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M-estimation activation functions for high-performance extreme learning machine ensemble classification.

Fathi Alimi1, Adnan Khan2, Hameed Ali3

  • 1Department of Chemistry, College of Science, University of Ha'il, P.O. Box 2440, Ha'il, 81441, Saudi Arabia.

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|September 1, 2025
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Summary
This summary is machine-generated.

This study introduces a robust ensemble framework for Extreme Learning Machines (ELMs) using M-estimation theory. The novel approach enhances machine learning model accuracy and resilience against noisy data in cybersecurity applications.

Keywords:
Activation functionsBrier score optimizationClassification accuracyExtreme learning machine (ELM)M-estimation theoryPsi functions ensemble learning

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Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Cybersecurity

Background:

  • Machine learning, particularly AI in Software-Defined Networking, is crucial for cybersecurity tasks like traffic monitoring and anomaly detection.
  • Existing ensemble methods often struggle with noisy or contaminated data, limiting their effectiveness in real-world security scenarios.

Purpose of the Study:

  • To develop a robust ensemble framework for Extreme Learning Machines (ELMs) that is resilient to data irregularities.
  • To improve the generalization, predictive precision, and stability of neural classifiers.

Main Methods:

  • Proposed a novel ensemble framework for ELMs incorporating redescending ψ-activation functions based on M-estimation theory.
  • Utilized grid search to determine the optimal hidden-node count by minimizing the Brier score.
  • Combined ensemble outputs using least-squares optimization instead of traditional voting for precise parameter estimation.

Main Results:

  • The proposed method demonstrated consistently superior accuracy and reduced variance across five benchmark datasets compared to existing ELM ensembles.
  • Validated performance gains through rigorous statistical testing, including Kruskal-Wallis and Dunn's post-hoc analyses.
  • The framework showed marked improvements in generalization, predictive precision, and resilience to data irregularities.

Conclusions:

  • Embedding robust M-estimator-based activations within a controlled ensemble significantly enhances ELM performance.
  • The developed framework offers a substantial advancement in designing efficient and resilient neural classifiers for machine learning applications.