João E. Strapasson

Fisher information distance

This paper presents a geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. The Fisher distance, as well as other divergence measures, is also used in many applications to establish a proper data average. The main purpose is to widen the range of possible interpretations and relations of the Fisher distance and its associated geometry for the prospective applications. It focuses on statistical models of the normal probability distribution functions and takes advantage of the connection with the classical hyperbolic geometry to derive closed forms for the Fisher distance in several cases. Connections with the well-known Kullback-Leibler divergence measure are also devised.

Optimum commutative group codes

A method for finding an optimum

On bounds for the Fisher-Rao distance between multivariate normal distributions

n

On sequences of projections of the cubic lattice

n-dimensional commutative group code of a given order

Clustering using the fisher-rao distance

M

Spherical Codes from Lattices

M is presented. The approach explores the structure of lattices related to these codes and provides a significant reduction in the number of non-isometric cases to be analyzed. The classical factorization of matrices into Hermite and Smith normal forms and also basis reduction of lattices are used to characterize isometric commutative group codes. Several examples of optimum commutative group codes are also presented.