Extension Support Vector Machine for Extension Classification

Support vector machine (SVM) method has been successfully applied to classification, in which a classifying rule between features and class is pursued. Sometimes, a specific transformation can influence the feature values of an example, according to the classifying rule, further leading to a possible change of its corresponding class. How to apply such examples to obtain knowledge about the transformation is a new issue, called extension classification (EC). In this paper, an extension support vector machine (ESVM) is developed, in which a mathematic model involving a series of sub-models between feature values of the examples before and after transformation is considered. Dependent function is established to replace the classifying rule. Based on dependent function, nonlinear constraints are requested to ensure the reasonability of the model, in which sub-models are coupled with each other. By introducing the concept of dependent radius, each original constraint is decoupled into several linear sub-constraints so that each sub-model can be established independently. For each sub-model, a non-convex example-dependence loss function is proposed and concave-convex programming (CCCP) procedure is suggested to process the non-convexity. Experimental results on two cases confirm the effectiveness of the ESVM.