Affiliations: [a]
College of Science, China Agricultural University, Beijing, 100083, China
| [b]
School of Automation, Northwestern Polytechnical University, Xian, China
Correspondence:
[*]
Corresponding author. Liming Yang, College of Science, China Agricultural University, Beijing, 100083, China. E-mail: cauyanglm@163.com.
Abstract: Applying semi-supervised learning to extreme learning machine (ELM), we propose a semi-supervised extreme learning machine classification framework (SSELM) with arbitrary norm (q-norm, q=0,1 and 2). However, the SSELM involves nonconvex and nonsmooth problem. In this work, two types of optimization methods are developed to solve the proposed SSELM. The first one is an exact solution approach that reformulates SSELM as mixed integer programming. The second is an approximation approach that approximates the SSELM framework by DC (difference of convex functions) programming. Several formulations for SSELM are presented with different norm. Furthermore, the proposed methods are applied in a practical medical dataset using near-infrared spectral technology. Experimental results in different spectral regions show that incorporating unlabeled samples in training improves the generalization compared with the supervised ELM when insufficient training information is available. Moreover, the proposed methods achieve equivalent performance in benchmark data sets compared to the supervised ELM algorithms and other semi-supervised methods. These results show the feasibility and effectiveness of the proposed algorithms.
