Mercurial > hg > camir-aes2014
comparison toolboxes/FullBNT-1.0.7/KPMtools/mahal2conf.m @ 0:e9a9cd732c1e tip
first hg version after svn
| author | wolffd |
|---|---|
| date | Tue, 10 Feb 2015 15:05:51 +0000 |
| parents | |
| children |
comparison
equal
deleted
inserted
replaced
| -1:000000000000 | 0:e9a9cd732c1e |
|---|---|
| 1 % MAHAL2CONF - Translates a Mahalanobis distance into a confidence | |
| 2 % interval. Consider a multivariate Gaussian | |
| 3 % distribution of the form | |
| 4 % | |
| 5 % p(x) = 1/sqrt((2 * pi)^d * det(C)) * exp((-1/2) * MD(x, m, inv(C))) | |
| 6 % | |
| 7 % where MD(x, m, P) is the Mahalanobis distance from x | |
| 8 % to m under P: | |
| 9 % | |
| 10 % MD(x, m, P) = (x - m) * P * (x - m)' | |
| 11 % | |
| 12 % A particular Mahalanobis distance k identifies an | |
| 13 % ellipsoid centered at the mean of the distribution. | |
| 14 % The confidence interval associated with this ellipsoid | |
| 15 % is the probability mass enclosed by it. | |
| 16 % | |
| 17 % If X is an d dimensional Gaussian-distributed vector, | |
| 18 % then the Mahalanobis distance of X is distributed | |
| 19 % according to the Chi-squared distribution with d | |
| 20 % degrees of freedom. Thus, the confidence interval is | |
| 21 % determined by integrating the chi squared distribution | |
| 22 % up to the Mahalanobis distance of the measurement. | |
| 23 % | |
| 24 % Usage: | |
| 25 % | |
| 26 % c = mahal2conf(m, d); | |
| 27 % | |
| 28 % Inputs: | |
| 29 % | |
| 30 % m - the Mahalanobis radius of the ellipsoid | |
| 31 % d - the number of dimensions of the Gaussian distribution | |
| 32 % | |
| 33 % Outputs: | |
| 34 % | |
| 35 % c - the confidence interval, i.e., the fraction of | |
| 36 % probability mass enclosed by the ellipsoid with the | |
| 37 % supplied Mahalanobis distance | |
| 38 % | |
| 39 % See also: CONF2MAHAL | |
| 40 | |
| 41 % Copyright (C) 2002 Mark A. Paskin | |
| 42 % | |
| 43 % This program is free software; you can redistribute it and/or modify | |
| 44 % it under the terms of the GNU General Public License as published by | |
| 45 % the Free Software Foundation; either version 2 of the License, or | |
| 46 % (at your option) any later version. | |
| 47 % | |
| 48 % This program is distributed in the hope that it will be useful, but | |
| 49 % WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 50 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 51 % General Public License for more details. | |
| 52 % | |
| 53 % You should have received a copy of the GNU General Public License | |
| 54 % along with this program; if not, write to the Free Software | |
| 55 % Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 | |
| 56 % USA. | |
| 57 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 58 function c = mahal2conf(m, d) | |
| 59 | |
| 60 c = chi2cdf(m, d); |