mvn-1.0/COPYING.txt0000644000175000017500000010451311627400677013707 0ustar dominikdominik GNU GENERAL PUBLIC LICENSE
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.
mvn-1.0/mvn_bregmancentroid_geodesic.m0000644000175000017500000000362111627401010020055 0ustar dominikdominikfunction [c] = mvn_bregmancentroid_geodesic(d, c1, c2)
%MVN_BREGMANCENTROID_GEODESIC Computes an arbitrary wieghted KL centroid
% on the geodesic linking between two sided centroids c1 and c2.
%
% [c] = MVN_BREGMANCENTROID_GEODESIC(d, m1, m2) computes the KL centroid
% for the given sided centroids m1 and m2 weighting m1 with d and m2
% with (1-d).
%
% See: On the centroids of symmetrized bregman divergences, Nielsen, F.
% and Nock, R., 2007.
%
% (c) 2010-2011, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
c.m = d*c1.m + (1-d)*c2.m;
c.cov = d*(c1.cov + c1.m*c1.m') + ...
(1-d)*(c2.cov + c2.m*c2.m') - ...
c.m*c.m';
c_chol = chol(c.cov);
c.logdet = 2*sum(log(diag(c_chol)));
c_ui = c_chol\eye(length(c.m));
c.icov = c_ui*c_ui';
% Original version
%
% % compute gradient (gradF)
% c1GF.m = c1.m;
% c1GF.cov = -(c1.cov + c1.m*c1.m');
% c2GF.m = c2.m;
% c2GF.cov = -(c2.cov + c2.m*c2.m');
%
% % geodesic walk
% gcGF.m = d*c1GF.m + (1-d)*c2GF.m;
% gcGF.cov = d*c1GF.cov + (1-d)*c2GF.cov;
%
% % compute inverse gradient (gradF^-1)
% c.m = gcGF.m;
% c.cov = -(gcGF.cov + gcGF.m*gcGF.m');
end
mvn-1.0/mvn_bregmancentroid_kl_left.m0000644000175000017500000000360111627400773017730 0ustar dominikdominikfunction [c] = mvn_bregmancentroid_kl_left(models)
%MVN_BREGMANCENTROID_KL_LEFT Compute the left sided Kullback-Leibler
% (KL) centroid given mvn models. (GARDIENT SPACE CENTER OF MASS)
%
% [c] = MVN_BREGMANCENTROID_KL_LEFT(models) computes the left sided KL
% centroid for the given multivariate normals.
%
% (c) 2010-2011, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
c.m = 0 .* models(1).m;
% new means
len = length(models);
for i=1:len
c.m = c.m + 1/len .* models(i).m;
end
% new covariance
% % original:
% c.cov = c.m*c.m';
% for i=1:len
% c.cov = c.cov + 1/len .* (models(i).cov +...
% models(i).m*models(i).m' - models(i).m*c.m' -...
% c.m*models(i).m');
c.cov = -1 .* c.m*c.m';
for i=1:len
c.cov = c.cov + 1/len.*(models(i).cov + models(i).m*models(i).m');
end
% compute inverse covariance
% speedup for
%
% c.logdet = log(det(c.cov));
% c.icov = inv(c.cov);
%
% using Cholesky:
c_chol = chol(c.cov);
c.logdet = 2*sum(log(diag(c_chol)));
c_ui = c_chol\eye(length(c.m));
c.icov = c_ui*c_ui';
end
mvn-1.0/mvn_bregmancentroid_kl_right.m0000644000175000017500000000324611627401015020106 0ustar dominikdominikfunction [c] = mvn_bregmancentroid_kl_right(models)
%MVN_BREGMANCENTROID_RIGHT Compute the right centroid given mvn
% models ("center of mass").
%
% [c] = MVN_BREGMANCENTROID_RIGHT(models) computes the right sided
% centroid for the given multivariate normals.
