My knowledge of Math is limited. I was looking up Mahalanobis distance out of curiosity, after seeing a reference.
From Wikipedia: Mahalanobis distance - Intuitive explanation
Putting this on a mathematical basis, the ellipsoid that best represents the set's probability distribution can be estimated by building the covariance matrix of the samples. The Mahalanobis distance is the distance of the test point from the center of mass divided by the width of the ellipsoid in the direction of the test point.
Maybe naively, I don't understand the use of width. Why not radius instead, and what would be the difference? I didn't see why radius would be symmetric along the width, unless the shape is a perfect ellipsoid and also if the center of mass coincides with the center of the ellipsoid.
Have I misunderstood?
Specifically, as this may apply to ML and classification, I don't see why it has to be a perfect ellipsoid. I was wondering if the accuracy could be improved.