SUPPORT VECTOR MACHINES Presented by: Naman Fatehpuria Sumana Venkatesh

 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

 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

Which Hyperplane?

“ 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

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.

 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

Support Vectors  Data points that lie closest to the decision surface  Critical elements of the data set and the most difficult to classify

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)

 #Formal_definition #Formal_definition  rs/Berwick2003.pdf rs/Berwick2003.pdf  to_svm/introduction_to_svm.html to_svm/introduction_to_svm.html References