%
% (c) 2010, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
% compute the new mean in the natural parameter space
len = length(models);
c.m = 0 .* models(1).m;
for i=1:len
c.m = c.m + 1/len * (models(i).icov * models(i).m);
end
% compute the covariance in the natural parameter space
c.cov = [];
c.logdet = NaN;
c.icov = 0 .* models(1).cov;
for i=1:len
c.icov = c.icov + 1/len * models(i).icov;
end
% recover the the parameters of the multivariate gaussian distribution
% from the natual parameters
c.cov = inv(c.icov);
c.m = c.cov * c.m;
c_chol = chol(c.cov);
c.logdet = 2*sum(log(diag(c_chol)));
end
mvn-1.0/mvn_bregmancentroid_skl.m0000644000175000017500000000355511627401023017076 0ustar dominikdominikfunction [c] = mvn_bregmancentroid_skl(models, approx, lc, rc)
%MVN_BREGMANCENTROID_SKL Compute the symmetric Kullback-Leibler (KL)
% centroid given mvn models.
%
% [c] = MVN_BREGMANCENTROID_SKL(models) computes the SKL centroid
% for the given multivariate normals.
%
% [c] = MVN_BREGMANCENTROID_SKL(models, 1) computes the SKL centroid
% mid-point approximation for the given multivariate normals.
%
% (c) 2010-2011, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
c = [];
if (nargin < 3)
if (length(models) < 1)
return;
end
lc = mvn_bregmancentroid_kl_left(models);
rc = mvn_bregmancentroid_kl_right(models);
end
% compute the mid-point approximation if requested.
if ((nargin > 1) && (approx == 1))
c = mvn_bregmancentroid_geodesic(0.5, lc, rc);
return;
end
d = 0;
d1 = 1;
while ((d1 - d) > 0.00001)
d2 = 0.5 * (d + d1);
c = mvn_bregmancentroid_geodesic(d2, lc, rc);
bisector = mvn_div_kl(c, lc) - mvn_div_kl(rc, c);
if (bisector < 0)
d1 = d2;
else
d = d2;
end
end
end
mvn-1.0/mvn_div_bc.m0000644000175000017500000000252311627401030014300 0ustar dominikdominikfunction d = mvn_div_bc(m1, m2)
%MVN_DIV_BC Compute the Bhattacharyya coefficient between two
% multivariate normals.
%
% [d] = MVN_DIV_BC(m1, m2) computes the BC between two
% multivariate normals. d is never negative.
%
% (c) 2010-2011, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
mdiff = m1.m - m2.m;
covsum = 0.5*(m1.cov + m2.cov);
% % Original
% d = 1/8 * ((mdiff' * inv(covsum)) * mdiff) +...
% 1/2*log(det(covsum)) - 1/4*m1.logdet - 1/4*m2.logdet;
d = 1/8 * ((mdiff' / covsum) * mdiff) +...
1/2*log(det(covsum)) - 1/4*m1.logdet - 1/4*m2.logdet;
d = max(d, 0);
end
mvn-1.0/mvn_div_js.m0000644000175000017500000000360011627401035014332 0ustar dominikdominikfunction d = mvn_div_js(m1, m2, use_kl)
%MVN_DIV_JS Compute the Jensen-Shannon (JS) divergence between two
% multivariate normals.
%
% [d] = MVN_DIV_JS(m1, m2) computes the JS divergence between two
% multivariate normals. d is never negative.
%
% The JS divergence is defined as:
% d = 0.5*KL(m1, m1+m2) + 0.5*KL(m2, m1+m2)
%
% (c) 2010-2011, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
% Speedup:
%
% m12 = mvn_bregmancentroid_kl_left([m1 m2]);
%
% using Cholesky & more Optimization
m12.m = 0.5*m1.m + 0.5*m2.m;
m12.cov = 0.5*(m1.cov + m1.m*m1.m') + 0.5*(m2.cov + m2.m*m2.m') ...
- m12.m*m12.m';
m12_chol = chol(m12.cov);
m12.logdet = 2*sum(log(diag(m12_chol)));
if ((nargin > 2) && (use_kl == 1))
m12_ui = m12_chol\eye(length(m12.m));
m12.icov = m12_ui*m12_ui';
d = 0.5*mvn_div_kl(m1, m12) + 0.5*mvn_div_kl(m2, m12);
else
% Speedup original (entropy):
%
% d = mvn_entropy(m12) - 0.5*mvn_entropy(m1) - 0.5*mvn_entropy(m2);
%
% faster:
d = 0.5*m12.logdet - 0.25*m1.logdet - 0.25*m2.logdet;
end
d = max(d, 0);
end
mvn-1.0/mvn_div_kl.m0000644000175000017500000000222611627401045014330 0ustar dominikdominikfunction [d] = mvn_div_kl(p, q)
%MVN_DIV_KL Compute the Kullback-Leibler (KL) divergence.
