## Abstract

There are efficient software programs for

extracting from large data sets and image sequences certain mixtures of probability distributions, such as multivariate Gaussians, to represent the important features and

their mutual correlations needed for accurate document retrieval from databases.

This note describes a method to use information geometric methods for distance measures

between distributions in mixtures of arbitrary 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 may not be essential and comparative

values suffice for proximity testing and document retrieval.

Also, for two {\em mixtures} of different 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 consider some choices for the incorporation of

weightings in distance estimation and provide illustrative results from simulations of

differently weighted mixtures of multivariate Gaussians.

extracting from large data sets and image sequences certain mixtures of probability distributions, such as multivariate Gaussians, to represent the important features and

their mutual correlations needed for accurate document retrieval from databases.

This note describes a method to use information geometric methods for distance measures

between distributions in mixtures of arbitrary 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 may not be essential and comparative

values suffice for proximity testing and document retrieval.

Also, for two {\em mixtures} of different 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 consider some 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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Pages (from-to) | 439-447 |

Number of pages | 9 |

Journal | AIMS Mathematics |

Volume | 3 |

Issue number | 4 |

DOIs | |

Publication status | Published - 19 Oct 2018 |