Double capped L1-norm extreme learning machine for regression and classification

Xiaoxue Wang, Kuaini Wang, Jinge Li, Jinde Cao,
Double capped L1-norm extreme learning machine for regression and classification,
Journal of the Franklin Institute,
Volume 362, Issue 17,
2025,
108127,
ISSN 0016-0032,
https://doi.org/10.1016/j.jfranklin.2025.108127.
(https://www.sciencedirect.com/science/article/pii/S0016003225006192)
Abstract: Extreme learning machine has excellent performance in both regression and classification problems, but its robustness and sparsity in real-world problems are slightly insufficient. Considering that the capped L1-norm is derived from the L1-norm, it can inherit the sparsity of the L1-norm. Meanwhile, the nonconvexity of the capped L1-norm allows it to enhance the robustness of the algorithm. In this paper, the capped L1-norm is introduced into the regularization and loss function of ELM simultaneously, which constitutes the double capped L1-norm extreme learning machine (DCELM). Since the objective function of DCELM is nonconvex, it can be reformulated as difference of convex functions and then solved by difference of convex functions algorithm. In addition, this paper verifies the performance of the proposed model by artificial data set, regression and classification data sets. Experiments prove that DCELM has good robustness and sparsity in both regression and classification problems.
Keywords: Extreme learning machine; Capped L1-norm; Difference of convex functions; Robustness; Sparsity