# ITE / code / estimators / quick_tests / quick_test_Kpos_semidef.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 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 %function [] = quick_test_Kpos_semidef() %Quick test for the positive semi-definiteness of the Gram matrix determined by kernel K. In the test, uniform/normal variables are considered. %Copyright (C) 2013 Zoltan Szabo ("http://www.gatsby.ucl.ac.uk/~szabo/", "zoltan (dot) szabo (at) gatsby (dot) ucl (dot) ac (dot) uk") % %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: distr = 'uniform'; %possibilities: 'uniform', 'normal' d = 1; %dimension of the distribution num_of_distributions = 5; %number of distributions num_of_samples = 5000;%a given distribution is represented by num_of_samples samples %kernel used to evaluate the distributions: %base: cost_name = 'expected'; %cost_name = 'Bhattacharyya_kNN_k'; %cost_name = 'PP_kNN_k'; %meta: %cost_name = 'JS_DJS'; %cost_name = 'EJS_DJS'; %cost_name = 'JT_HJT'; %initialization: num_of_samples_half = floor(num_of_samples/2); co = K_initialization(cost_name,1); Ys = {}; %generate samples from the distributions (Ys): for n = 1 : num_of_distributions %generate samples from the n^{th} distribution (Y): switch distr case 'uniform' %a,b: a = -rand(d,1); b = rand(d,1); %a = zeros(d,1); b = ones(,1); %(random) linear transformation applied to the data: A = rand(d); %A = eye(d);%do not transform the data Y = A * (rand(d,num_of_samples) .* repmat(b-a,1,num_of_samples) + repmat(a,1,num_of_samples)); %AxU[a,b] case 'normal' %expectation: e = rand(d,1); %e = zeros(d,1); %(random) linear transformation applied to the data: A = rand(d); %A = eye(d); %do not transform the data Y = A * randn(d,num_of_samples) + repmat(e,1,num_of_samples); %AxN(0,I)+e end Ys{n} = Y; end %sampled distributions (Ys) -> Gram matrx ( G = [K(Ys{i},Ys{j})] ): G = zeros(num_of_distributions); for k1 = 1 : num_of_distributions %k1^{th} distribution for k2 = k1 : num_of_distributions %k2^{th} distribution if k1==k2 %to guarantee independence G(k1,k2) = K_estimation(Ys{k1}(:,1:num_of_samples_half),Ys{k1}(:,num_of_samples_half+1:end),co); %K(Ys{k1}(first half),Ys{k1}(second half)) else G(k1,k2) = K_estimation(Ys{k1},Ys{k2},co);%K(Ys{k1},Ys{k2}) end G(k2,k1) = G(k1,k2);%symmetry; assumption end end %compute the eigenvalues of the Gram matrix (eigenvalues): eigenvalues = eig(G); min_eig = min(eigenvalues); %minimal eigenvalue; ideally it is non-negative %plot: plot([1:num_of_distributions],eigenvalues); xlabel('Index of the sorted eigenvalues: i'); ylabel('Eigenvalues of the (estimated) Gram matrix: \lambda_i'); title(strcat(['Minimal eigenvalue: ',num2str(min_eig)]));