started.'); %ICA step (e_ICA,W_ICA): [e_ICA,W_ICA] = estimate_ICA(x,ICA_method,dim_reduction); %clustering of the ICA elements (=permutation search; perm_ICA): switch unknown_dimensions case 0 perm_ICA = clustering_UD0(e_ICA,de,opt_type,cost_type,cost_name);%'UD0': unknown_dimensions=0 de_hat = de;%it is given case 1 if strcmp(cost_type,'Ipairwise1d') num_of_comps = length(de); [perm_ICA,de_hat] = clustering_UD1(e_ICA,num_of_comps,opt_type,cost_name);%'UD1': unknown_dimensions=1 [de_hat,per] = sort_subspaces_dimensions(de_hat);%sort the subspaces in increasing order with respect to their dimensions. perm_ICA = perm_ICA(per);%apply permutation 'perm_ICA' and then permutation 'per' else error('cost type=?'); end otherwise error('unknown dimensions=?'); end %estimated ISA source(e_hat), ISA demixing matrix (W_hat): e_hat = e_ICA(perm_ICA,:); W_hat = W_ICA(perm_ICA,:); disp('ISA estimation: ready.'); ```