1function d = mvn_div_js(m1, m2, use_kl) 2%MVN_DIV_JS Compute the Jensen-Shannon (JS) divergence between two multivariate normals. 3% 4% [d] = MVN_DIV_JS(m1, m2) computes the JS divergence between two 5% multivariate normals. d is never negative. 6% 7% The JS divergence is defined as: 8% d = 0.5*KL(m1, m1+m2) + 0.5*KL(m2, m1+m2) 9 10% (c) 2010-2011, Dominik Schnitzer, <dominik.schnitzer@ofai.at> 11% http://www.ofai.at/~dominik.schnitzer/mvn 12% 13% This file is part of the MVN Octave/Matlab Toolbox 14% MVN is free software: you can redistribute it and/or modify 15% it under the terms of the GNU General Public License as published by 16% the Free Software Foundation, either version 3 of the License, or 17% (at your option) any later version. 18% 19% MVN is distributed in the hope that it will be useful, 20% but WITHOUT ANY WARRANTY; without even the implied warranty of 21% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 22% GNU General Public License for more details. 23% 24% You should have received a copy of the GNU General Public License 25% along with MVN. If not, see <http://www.gnu.org/licenses/>. 26 27 % Speedup: 28 % 29 % m12 = mvn_bregmancentroid_kl_left([m1 m2]); 30 % 31 % using Cholesky & more Optimization 32 33 m12.m = 0.5*m1.m + 0.5*m2.m; 34 m12.cov = 0.5*(m1.cov + m1.m*m1.m') + 0.5*(m2.cov + m2.m*m2.m') ... 35 - m12.m*m12.m'; 36 m12_chol = chol(m12.cov); 37 m12.logdet = 2*sum(log(diag(m12_chol))); 38 39 if ((nargin > 2) && (use_kl == 1)) 40 m12_ui = m12_chol\eye(length(m12.m)); 41 m12.icov = m12_ui*m12_ui'; 42 43 d = 0.5*mvn_div_kl(m1, m12) + 0.5*mvn_div_kl(m2, m12); 44 else 45 % Speedup original (entropy): 46 % 47 % d = mvn_entropy(m12) - 0.5*mvn_entropy(m1) - 0.5*mvn_entropy(m2); 48 % 49 % faster: 50 51 d = 0.5*m12.logdet - 0.25*m1.logdet - 0.25*m2.logdet; 52 end 53 54 d = max(d, 0); 55end 56