Structural Regularized Support Vector Machine: A Framework for Structural Large Margin Classifier

Support vector machine (SVM), as one of the most popular classifiers, aims to find a hyperplane that can separate two classes of data with maximal margin. SVM classifiers are focused on achieving more separation between classes than exploiting the structures in the training data within classes. However, the structural information, as an implicit prior knowledge, has recently been found to be vital for designing a good classifier in different real-world problems. Accordingly, using as much prior structural information in data as possible to help improve the generalization ability of a classifier has yielded a class of effective structural large margin classifiers, such as the structured large margin machine (SLMM) and the Laplacian support vector machine (LapSVM). In this paper, we unify these classifiers into a common framework from the concept of structural granularity and the formulation for optimization problems. We exploit the quadratic programming (QP) and second-order cone programming (SOCP) methods, and derive a novel large margin classifier, we call the new classifier the structural regularized support vector machine (SRSVM). Unlike both SLMM at the cross of the cluster granularity and SOCP and LapSVM at the cross of the point granularity and QP, SRSVM is located at the cross of the cluster granularity and QP and thus follows the same optimization formulation as LapSVM to overcome large computational complexity and non-sparse solution in SLMM. In addition, it integrates the compactness within classes with the separability between classes simultaneously. Furthermore, it is possible to derive generalization bounds for these algorithms by using eigenvalue analysis of the kernel matrices. Experimental results demonstrate that SRSVM is often superior in classification and generalization performances to the state-of-the-art algorithms in the framework, both with the same and different structural granularities.