ITE / code / IPA / demos / demo_complex_ISA_C.m

Full commit
%function [] = demo_complex_ISA_C()
%Complex ISA (Independent Subspace Analysis) illustration. Method: complex ICA + clustering of the complex ICA elements (=complex ISA separation theorem).
%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 ("", "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;
        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
        unknown_dimensions = 0;%0: '{d_m}_{m=1}^M: known'; 1: 'M is known'
        ICA_method = 'fastICA'; %see 'estimate_complex_ICA.m'
        %ISA cost (during the clustering of the ICA elements):
            cost_type = 'sum-I'; %'I','sumH', 'sum-I','Irecursive', 'Ipairwise', 'Ipairwise1d'
            cost_name = 'complex'; %example: cost_type = 'sumH', cost_name = 'complex' means that we use an entropy sum ISA formulation ('sumH'), where the entropies are estimated via the 'complex' method.
            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_hat,W_hat,de_hat):
    [e_hat,W_hat,de_hat] = estimate_complex_ISA_C(x,ICA_method,opt_type,cost_type,cost_name,unknown_dimensions,de);

    %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),