Numerical analysis of 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 equation of geometrically local isotropic independence, which is proposed to define normal distributions in a manifold. In this paper we provide experimental results of calculating the Mahalanobis metric by the Newton-Raphson method. We add error to the original probability density function and calculate the Mahalanobis metric to investigate the effect of the error in a probability density function to the solution.