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ITE / code / IPA / demos / estimate_AR_IPA.m

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function [s_hat,e_hat,W_hat,de_hat,Fx_hat,Fs_hat] = estimate_AR_IPA(x,AR,ICA,ISA,unknown_dimensions,de)
%Estimates the AR-IPA model. Method: AR identification + ISA on the estimated innovation.
%
%INPUT:
%   x: x(:,t) is the observation at time t.
%   AR: AR estimator, see 'estimate_AR.m'.
%   ICA: solver for independent component analysis, see 'estimate_ICA.m'.
%   ISA: solver for independent subspace analysis (=clustering of the ICA elements). ISA.cost_type, ISA.cost_name, ISA.opt_type: cost type, cost name, optimization type. Example: ISA.cost_type = 'sumH', ISA.cost_name = 'Renyi_kNN_1tok', ISA.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.
%OUTPUT:
%   s_hat: estimated source, s_hat(:,t) corresponds to time t
%   e_hat: estimated driving noise, e_hat(:,t) corresponds to time t
%   W_hat: estimated demixing matrix.
%   de_hat: estimated subspace dimensions.
%   Fx_hat: estimated observation dynamics.
%   Fs_hat: estimated source dynamics.
%
%REFERENCE:
%  Barnabas Poczos, Balint Takacs, and Andras Lorincz. Independent Subspace Analysis on Innovations. European Conference on Machine Learning (ECML), pp. 698-706, 2005. (multidimensional sources)
%  Aapo Hyvarinen. Independent component analysis for time-dependent stochastic processes. International Conference on Artificial Neural Networks (ICANN), pp. 541-546, 1998. (one-dimensional sources)
%
%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 <http://www.gnu.org/licenses/>.

%AR fit to x:
   [x_innovation_hat,Fx_hat,SBCs] = estimate_AR(x,AR);
   
%ISA on the estimated innovation of x:
   [e_hat,W_hat,de_hat] = estimate_ISA(x_innovation_hat,ICA,ISA,unknown_dimensions,de,size(x_innovation_hat,1));
   
%estimated source(s_hat) and its dynamics:
   s_hat = W_hat * x;
   Fs_hat = basis_transformation_AR(Fx_hat,W_hat,inv(W_hat));