What is Mahalanobis Distance 🌱

Last updated on March 13, 2021

https://en.wikipedia.org/wiki/Mahalanobis_distance

d (\vec{x}, \vec{y}) = \sqrt{(\vec{x} - \vec{y})^{T} S^{- 1} (\vec{x} - \vec{y})}

The Mahalanobis distance is the distance of a point from the center of mass divided by the width of the ellipsoid in the direction of that point.
Ellipsoid is constructed by covariance matrix to account for correlations between features

Suppose I wanted to calculate the Mahalanobis nearest neighbor

Calculate covariance matrix between all features which will allow you to scale your multidimensional ellipsoid
Then calculate the Mahalanobis distance between your point of interest and every other point
Report the $k$ closest points

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