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[[Category:2010 Spring ECE 662 mboutin]] | [[Category:2010 Spring ECE 662 mboutin]] | ||
| − | =Details of Lecture 22, [[ECE662]] Spring 2010= | + | =Details of Lecture 22, [[ECE662]] Spring 2010, [[User:mboutin|Prof. Boutin]]= |
| − | In Lecture 22, we continued our discussion of Fisher's linear discriminant. We began by answering the question: why not use | + | In Lecture 22, we continued our discussion of [[Fisher Linear Discriminant|Fisher's linear discriminant]]. We began by answering the question: why not use |
<math>J(\vec{w})=\frac{\| \tilde{m}_1-\tilde{m}_2\|^2}{\|\vec{w} \|^2}</math> | <math>J(\vec{w})=\frac{\| \tilde{m}_1-\tilde{m}_2\|^2}{\|\vec{w} \|^2}</math> | ||
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We then presented the analytic expression for <math>\vec{w}_0</math>, the argmax of <math>J(\vec{w})</math>, and related <math>\vec{w}_0</math> to the least square solution of <math>Y \vec{c}=b</math>. We noted the relationship between [[Fisher Linear Discriminant|Fisher's linear discriminant]] and [[Feature Extraction|feature extraction]]. | We then presented the analytic expression for <math>\vec{w}_0</math>, the argmax of <math>J(\vec{w})</math>, and related <math>\vec{w}_0</math> to the least square solution of <math>Y \vec{c}=b</math>. We noted the relationship between [[Fisher Linear Discriminant|Fisher's linear discriminant]] and [[Feature Extraction|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. | 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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Previous: [[Lecture21ECE662S10|Lecture 21]] | Previous: [[Lecture21ECE662S10|Lecture 21]] | ||
Latest revision as of 10:49, 13 April 2010
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.
Previous: Lecture 21 Next: Lecture 23
