Robust twin extreme learning machine with adaptive fractional loss

Xiang Jin; Guolin Yu; Jun Ma; Xiang Jin; Guolin Yu; Jun Ma

doi:10.3934/math.2026381

AIMS Mathematics

2026, Volume 11, Issue 4: 9228-9259. doi: 10.3934/math.2026381

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Robust twin extreme learning machine with adaptive fractional loss

School of Mathematics and Information Sciences, North Minzu University, Yinchuan 750021, Ningxia, China

Received: 16 January 2026 Revised: 08 March 2026 Accepted: 18 March 2026 Published: 03 April 2026
MSC : 68T10, 91C20

The twin extreme learning machine (TELM), based on the hinge-loss function, demonstrates significant potential for pattern classification tasks. However, the hinge-loss function, which minimizes the shortest distance between sets, results in classifiers that are sensitive to noise and unstable in the presence of overfitting. To enhance TELM's performance, a novel learning framework, termed adaptive fractional loss TELM (AFTELM), is proposed. This framework incorporates an adaptive fractional loss (AF-loss) function, offering improved robustness to noise compared to TELM with hinge loss. A theoretical analysis is provided to examine the noise insensitivity of AFTELM. The concave-convex procedure (CCCP) is employed for efficient optimization. Extensive experiments on benchmark datasets validate the superior performance of AFTELM, demonstrating its robustness to noise and enhanced classification ability.
- twin extreme learning machine,
- adaptive fractional loss,
- robustness,
- noise insensitivity
Citation: Xiang Jin, Guolin Yu, Jun Ma. Robust twin extreme learning machine with adaptive fractional loss[J]. AIMS Mathematics, 2026, 11(4): 9228-9259. doi: 10.3934/math.2026381

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Abstract

The twin extreme learning machine (TELM), based on the hinge-loss function, demonstrates significant potential for pattern classification tasks. However, the hinge-loss function, which minimizes the shortest distance between sets, results in classifiers that are sensitive to noise and unstable in the presence of overfitting. To enhance TELM's performance, a novel learning framework, termed adaptive fractional loss TELM (AFTELM), is proposed. This framework incorporates an adaptive fractional loss (AF-loss) function, offering improved robustness to noise compared to TELM with hinge loss. A theoretical analysis is provided to examine the noise insensitivity of AFTELM. The concave-convex procedure (CCCP) is employed for efficient optimization. Extensive experiments on benchmark datasets validate the superior performance of AFTELM, demonstrating its robustness to noise and enhanced classification ability.

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