A way of thinking about the role of the
inverse covariance matrix
If the Gaussian is spherical we
don’t need to worry about the
covariance matrix.
So we could start by
transforming the data space to
make the Gaussian spherical
This is called “whitening”
the data.
It pre-multiplies by the
matrix square root of the
inverse covariance matrix.
In the transformed space, the
weight vector is just the
difference between the
transformed means.