The Method Unification Of Gravitation Based Classification And Hypersphere Support Vector Machine

Classification problem is the common rearch hotspot of pattern recognition and machine learning, and classification problem is, essentially, the mathematical optimization problem of finding the discriminant surface among different classes.Gravitation classification is a category of lazy classification learning method, while support vector machine is an eager learning method to find the largest margin separating hypersphere. Past research has been centered on the development of the two methods independently, and the relationship between these two methods and the unification of these two methods was not considered.The paper investigates the relationship and unification for gravitation classification and hypersphere support vector machine. The data sample is applied mass attribute and one whole class is represented by a gravitation center possessing the mass sum of all the data samples belonging to the class. One data sample belongs to a class when and only when gravitation center of this class has larger gravitation towards the sample than that from the gravitation centers of other classes. As for the binary classification problem, classification surface is a hypersphere depending on the mass proportion of two classes ?2, and the hypersphere encloses the positive class when ?2< 1; the hypersphere encloses the negative class when ?2> 1. Following these, gravitation support support vector(GSVM in short) is proposed, which is a mathematical optimization problem about the positive and negative gravitation center G+,G-, the mass proportion of positive and negative class ?2, class margin ?2. And in some sense, GSVM can be regarded as the unification of gravitation classification and support vector machine.Finally, the simulation experiments on synthetic and benchmark datasets prove the feasibility and correctness of GSVM.