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=Lecture 8 Blog, [[ECE662]] Spring 2012, [[user:mboutin|Prof. Boutin]]=
 
=Lecture 8 Blog, [[ECE662]] Spring 2012, [[user:mboutin|Prof. Boutin]]=
 
Thursday February second, 2012 (Week 4)  
 
Thursday February second, 2012 (Week 4)  
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Quick link to lecture blogs: [[Lecture1ECE662S12|1]]|[[Lecture2ECE662S12|2]]|[[Lecture3ECE662S12|3]]|[[Lecture4ECE662S12|4]]|[[Lecture5ECE662S12|5]]|[[Lecture6ECE662S12|6]]|[[Lecture7ECE662S12|7]]|[[Lecture8ECE662S12|8]]| [[Lecture9ECE662S12|9]]|[[Lecture10ECE662S12|10]]|[[Lecture11ECE662S12|11]]|[[Lecture12ECE662S12|12]]|[[Lecture13ECE662S12|13]]|[[Lecture14ECE662S12|14]]|[[Lecture15ECE662S12|15]]|[[Lecture16ECE662S12|16]]|[[Lecture17ECE662S12|17]]|[[Lecture18ECE662S12|18]]|[[Lecture19ECE662S12|19]]|[[Lecture20ECE662S12|20]]|[[Lecture21ECE662S12|21]]|[[Lecture22ECE662S12|22]]|[[Lecture23ECE662S12|23]]|[[Lecture24ECE662S12|24]]|[[Lecture25ECE662S12|25]]|[[Lecture26ECE662S12|26]]|[[Lecture27ECE662S12|27]]|[[Lecture28ECE662S12|28]]|[[Lecture29ECE662S12|29]]|[[Lecture30ECE662S12|30]]
 
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Today we continued our study of the separating hypersurface in the case where, for all class <math>i=1,\ldots,c</math>,  
 
Today we continued our study of the separating hypersurface in the case where, for all class <math>i=1,\ldots,c</math>,  
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==Relevant Rhea Pages==
 
==Relevant Rhea Pages==
 
*[[Lecture_6_-_Discriminant_Functions_Old_Kiwi|Spring 2008-Lecture 6, student lecture notes]]
 
*[[Lecture_6_-_Discriminant_Functions_Old_Kiwi|Spring 2008-Lecture 6, student lecture notes]]
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*[[Bayes_Classification:_Experiments_and_Notes_OldKiwi|The effect of adding correlated features]] (some inspiration for the [[hw1_ECE662_S12|first homework]]?)
 
*[[Bayes_Rate_Fallacy:_Bayes_Rules_under_Severe_Class_Imbalance|A student page about the effect of severe class imabalance]] (a topic mentioned in class today)
 
*[[Bayes_Rate_Fallacy:_Bayes_Rules_under_Severe_Class_Imbalance|A student page about the effect of severe class imabalance]] (a topic mentioned in class today)
  

Latest revision as of 12:31, 23 February 2012


Lecture 8 Blog, ECE662 Spring 2012, Prof. Boutin

Thursday February second, 2012 (Week 4)


Quick link to lecture blogs: 1|2|3|4|5|6|7|8| 9|10|11|12|13|14|15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30


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

Previous: Lecture 7

Next: Lecture 9


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