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Unformatted text preview: that reduce the multi- class task to several binary problems have to be applied, see the Multi- class SVM section. 3.How to select the kernel function parameters - for Gaussian kernels the width parameter , and the value of in the - insensitive loss function have not entirely solved yet. some resouces: 1. introduction of SVM[36] (http://www.fml.tuebingen.mpg.de/raetsch/lectures/ismb09tutorial/images/WhatIsASVM.pdf) 2. SVM in computational biology[37] (http://noble.gs.washington.edu/papers/noble_support.pdf) wikicour senote.com/w/index.php?title= Stat841&pr intable= yes 70/74 10/09/2013 Stat841 - Wiki Cour se Notes Finishing up SVM - November 25, 2009 Does SVM find a global minimum? When we discussed KKT conditions, we listed the necessary conditions for minimum (unlike, say, neural networks that find a local minimum). Recall that our conditions, for the non- separable case, are Our lagrangian equation is to be a local minimum. However, it would be ideal if we could show that SVM finds a global and . These are both convex. . Since this is quadratic, it might be convex, but it also may not be; it depends on the matrix . If is a positive semi- definite matrix, then the lagrangian equation is convex. Recall that is the product of , where . Similar to the notion that squaring any number will give us a positive number in the end, a matrix that is the product of a matrix transposed times itself will result in a positive semi- definite matrix. So, we know that is positive semi- definite. The lagrangian equation is convex, and therefore, the SVM algorithm finds a global minimum. Naive Bayes, Decision Trees, K Nearest Neighbours, Boosting, and Bagging - November 25, 2009 Now that we've covered a number of more advanced classification algorithms, we can look at some of the simpler classification algorithms that are usually discussed at the beginning of a discussion on classification. Naive Bayes Clas s ifiers (http://en.wikipedia.org/wiki/Naive_Bayes _clas s ifier) Recall that one of the major drawbacks of the...
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