υ-Support vector machine based on discriminant sparse neighborhood preserving embedding

In this paper, we mainly focus on two issues (1) SVM is very sensitive to noise. (2) The solution of SVM does not take into consideration of the intrinsic structure and the discriminant information of the data. To address these two problems, we first propose an integration model to integrate both the local manifold structure and the local discriminant information into a""(1) graph embedding. Then we add the integration model into the objection function of upsilon-support vector machine. Therefore, a discriminant sparse neighborhood preserving embedding upsilon-support vector machine (upsilon-DSNPESVM) method is proposed. The theoretical analysis demonstrates that upsilon-DSNPESVM is a reasonable maximum margin classifier and can obtain a very lower generalization error upper bound by minimizing the integration model and the upper bound of margin error. Moreover, in the nonlinear case, we construct the kernel sparse representation-based a""(1) graph for upsilon-DSNPESVM, which is more conducive to improve the classification accuracy than a""(1) graph constructed in the original space. Experimental results on real datasets show the effectiveness of the proposed upsilon-DSNPESVM method.