%
% [d] = MVN_DIV_KL(m1, m2) computes the KL divergence between two
% multivariate normals. d is never negative.
%
% (c) 2010-2011, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
n = length(p.m);
m = q.m - p.m;
d = 0.5 * ((q.logdet - p.logdet) + mvn_traceprod(q.icov, p.cov) + ...
m' * q.icov * m - n);
d = max(d, 0);
end
mvn-1.0/mvn_divmat.m0000644000175000017500000000370111627401053014342 0ustar dominikdominikfunction [d] = mvn_divmat(models, t)
%MVN_DIVMAT Compute a distance/divergence matrix using the specified MODELS
% and the given divergence T.
%
% [d] = MVN_DIVMAT(models, t) Computes a divergence matrix using the given
% mvn MODELS models and divergence T. T can be 'kl_left', 'kl_right',
% 'skl', 'js', 'js_kl'. It defaults to the 'skl'.
%
% (c) 2010-2011, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
if (nargin < 2)
t = 'skl';
end
if (strcmp(t, 'kl_left') == 1)
mvn_div = @(x, c) mvn_div_kl(x, c);
elseif (strcmp(t, 'kl_right') == 1)
mvn_div = @(x, c) mvn_div_kl(c, x);
elseif (strcmp(t, 'skl') == 1)
mvn_div = @(x, c) mvn_div_skl(x, c);
elseif (strcmp(t, 'js') == 1)
mvn_div = @(x, c) mvn_div_js(x, c);
elseif (strcmp(t, 'js_kl') == 1)
mvn_div = @(x, c) mvn_div_js(x, c, 1);
end
d = zeros(length(models), length(models), 'single');
for i=1:length(models)
if (isempty(models(i).m))
continue;
end
for j=i+1:length(models)
if (isempty(models(j).m))
continue;
end
d(i, j) = mvn_div(models(i), models(j));
d(j, i) = d(i, j);
end
end
end
mvn-1.0/mvn_div_skl.m0000644000175000017500000000252211627401056014514 0ustar dominikdominikfunction d = mvn_div_skl(m1, m2)
%MVN_DIV_SKL Compute the symmetric Kullback-Leibler (KL) divergence.
%
% [d] = MVN_DIV_SKL(m1, m2) computes the SKL divergence between two
% multivariate normals. d is never negative.
%
% The SKL divergence is defined as:
% d = 0.5*KL(m1, m2) + 0.5*KL(m2, m1)
%
% Note: This function computes a faster version.
%
% (c) 2010-2011, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
n = length(m1.m);
m = m1.m - m2.m;
d = (mvn_traceprod(m1.cov, m2.icov) + mvn_traceprod(m2.cov, m1.icov) + ...
mvn_traceprod(m1.icov+m2.icov, m*m') - 2*n) / 4;
d = max(d, 0);
end
mvn-1.0/mvn_entropy.m0000644000175000017500000000200611627401063014554 0ustar dominikdominikfunction [h] = mvn_entropy(m)
%MVN_ENTROPY Compute the Entropy of the given multivariate normal.
%
% [h] = MVN_ENTROPY(m) computes the entopy of mvn model M.
%
% (c) 2010-2011, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
n = length(m.m);
h = (n + n*log(2*pi))/2 + m.logdet/2;
end
mvn-1.0/mvn_fn2class.m0000644000175000017500000000241311627401070014567 0ustar dominikdominikfunction [cl_names, cl_assig] = mvn_fn2class(filenames, cl_pos, delim)
%MVN_FN2CLASS
%
% (c) 2010-2011, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
cl_names_all = cell(length(filenames), 1);
for i = 1:length(filenames)
fn = filenames{i};
sp = strfind(fn, delim);
cl_names_all{i} = fn(sp(cl_pos)+1:sp(cl_pos+1)-1);
end
cl_names = unique(cl_names_all);
cl_assig = zeros(length(filenames), 1);
for i = 1:length(filenames)
cl_assig(i) = find(strcmp(cl_names, cl_names_all{i}) == 1);
end
end
mvn-1.0/mvn_ismetric.m0000644000175000017500000000266311627401075014707 0ustar dominikdominikfunction [ ismetric ] = mvn_ismetric(d)
%MVN_ISMETRIC Analyzes the distance matrix D and retruns the percentage
% of triples fulfilling the trinangle inequality.
