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SUPPORT VECTOR MACHINES Presented by: Naman Fatehpuria Sumana Venkatesh
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SVMs are supervised learning models with associated learning algorithms that analyze data and recognize patterns, used for classification and regression analysis. Basic SVM takes a set of input data and predicts, for each given input, which of two possible classes forms the output Introduction
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Classification of data In the case of SVM, a data point is viewed as a p- dimensional vector, and we want to know whether we can separate such points with a (p − 1)- dimensional hyperplane Optimal hyperplane for linearly separable patterns(Linear Classifier) Motivation
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Which Hyperplane?
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“ A good separation is achieved by the hyperplane that has the largest distance to the nearest training data point of any class (so-called functional margin), since in general the larger the margin the lower the generalization error of the classifier.” Intuition
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Linear Classifier H1 does not separate the classes H 2 does, but only with a small margin. H 3 separates them with the maximum margin.
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The one that represents the largest separation, or margin, between the two classes. So we choose the hyperplane so that the distance from it to the nearest data point on each side is maximized. If such a hyperplane exists, it is known as the maximum- margin hyperplane and the linear classifier it defines is known as a maximum margin classifier; or equivalently, the perceptron of optimal stability. Optimal Hyperplane
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Support Vectors Data points that lie closest to the decision surface Critical elements of the data set and the most difficult to classify
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Maximum Margin Hyperplane We need to find a separating line between the data points that maximizes the margin. Find w with large margin(w perpendicular to plane)
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http://en.wikipedia.org/wiki/Support_vector_machine #Formal_definition http://en.wikipedia.org/wiki/Support_vector_machine #Formal_definition http://www.cs.ucf.edu/courses/cap6412/fall2009/pape rs/Berwick2003.pdf http://www.cs.ucf.edu/courses/cap6412/fall2009/pape rs/Berwick2003.pdf http://docs.opencv.org/doc/tutorials/ml/introduction_ to_svm/introduction_to_svm.html http://docs.opencv.org/doc/tutorials/ml/introduction_ to_svm/introduction_to_svm.html References
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