$ \DeclareMathOperator{\arccosh}{arccosh} \DeclareMathOperator*{\argmin}{arg\,min} \DeclareMathOperator{\Exp}{Exp} \newcommand{\geo}[2]{\gamma_{\overset{\frown}{#1,#2}}} \newcommand{\geoS}{\gamma} \newcommand{\geoD}[2]{\gamma_} \newcommand{\geoL}[2]{\gamma(#2; #1)} \newcommand{\gradM}{\nabla_{\M}} \newcommand{\gradMComp}[1]{\nabla_{\M,#1}} \newcommand{\Grid}{\mathcal G} \DeclareMathOperator{\Log}{Log} \newcommand{\M}{\mathcal M} \newcommand{\N}{\mathcal N} \newcommand{\mat}[1]{\mathbf{#1}} \DeclareMathOperator{\prox}{prox} \newcommand{\PT}[3]{\mathrm{PT}_{#1\to#2}#3} \newcommand{\R}{\mathbb R} \newcommand{\SPD}[1]{\mathcal{P}(#1)} \DeclareMathOperator{\Tr}{Tr} \newcommand{\tT}{\mathrm{T}} \newcommand{\vect}[1]{\mathbf{#1}} $

Variance

Compute the variance of the data, i.e. the mean distance to the mean.

For given data let denote the Riemannian center of mass. Then the variance is given by

Note that is the dimension of the manifold .

Matlab Documentation

1
2
3
4
5
6
7
8
9
10
11
12
% var(f) computes the empirical variance
%       1/(numel(f)-1) * sum (f-mean(f))^2
% of f
% INPUT
% f      : manifold valued Set
% OUTPUT
% v      : variance of the set (scalar)
% mean_f : mean value of the set
%
% ---
% Manifold-valued Image Restoration Toolbox 1.2
% J. Persch, R. bergmann, 2017-01-06

See also