%
% ATTENTION: Symmetry and Identity is presumed.
%
% ismetric = MVN_ISMETRIC(d) Analyzes the given distance matrix and returns
% the percentage of all possible triples fulfilling the triangle inequality.
%
% (c) 2010-2011, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
ismetric = 0;
for x = 1:length(d)
ismetric = ismetric + sum((d(x,x) <= d(x,:) + d(x,:)));
for y = (x+1):length(d)
ismetric = ismetric + 2*sum( d(x, y) <= (d(x, :) + d(y, :)) );
end
end
ismetric = ismetric / (length(d)^3);
end
mvn-1.0/mvn_kmeans.m0000644000175000017500000001112611627401101014326 0ustar dominikdominikfunction [centers, assig, qe] = mvn_kmeans(models, k, t)
%MVN_KMEANS Compute K-Means clustering on the given mvn models in
% respect to the given divergence. Standard is the symmetric
% Kullback-Leibler divergence between the models.
%
% [centers, assig] = MVN_KMEANS_SKL(models, k, type) computes a k-means
% clustering using the given the SKL divergence. We return k mvn
% centers and the assignment of the models to their centers.
%
% See: Clustering with Bregman divergences, A. Banerjee et al., The
% Journal of Machine Learning Research 2005, Volume 6.
%
% (c) 2010-2011, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
items = length(models);
assig = zeros(items, 1);
ri = randi(items, k, 1);
centers = models(ri);
if ((nargin < 2) || (nargin > 3))
error('Wrong number of input arguments');
end
if (nargin < 3)
t = 'skl';
end
if (strcmp(t, 'kl_left') == 1)
mvn_div = @(x, c) mvn_div_kl(x, c);
mvn_bregmancentroid = @(x) mvn_bregmancentroid_kl_left(x);
elseif (strcmp(t, 'kl_right') == 1)
mvn_div = @(x, c) mvn_div_kl(c, x);
mvn_bregmancentroid = @(x) mvn_bregmancentroid_kl_right(x);
elseif (strcmp(t, 'skl') == 1)
mvn_div = @(x, c) mvn_div_skl(x, c);
mvn_bregmancentroid = @(x) mvn_bregmancentroid_skl(x);
elseif (strcmp(t, 'skl_mid') == 1)
mvn_div = @(x, c) mvn_div_skl(x, c);
mvn_bregmancentroid = @(x) mvn_bregmancentroid_skl(x, 1);
% elseif (strcmp(t, 'js') == 1)
% mvn_div = @(x, c) mvn_div_js(x, c, 0);
% mvn_bregmancentroid = @(x) mvn_bregmancentroid_js(x, 1);
%
% elseif (strcmp(t, 'js_mid') == 1)
% mvn_div = @(x, c) mvn_div_js(x, c);
% mvn_bregmancentroid = @(x) mvn_bregmancentroid_js(x, 1);
%
% elseif (strcmp(t, 'burbearao') == 1)
% mvn_div = @(x, c) mvn_div_js(x, c);
% mvn_bregmancentroid = @(x) mvn_bregmancentroid_burbearao(x);
else
error('Unknown divergence given.');
end
iter = 0;
oldqe = 1;
qe = 0;
reiterate = 3;
while (reiterate > 0)
% assign the models to their closest centroid
oldqe = qe;
qe = 0;
for i = 1:items
c = intmax();
cidx = k+1;
for j = 1:k
dist = mvn_div(models(i), centers(j));
if (dist < c)
c = dist;
cidx = j;
end
end
qe = qe + c;
assig(i) = cidx;
end
qe = qe/items;
fprintf('#%d, average bregman quantization error = %f\n', iter, qe);
% check for failing clentroids
reiterate = max(reiterate - 1, 0);
i = 1;
while (i <= k)
sel = find(assig == i);
if (length(sel) < 1)
fprintf('%d, reinitializing centroid #%d (%d)\n', ...
