The Formulation of Support Vector Machine

 

In this chapter the idea of using Support Vector Machines in pattern classification is presented. The formulation of SVM is constructed starting from a simple linear maximum margin classifier. The importance of capacity control to avoid over fitting discussed. Finally the claim that SVM training achieves the lowest necessary capacity for a given classification task will be investigated.

A general two-class pattern classification problem is posed as follows :

• Given l i.i.d. sample:
  where , for i=1, ... , l is a feature vector of length d and is the class label for data point .
• Find a classifier with the decision function, f(x) such that y = f(x), where y is the class label for x.

The performance of the classifier is measured in terms of classification error which is defined in Eqn. .

 

• Empirical Risk Minimisation
• Structural Risk Minimisation
• VC dimension and VC confidence
• Linear Support Vector Machine - A Maximum Margin Classifier
• Extending SVM to a Soft Margin Classifier
• Nonlinear Support Vector Machine
• SVM training and SRM