A hybrid approach of PTSVM and ELM inspired by samples´ geometric distribution structure

In this paper, we try to hybrid projection twin support vector machine (PTSVM) and Extreme Learning Machine(ELM). The experiments shows that ELM generally out performs SVM/LS-SVM in various kinds of cases. PTELM tries to use ELM to overcome the shortness of PTSVM, which lacks of flexibility to change nonlinear kernel mapping for complex samples distribution regions. In order to overcome the shortness of ELMs, we try to maintain the geometric structure of the samples distribution in the initial setting of ELM parameters by starting with an auto-encoder ELM, a sufficient condition for such kind auto-encoder ELM to keep the equivalence of topological homology before and after nonlinear mapping is proved by us. For an auto-encoder, in order to do feature abstraction and find the exact manifold in which samples are located, the number of inner layers nodes should be small enough. For this purpose, we prove that the whole samples set can be at least replaced by a small subset which located on the boundary of distribution region. For more, the weights are modified by a ELM approach to make samples of a class move toward this classs hyperplane found by PTSVM. The experimental results on several UCI benchmark data sets show the feasibility and effectiveness of the proposed method.