Multivariate Gaussian (MVG)

  1. multivariate Gaussian distribution N (μij , Σij )

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    2D normal distribution examples

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Mahalanobis distance

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  1. Mahalanobis distance (MD) is a statistical measure of the distance between a point (y) & a distribution (its mean is $\mu$), representing how many standard deviations away a point is from the center.

    $$ d = \sqrt{(y - \mu)^T C^{-1} (y - \mu)} $$

  2. It measures distance by accounting for the covariance matrix C.

  3. Unlike Euclidean distance measures distance by a identity matrix, which treats all directions equally,

  4. MD uses the covariance matrix to scale distances, effectively creating ellipses of equal distance around a data center.