iter, i, length(sel));
r = randi(items, 1, 1);
centers(i) = models(r);
assig(r) = i;
reiterate = reiterate + 3;
i=0;
end
i = i+1;
end
% compute the new centroids
for i = 1:k
aaa = mvn_bregmancentroid(models(assig == i));
% fprintf('centroids = %d = %d, %d\n', i , length(aaa), length(models(assig == i)));
centers(i) = aaa;
end
iter = iter + 1;
if (((oldqe - qe) >= 0.0001) && (reiterate == 0))
reiterate = 1;
end
end
% assign the models to their closest centroid
for i = 1:items
c = intmax();
cidx = k+1;
for j = 1:k
dist = mvn_div(models(i), centers(j));
if (dist < c)
c = dist;
cidx = j;
end
end
assig(i) = cidx;
end
end
mvn-1.0/mvn_knnclass.m0000644000175000017500000000313711627401106014674 0ustar dominikdominikfunction accuracy = mvn_knnclass(D, cl_assig, k, cl_filter)
%MVN_KNNCLASS
%
% (c) 2011, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
accuracy = 0;
if (nargin < 4)
cl_filter = [];
end
for i = 1:length(cl_assig)
D(i, i) = +Inf;
[~, nn_idx] = sort(D(i, :));
if (~isempty(cl_filter))
kk = 0;
for j = 1:length(cl_assig)
if (cl_filter(nn_idx(j)) ~= cl_filter(i))
kk = kk + 1;
if (cl_assig(nn_idx(j)) == cl_assig(i))
accuracy = accuracy + 1/k;
end
if (kk == k)
break;
end
end
end
else
for kk = 1:k
if (cl_assig(nn_idx(k)) == cl_assig(i))
accuracy = accuracy + 1/k;
end
end
end
end
accuracy = accuracy / length(cl_assig);
mvn-1.0/mvn_new.m0000644000175000017500000000254311627401112013646 0ustar dominikdominikfunction [g] = mvn_new(cov, m)
%MVN_NEW Initialize a mvn struct
%
% [d] = MVN_NEW(cov, m) initializes a MVN struct using the given covariance
% matrix COV and mean vector M.
%
% (c) 2010-2011, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
g.m = m(:);
g.cov = cov;
if (rcond(cov) < 1e-15)
throw(MException('mvn:cov', 'Covariance is badly scaled!'));
end
% speedup for
%
% g.logdet = log(det(g.cov));
% g.icov = inv(g.cov);
%
% using Cholesky:
g_chol = chol(cov);
g.logdet = 2*sum(log(diag(g_chol)));
g_ui = g_chol\eye(length(g.m));
g.icov = g_ui*g_ui';
end
mvn-1.0/mvn_som_skl.m0000644000175000017500000001161011627414153014530 0ustar dominikdominikfunction [grid D] = mvn_som_skl(cm, n, global_training, local_training)
%MVN_SOM_SKL Computes a NxN SOM using the MVN models and the
% Symmetric Kullback-Leibler divergence. The algorithm was published
% in 2010:
% "Islands of Gaussians: The Self Organizing Map and Gaussian
% Music Similarity Features", D. Schnitzer, A. Flexer, G. Widmer and
% M. Gasser, Proceedings of the 11th International Society for Music
% Information Retrieval Conference, 2010.
%
% [grid D] = MVN_SOM_SKL(models, n) Select the models to compute
% the NxN SOM.
%
% [grid D] = MVN_SOM_SKL(models, n, global_training, local_training)
% Select the models to compute the NxN SOM. global/local_training sets
% the global/local training iterations of the SOM
% MVN is (c) 2010-2011, Dominik Schnitzer,
%
%
% This file is part of the MVN Octave/Matlab Toolbox
%
% MVN 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.
