Revision as of 12:09, 2 February 2012

Lecture 8 Blog, ECE662 Spring 2012, Prof. Boutin

Thursday February second, 2012 (Week 4)

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.

Relevant Rhea Pages

• Spring 2008-Lecture 6, student lecture notes
• The effect of adding correlated features (some inspiration for the first homework?)
• A student page about the effect of severe class imabalance (a topic mentioned in class today)

Previous: Lecture 7

Next: Lecture 9

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