Details of Lecture 22, ECE662 Spring 2010, Prof. Boutin
In Lecture 22, we continued our discussion of Fisher's linear discriminant. We began by answering the question: why not use
$ J(\vec{w})=\frac{\| \tilde{m}_1-\tilde{m}_2\|^2}{\|\vec{w} \|^2} $ instead of $ J(\vec{w})=\frac{\| \tilde{m}_1-\tilde{m}_2 \|^2}{\tilde{s}_1^2+\tilde{s}_2^2} $ ?
We then presented the analytic expression for $ \vec{w}_0 $, the argmax of $ J(\vec{w}) $, and related $ \vec{w}_0 $ to the least square solution of $ Y \vec{c}=b $. We noted the relationship between Fisher's linear discriminant and feature extraction. Finally, we began Section 9 of the course on Support Vector Machines by introducing the idea of extending the feature vector space into a space spanned by monomials.
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