Support Vector Machines Based on Spread Directions of Manifold

This paper aims at settling the shortcomings in SVM such as it is sensitive to the distribution of samples near separating margin. Inspired by spread directions of manifold, we propose a new SVM learning method. This method, constructs scalar field and corresponding gradient field in observation space according to the classification decision function, and then, from viewpoints of field and principal spread directions, establishes an evaluation approach of classification performance under nonlinear mapping from observation space to intrinsic embedding space, which maximizes the classification margin of training samples in observation space and maintains intrinsic regularity of manifold distributed in embedded space. Numerical experiments on artificial dataset and practical dataset show that proposed algorithm, which have higher classification accuracy rate and stabilization than C-SVM, is reasonable and effective.