## Abstract

There are efficient software programs for extracting from image sequences certain mixtures of

distributions, such as multivariate Gaussians, to represent the important features needed for

accurate document retrieval from databases. This note describes a method to use information

geometric methods to measure distances between distributions in mixtures of multivariate

Gaussians. There is no general analytic solution for the information geodesic distance between

two k-variate Gaussians, but for many purposes the absolute information distance is

not essential and comparative values suffice for proximity testing. For two mixtures of multivariate

Gaussians we must resort to approximations to incorporate the weightings. In practice,

the relation between a reasonable approximation and a true geodesic distance is likely to be

monotonic, which is adequate for many applications. Here we compare several choices for

the incorporation of weightings in distance estimation and provide illustrative results from

simulations of differently weighted mixtures of multivariate Gaussians.

distributions, such as multivariate Gaussians, to represent the important features needed for

accurate document retrieval from databases. This note describes a method to use information

geometric methods to measure distances between distributions in mixtures of multivariate

Gaussians. There is no general analytic solution for the information geodesic distance between

two k-variate Gaussians, but for many purposes the absolute information distance is

not essential and comparative values suffice for proximity testing. For two mixtures of multivariate

Gaussians we must resort to approximations to incorporate the weightings. In practice,

the relation between a reasonable approximation and a true geodesic distance is likely to be

monotonic, which is adequate for many applications. Here we compare several choices for

the incorporation of weightings in distance estimation and provide illustrative results from

simulations of differently weighted mixtures of multivariate Gaussians.

Original language | English |
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Title of host publication | Computational Information Geometry: For Image And Signal Processing , Heidelberg 2017. |

Place of Publication | Heidelberg |

Publisher | Springer Nature |

Number of pages | 9 |

Publication status | Accepted/In press - 2017 |

### Publication series

Name | Springer Series in Signals and Communication Technology |
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## Keywords

- Information geometry, multivariate spatial covariance, Gaussian mixtures, geodesic distance, approximations.