Maxwell normal distribution in a manifold and mahalanobis metric

Abstract

The normal distribution in Euclidean space is used widely for statistical models. However, for pattern recognition, since pattern vectors are often normalized by their norm, they are on a hyper-spherical surface. Therefore, we have to study a normal distribution in a non-Euclidean space. Here, we provide the new concept of geometrically local Isotropie independence and define the Maxwell normal distribution in a manifold. We also define the Mahalanobis metric, which is an extension of the Mahalanobis distance in Euclidean space. We provide the Mahalanobis metric equation, which is covariant with coordinate transformation. Furthermore, we show its experimental results. © Springer-Verlag Berlin Heidelberg 2006.