Details of Lecture 22, ECE662 Spring 2010
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 $. 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.
Useful Links
For more info, you may look at these students' pages on Fisher's linear discriminant:
Previous: Lecture 21
Next: Lecture 23
