(New page: Category:2010 Spring ECE 662 mboutin =Details of Lecture 22, ECE662 Spring 2010= In Lecture 22, we will continue our discussion of Fisher's linear discriminant. We will begin by ...)
 
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=Details of Lecture 22, [[ECE662]] Spring 2010=
 
=Details of Lecture 22, [[ECE662]] Spring 2010=
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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 will continue our discussion of Fisher's linear discriminant. We will begin by answering the question: why not use <math>J(\omega)=\frac{\|  \tilde{m}_1-\tilde{m}_2\|^2}{\| w \|^2}</math>  
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<math>J(\vec{w})=\frac{\|  \tilde{m}_1-\tilde{m}_2\|^2}{\|\vec{w} \|^2}</math>  
 
instead of  
 
instead of  
<math> J(\omega)=\frac{\| \tilde{m}_1-\tilde{m}_2 \|^2}{\tilde{s}_1^2+\tilde{s}_2^2}</math>  
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<math> J(\vec{w})=\frac{\| \tilde{m}_1-\tilde{m}_2 \|^2}{\tilde{s}_1^2+\tilde{s}_2^2}</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>. 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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==Useful Links==
  
 
For more info, you may look at these students' pages on Fisher's linear discriminant:
 
For more info, you may look at these students' pages on Fisher's linear discriminant:
 
* [[Derivation_of_Fisher's_Linear_Discriminant_OldKiwi|Definition Fisher's linear discriminant]],  
 
* [[Derivation_of_Fisher's_Linear_Discriminant_OldKiwi|Definition Fisher's linear discriminant]],  
 
* [[Fisher_Linear_Discriminant_OldKiwi| Fisher's linear discriminant in brief]]
 
* [[Fisher_Linear_Discriminant_OldKiwi| Fisher's linear discriminant in brief]]
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Previous: [[Lecture21ECE662S10|Lecture 21]]
 
Previous: [[Lecture21ECE662S10|Lecture 21]]

Revision as of 10:10, 13 April 2010


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


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