classification2

# classification2 - Road Map Basic concepts Decision tree...

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90 Spring 2008 Web Mining Seminar Road Map Basic concepts Decision tree induction Evaluation of classifiers Rule induction Classification using association rules Naïve Bayesian classification Naïve Bayes for text classification Support vector machines K-nearest neighbor Ensemble methods: Bagging and Boosting Summary

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104 Spring 2008 Web Mining Seminar Road Map Basic concepts Decision tree induction Evaluation of classifiers Rule induction Classification using association rules Naïve Bayesian classification Naïve Bayes for text classification Support vector machines K-nearest neighbor Ensemble methods: Bagging and Boosting Summary
105 Spring 2008 Web Mining Seminar Introduction Support vector machines were invented by V. Vapnik and his co-workers in 1970s in Russia and became known to the West in 1992. SVMs are linear classifiers that find a hyperplane to separate two class of data, positive and negative. Kernel functions are used for nonlinear separation. SVM not only has a rigorous theoretical foundation, but also performs classification more accurately than most other methods in applications, especially for high dimensional data. It is perhaps the best classifier for text classification.

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106 Spring 2008 Web Mining Seminar Basic concepts Let the set of training examples D be {( x 1 , y 1 ), ( x 2 , y 2 ), …, ( x r , y r )}, where x i = ( x 1 , x 2 , …, x n ) is an input vector in a real- valued space X R n and y i is its class label (output value), y i {1, -1}. 1: positive class and -1: negative class. SVM finds a linear function of the form ( w : weight vector) f ( x ) = w x + b < + - + = 0 1 0 1 b if b if y i i i x w x w
107 Spring 2008 Web Mining Seminar The hyperplane The hyperplane that separates positive and negative training data is w x + b = 0 It is also called the decision boundary ( surface) . So many possible hyperplanes, which one to choose?

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108 Spring 2008 Web Mining Seminar Maximal margin hyperplane SVM looks for the separating hyperplane with the largest margin. Machine learning theory says this hyperplane minimizes the error bound
109 Spring 2008 Web Mining Seminar Linear SVM: separable case Assume the data are linearly separable. Consider a positive data point (

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## This note was uploaded on 08/06/2008 for the course CSE 450 taught by Professor Davison during the Spring '08 term at Lehigh University .

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classification2 - Road Map Basic concepts Decision tree...

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