ITE / code / IPA / demos / demo_PNL_ISA.m

%function [] = demo_PNL_ISA()
%PNL ISA (Post Nonlinear Independent Subspace Analysis) illustration.
%Model (PNL ISA):
%   x = g(Ae), A:invertible, e: ISA source (see 'demo_ISA.m'), g: coordinate-wise acting, invertible function (=post nonlinearity).
%Task: x -> [g^{-1},A (or W=A^{-1})],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 = 'Aw';%see 'sample_subspaces.m'
        num_of_comps = 6;%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_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'
        gaussianizationmethod_parameters.method = 'rank';%For possibilites, see 'estimate_gaussianization.m'.
        gaussianizationmethod_parameters.c = 0.97; %parameter of the 'rank' method
%data generation (x_LIN,A,e,de,num_of_comps):
    [x_LIN,A,e,de,num_of_comps] = generate_ISA(data_type,num_of_comps,num_of_samples);
    %PNL mixing:
        gs = create_PNL_mixing_functions(sum(de));
        x_PNL = PNL_mixing(x_LIN,gs);
        h = plot_subspaces(x_PNL,data_type,'post nonlinear mixture (x=g(Ae))');
%estimation (W_hat,e_hat,de_hat):    
    [W_hat,e_hat,de_hat] = estimate_PNL_ISA(x_PNL,ICA_method,opt_type,cost_type,cost_name,unknown_dimensions,de,gaussianizationmethod_parameters);

    %global matrix(G):
        %G: G * e = e_hat (XA=B => X=B/A)
            e_hat = E0(e_hat);
            G = e_hat / e;
            hinton_diagram(G,'global matrix (G: e -> \hat{e})');%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');