# Comparison toD&H Approach

## Comparison toD&H Approach

- Use Mahalanobis distance:
- D(n, x) = (x - n)T Sx-1 (x - n)

- Find SX s.t. SX-1 XT = 0 & SX-1 XR = 0, etc.
- (i.e. the tangent vectors of X are eliminated from the distance.)

- If XT is an eigenvector of SX then:

## Where XT and XR

## are the tangent

## vectors of X

** Notes: **

We can compare the tangent approach to that of D&H.

What we are looking for is a SX-1 projects “away” vectors that are in the tangent space of X. We can arrange that by constructing a matrix SX-1 whose eigenvectors include the tangent vectors and the corresponding eigenvalues are 0.