%
% MVN 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 MVN. If not, see .
cmsel = 1:length(cm);
% initialization
grid = [];
for i = 0:n-1
for j = 0:n-1
grid(i*n + (j+1)).x = i;
grid(i*n + (j+1)).y = j;
grid(i*n + (j+1)).n = [];
end
end
cmlen = length(cmsel);
mlen = n*n;
% RANDOM INIT
mperm = randperm(cmlen);
m = cm(mperm(1:mlen));
if (nargin <= 2)
global_training = 100;
local_training = 200;
end
for learniter = 1:global_training+local_training
if (learniter < global_training)
% select appropriate alpha
alpha = 0.9 * (1 - learniter/global_training);
% relatively large radius, decay to 1 during global learning
sigma = 1 + 2/3*n*(1 - learniter/global_training);
fprintf(1, 'global training; som iteration=%d, alpha=%f, sigma=%f\n', learniter,...
alpha, sigma);
else
local_learniter = learniter - global_training;
% attain alpha values in the range of 0.06 - 0.01
alpha = 0.01 + 0.05*(1 - local_learniter/local_training);
% only modify neighbours
sigma = 1.5;
fprintf(1, 'local training; som iteration=%d, alpha=%f, sigma=%f\n',...
local_learniter, alpha, sigma);
end
% select a random input
cm_now = randi(cmlen);
% compute the winner unit (c)
dc = realmax();
c = 0;
for i = 1:mlen
d = mvn_div_skl(cm(cmsel(cm_now)), m(i));
if (d < dc)
c = i;
dc = d;
end
end
for i = 1:mlen
e2dist = (grid(i).x - grid(c).x)^2 + (grid(i).y - grid(c).y)^2;
nkernel = alpha * exp(-e2dist/(2*sigma*sigma));
try
r = bregman_combine_r(m(i), cm(cmsel(cm_now)), nkernel);
l = bregman_combine_l(m(i), cm(cmsel(cm_now)), nkernel);
lrm = [mvn_new(l.cov, l.m), mvn_new(r.cov, r.m)];
sym = mvn_bregmancentroid_skl(lrm);
m(i).cov = sym.cov;
m(i).icov = sym.icov;
m(i).m = sym.m;
catch ex
fprintf(1, 'Skip this, this is dangerous (mainloop, i=%d)\n', i);
fprintf(1, 'Exception: %s\n', ex.message);
break;
end
end
end
% build the final grid
D = zeros(cmlen, mlen);
for i = 1:cmlen
fprintf(1, 'assignment iteration = %d\n', i);
dnn = realmax();
nn = 0;
for j = 1:mlen
D(i, j) = mvn_div_skl(cm(cmsel(i)), m(j));
if (D(i, j) < dnn)
dnn = D(i, j);
nn = j;
end
end
grid(nn).n = [grid(nn).n cmsel(i)];
end
end
function r = bregman_combine_r(x, y, ytheta)
% compute right centriod mixture
r.m = (1-ytheta) * (x.icov * x.m) + (ytheta)*(y.icov * y.m);
r.cov = (1-ytheta) * (0.5 * x.icov) + (ytheta)*(0.5 * y.icov);
r.icov = 2 * r.cov;
r.cov = inv(r.icov);
r.m = r.cov * r.m;
end
function l = bregman_combine_l(x, y, ytheta)
% compute left centriod mixture
l.m = (1-ytheta)*(x.m) + (ytheta)*(y.m);
l.cov = (1-ytheta)* (-(x.cov + x.m*x.m')) +...
(ytheta)*(-(y.cov + y.m*y.m'));
l.cov = -(l.cov + l.m*l.m');
l.icov = inv(l.cov);
end
mvn-1.0/mvn_test.m0000644000175000017500000000761311627401116014043 0ustar dominikdominikfunction [filenames, models_tc, models_oc] = mvn_test(testfile, t, tc_dim, oc_dim)
%MVN_TEST Load a testcollection and prepare for using with the mvn
% functions.
%
% (c) 2010-2011, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
data = load(testfile, 'data');
if (strcmp(t, 'me') == 1)
models_tc = struct('m', [], 'cov', [], 'logdet', [], 'icov', []);
models_oc = [];
type = 1;
elseif (strcmp(t, 'ep') == 1)
models_tc = struct('m', [], 'cov', [], 'logdet', [], 'icov', []);
models_oc = struct('fp', [], 'fpg', [], 'fpb', []);
type = 2;
elseif (strcmp(t, 'mots4') == 1)
models_tc = struct('m', [], 'cov', [], 'logdet', [], 'icov', []);
models_oc = struct('fp', [], 'fpg', [], 'fpb', []);
type = 3;
elseif (strcmp(t, 'andre') == 1)
models_tc = struct('m', [], 'cov', [], 'logdet', [], 'icov', []);
models_oc = struct('op', []);
type = 4;
else
models_tc = struct('m', [], 'cov', [], 'logdet', [], 'icov', []);
models_oc = struct('m', [], 'cov', [], 'logdet', [], 'icov', []);
type = 0;
end
filenames = [];
c = 1;
ocd = 1:oc_dim;
tcd = 1:tc_dim;
for i = 1:length(data.data.cm)
try
if (type == 1)
mtc = mvn_new(data.data.cm{i}.cov, data.data.cm{i}.mu);
models_tc(c) = mtc;
elseif (type == 2)
mtc = mvn_new(data.data.cm{i}.cov, ...
