Robust twin extreme learning machines with correntropy-based metric.

In this paper, we propose a novel distance metric based on correntropy and kernel learning. Some properties of the proposed metric are demonstrated such as nonnegativity, non-convexity, boundedness and approximation behaviors. The proposed metric includes and extends classical metrics such as L 0 -norm and L 1 -norm metrics. Moreover, we develop a fraction loss function satisfying the Bayes rule, and demonstrate its robustness from the perspective of M-estimation. With the proposed robust metric and loss function, a new robust twin extreme learning machines framework (called LCFTELM) is presented to reduce the negative effect of noises and outliers. The proposed LCFTELM retains the advantages of twin extreme machines (TELM) and promotes the robustness. However, the non-convexity of the proposed model makes it difficult to optimize. Furthermore, an effective iterative algorithm for LCFTELM is designed, we present theoretical analysis on the convergence of the proposed algorithm. Following that, we evaluate the proposed algorithm on real-world datasets and artificial dataset under different noise settings. Experimental results show that the proposed method achieves better generalization than the state-of-the-art methods in most cases, which demonstrates the feasibility and robustness of the proposed LCFTELM. • Based on correntropy and Laplacian kernel, a robust distance metric is proposed. A new non-convex fraction loss function is developed. Applying to TELM, a robust classification framework is proposed. • The proposed metric includes and extends the traditional metrics and fractional loss function is a powerful adaptive cost in the presence of noise. • An efficient optimization method is proposed to solve the model. • Numerical experiments show that the proposed LCFTELM is effective and more robust to outliers. [ABSTRACT FROM AUTHOR]