Lecture 8 Blog, ECE662 Spring 2012, Prof. Boutin

Thursday February second, 2012 (Week 4)

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Today we continued our study of the separating hypersurface in the case where, for all class $i=1,\ldots,c$ ,

$\Sigma_i=\sigma^2 {\mathbb I}.$

We noted the co-dimension two of the intersections of the segments of hyperplanes forming the decision boundary. We also drew a connection with a shape analysis tool called the "skeleton" of a shape.

We then slightly generalized our study to the case where the standard deviation matrix is the same for all classes $i=1,\ldots,c$ . We then noticed the presence of the Mahalanobis distance in the discriminant function, and derived the relationship between the Mahalanobis distance and the Euclidean distance through a simple change of coordinates. It was pointed out by Mark that this change of coordinates is called "whitening".

We also spent a lot of time discussing the first homework.