Mahalanobis distance

Wikipedia: It is a useful way of determining similarity of an unknown sample set to a known one. It differs from Euclidean distance in that it takes into account the correlations of the data set and is scale-invariant, i.e. not dependent on the scale of measurements.

For

 x= (x_1, x_2, x_3, ..., x_N)^T

, and covariance matrix S,

D_m(x) = \sqrt{(x-\mu)^TS^{-1}(x-\mu)}

d(x,y)=\sqrt{(x-y)^TS^{-1}(x-y)}