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comparison toolboxes/FullBNT-1.0.7/KPMtools/conf2mahal.m @ 0:e9a9cd732c1e tip

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author wolffd
date Tue, 10 Feb 2015 15:05:51 +0000
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1 % CONF2MAHAL - Translates a confidence interval to a Mahalanobis
2 % distance. 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. Similarly,
16 % a particular confidence interval uniquely determines
17 % an ellipsoid with a fixed Mahalanobis distance.
18 %
19 % If X is an d dimensional Gaussian-distributed vector,
20 % then the Mahalanobis distance of X is distributed
21 % according to the Chi-squared distribution with d
22 % degrees of freedom. Thus, the Mahalanobis distance is
23 % determined by evaluating the inverse cumulative
24 % distribution function of the chi squared distribution
25 % up to the confidence value.
26 %
27 % Usage:
28 %
29 % m = conf2mahal(c, d);
30 %
31 % Inputs:
32 %
33 % c - the confidence interval
34 % d - the number of dimensions of the Gaussian distribution
35 %
36 % Outputs:
37 %
38 % m - the Mahalanobis radius of the ellipsoid enclosing the
39 % fraction c of the distribution's probability mass
40 %
41 % See also: MAHAL2CONF
42
43 % Copyright (C) 2002 Mark A. Paskin
44 %
45 % This program is free software; you can redistribute it and/or modify
46 % it under the terms of the GNU General Public License as published by
47 % the Free Software Foundation; either version 2 of the License, or
48 % (at your option) any later version.
49 %
50 % This program is distributed in the hope that it will be useful, but
51 % WITHOUT ANY WARRANTY; without even the implied warranty of
52 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
53 % General Public License for more details.
54 %
55 % You should have received a copy of the GNU General Public License
56 % along with this program; if not, write to the Free Software
57 % Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
58 % USA.
59 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
60 function m = conf2mahal(c, d)
61
62 m = chi2inv(c, d);