Capped L1-norm distance metric-based fast robust twin extreme learning machine

In this paper, we propose a new 0.00,0.00,1.00 fast robust twin extreme learning machine (FRTELM) based on the least squares sense and capped L1-norm distance metric. FRTELM first replaced the inequality constraints in TELM with equality constraints, and then introduced the capped L1-norm distance metric to replace the L2-norm distance metric in TELM. FRTELM not only retains the advantages of TELM, but also overcomes the shortcomings of TELM exaggeration of outliers based on squared L2-norm distance metrics. This improvement improves the robustness and learning efficiency of TELM in solving outlier problems. An efficient optimization algorithm is exploited to solve the nonconvex and nonsmooth challenging problem. In theory, we analyze and discuss the complexity of the algorithm in detail, and prove the convergence and local optimality of the algorithm. Extensive experiments conducted across multiple datasets demonstrates that the proposed method is competitive with state-of-the-art methods in terms of robustness and feasibility.