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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>, | ||
Latest revision as of 11:31, 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
- Spring 2008-Lecture 6, student lecture notes
- The effect of adding correlated features (some inspiration for the first homework?)
- A student page about the effect of severe class imabalance (a topic mentioned in class today)
Previous: Lecture 7
Next: Lecture 9
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