Incorporating Method of Invariance and SVM Based on the Best Approximate Point

One of key points in developing support vector machine (SVM) is the incorporating prior knowledge of learning task into SVM. A very common type of a prior knowledge is invariance of the input data. The research on incorporating method of invariance and SVM is an important focus for SVM in recent years, and it can help to improve the generalization performance efficiently. This paper describes and reviews the popular methods for incorporating invariance into SVM, and discusses their respective merits. Especially, it presents a new incorporating approach, which represents the trajectory manifold of invariance transformation by the best approximate point. And simulation experiments show this approach has some desirable theoretical properties. Comparing with the traditional SVM and Virtual SV (VSV) based on MNIST handwritten digit database, the presented approach can greatly improve the generalization performance of SVM.