Geometrically local isotropic independence and numerical analysis of the Mahalanobis metric in vector space

The Mahalanobis metric was proposed by extending the Mahalanobis distance to provide a probabilistic distance for a non-normal distribution. The Mahalanobis metric equation is a nonlinear second order differential equation derived from the geometrically local isotropic independence equation, which was proposed to define normal distributions in a manifold. We explain the equations and show experimental results of calculating the Mahalanobis metric by the Newton–Raphson method. We add error to an original probability density function and calculate the Mahalanobis metric to investigate the effect on the solution of error in a probability density function. This paper is an extended version of “numerical analysis of Mahalanobis metric in vector space” (Track 2 IBM Best Student Paper Award in ICPR’08; Son, J., Inoue, N., Yamashita, Y., 2008. Numerical analysis of Mahalanobis metric in vector space. In: Proc. 19th Int. Conf. on Pattern Recognition (CD–ROM)).