data.data.cm{i}.m);
mop.fp = data.data.cm{i}.fp;
mop.fpg = data.data.cm{i}.fpg;
mop.fpb = data.data.cm{i}.fp_bass;
models_oc(c) = mop;
models_tc(c) = mtc;
elseif (type == 3)
mtc = mvn_new(data.data.cm{i}.co, ...
data.data.cm{i}.m);
mop.fp = data.data.cm{i}.fp;
mop.fpg = data.data.cm{i}.fpg;
mop.fpb = data.data.cm{i}.fpb;
models_oc(c) = mop;
models_tc(c) = mtc;
elseif (type == 4)
mtc = mvn_new(data.data.cm{i}.tc.cov(tcd, tcd), ...
data.data.cm{i}.tc.mu(tcd));
models_oc(c).op = data.data.cm{i}.op;
models_tc(c) = mtc;
else
mtc = mvn_new(data.data.cm{i}.tc.cov(tcd, tcd), ...
data.data.cm{i}.tc.mu(tcd));
moc = mvn_new(data.data.cm{i}.oc.cov(ocd, ocd), ...
data.data.cm{i}.oc.mu(ocd));
models_oc(c) = moc;
models_tc(c) = mtc;
end
filenames{c} = data.data.filenames{i};
c = c + 1;
catch eobj
if (strcmp(eobj.identifier, 'mvn:cov'))
fprintf(2, 'Skipping model with invalid covariance: %d\n', i);
elseif (strcmp(eobj.identifier, 'MATLAB:posdef'))
fprintf(2, ['Skipping model with non-positive definite ' ...
'covariance: %d\n'], i);
else
rethrow(eobj);
end
end
end
end
mvn-1.0/mvn_traceprod.m0000644000175000017500000000207211627401121015035 0ustar dominikdominikfunction [c] = mvn_traceprod(A, B)
%MVN_TRACEPROD Compute Matrix trace of the matrix product of a and b,
% given both matices are symmetric.
%
% [c] = MVN_TRACEPROD(A, B) computes the trace of the symmetric matices
% c = trace(A*B) in an efficient way.
%
% (c) 2010-2011, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
c = A(:).'*B(:);
end
mvn-1.0/mvn_version.m0000644000175000017500000000162011627401140014536 0ustar dominikdominikfunction [v] = mvn_version()
%MVN_VERSION
%
% [v] = MVN_VERSION() Returns the version of MVN.
%
% (c) 2010-2011, Dominik Schnitzer,
% http://www.ofai.at/~dominik.schnitzer/mvn
% This file is part of the MVN Octave/Matlab Toolbox
% MVN 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.
%
% MVN 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 MVN. If not, see .
v = 1;
end
mvn-1.0/README.txt0000644000175000017500000000156411627400727013532 0ustar dominikdominikThis is the Multivariate Normals (MVN) toolbox for Octave/Matlab.
http://www.ofai.at/~dominik.schnitzer/mvn
---
The MVN toolbox provides functions to handle multivariate Gaussians in Matlab.
It implements divergences for similarity computation:
- The Kullback-Leibler divergence
- The symmetrized Kullback-Leibler divergence
- A Jensen-Shannon approximation
- The Bhattacharyya coefficient
- and othe functions to work with these divergences.
We also include a k-means clustering method for the multivariate Gaussians
and a method to compute native Self-Organizing maps for multivatiate Gaussians
and their divergences.
The author uses the toolbox for Music Similarity estimation and experiments
(as the features there are multivariate Gaussians), but its methods are of
course not limited to that topic.
August, 31th 2011
Dominik Schnitzer
mvn-1.0/0000755000175000017500000000000011627435734012034 5ustar dominikdominik