A generalized robust twin extreme learning machine for robust classification under noisy data

Robust learning systems must simultaneously maintain sensitivity to clean data and resistance to corruptions, a challenge that traditional adaptive losses and regularization often address incompletely. To bridge this gap, we propose a novel generalized robust loss function, denoted as R ( x ) , which unifies logarithmic suppression, rational saturation, and L 1 -regularization into a single adaptive framework. Unlike fixed-shape losses such as Huber or Cauchy, our function dynamically interpolates between logarithmic suppression near zero and rational saturation in the tail, enabling adaptive down-weighting of outliers without manual threshold tuning. This design provides a principled mechanism for down-weighting outliers while preserving sensitivity to small errors. Theoretically, we prove that R ( x ) is definable in an o-minimal structure, guaranteeing the Kurdyka-Łojasiewicz (KL) property, which ensures that our optimization algorithm converges to a critical point from any initialization. We further establish robustness within the M -estimation framework by demonstrating its bounded influence function. Building upon R ( x ) , we propose the generalized robust twin extreme learning machine (GR-TELM), which integrates R ( x ) into the twin extreme learning machine (TELM) framework to enhance resistance to noise and outliers. To efficiently solve the resulting non-convex and non-smooth optimization, we develop an alternating direction method of multipliers based scheme that decomposes the problem into sub-problems with closed-form updates for hyperplane weights and proximal gradient steps for slack variables, ensuring computational efficiency and scalability. Comprehensive experiments on 20 University of California, Irvine (UCI) benchmark datasets under severe noise conditions, including feature noise and label noise, validate our approach. GR-TELM outperforms state-of-the-art methods including extreme learning machine with Incosh loss (LnELM), extreme learning machine with Correntropy induced loss function (CELM), correntropy hinge loss-based extreme learning machine (CHELM), homotopy loss-based extreme learning machine with Laplacian kernel (LKELM), regularized extreme learning machine (RELM), and classical twin extreme learning machine (TELM) in the field of artificial intelligence (AI), achieving an average accuracy improvement of 3%–6% while retaining high breakdown points. This robust performance comes with a manageable increase in computational cost (approximately 30–50x relative to standard TELM), a well-justified trade-off for applications requiring reliable performance in noisy environments.