Robust Fisher-Regularized Twin Extreme Learning Machine with Capped L1-Norm for Classification

Twin extreme learning machine (TELM) is a classical and high-efficiency classifier. However, it neglects the statistical knowledge hidden inside the data. In this paper, in order to make full use of statistical information from sample data, we first come up with a Fisher-regularized twin extreme learning machine (FTELM) by applying Fisher regularization into TELM learning framework. This strategy not only inherits the advantages of TELM, but also minimizes the within-class divergence of samples. Further, in an effort to further boost the anti-noise ability of FTELM method, we propose a new capped L-1-norm FTELM (CL1-FTELM) by introducing capped L-1-norm in FTELM to dwindle the influence of abnormal points, and CL1-FTELM improves the robust performance of our FTELM. Then, for the proposed FTELM method, we utilize an efficient successive overrelaxation algorithm to solve the corresponding optimization problem. For the proposed CL1-FTELM, an iterative method is designed to solve the corresponding optimization based on re-weighted technique. Meanwhile, the convergence and local optimality of CL1-FTELM are proved theoretically. Finally, numerical experiments on manual and UCI datasets show that the proposed methods achieve better classification effects than the state-of-the-art methods in most cases, which demonstrates the effectiveness and stability of the proposed methods.