Overview
The Mahalanobis Distance is a distance measure between a point and a statistical distribution, representing some category of data points. The Minmum Mahalanobis Distance algorithm classifies a point by the category with the distribution that has the smallest distance to the point.
The Mahalanobis Distance is implemented in the Distance API
Mahalanobis Distance
Given a probability distribution with mean = {% \vec{\mu} %} and covariance matrix {% S %}, the mahalanobis distance between amy point {% \vec{x} %} and the distribtution is defined to be
{% d(\vec{x}) = \sqrt{(\vec{x} - \vec{\mu})^T S ^{-1} (\vec{x} - \vec{\mu})} %}
Minimum Mahalanobis Distance
Given several probability distributions, {% P_1,P_2,...,P_n %}, the minimum mahalanobis classifier classifies a point {% \vec{x} %} with the distribution to which it has a minimum mahalanobis distance.