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All Journal Control Systems and Optimization Letters
Shafarin, Muhammad Ijaz
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Aerospace Engineering Automotive Engineering Computer Science & IT Control & Systems Engineering Electrical & Electronics Engineering Engineering

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Broad Learning System: A Derivation-Based Mathematical Formulation Saputra, Dimas Chaerul Ekty; Rahmawati, Dyah Putri; Pertiwi, Affifah Mutiara; Shafarin, Muhammad Ijaz; Pertiwi, Kharisma Monika Dian; Win, Thinzar Aung; Futri, Irianna; Safitri, Pima Hani
Control Systems and Optimization Letters Vol 4, No 1 (2026)
Publisher : Peneliti Teknologi Teknik Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59247/csol.v4i1.294

Abstract

Broad Learning System is a wide learning framework that constructs nonlinear feature representations while enabling efficient model training through analytical solutions. This paper presents a derivation-based formulation of Broad Learning System that explains the mathematical structure underlying the learning process. The model constructs an expanded feature representation through feature mapping nodes followed by enhancement nodes that further enrich the learned representation. The learning problem is then expressed as a linear model in the constructed feature space, and the output weights are obtained using ridge regularized least squares optimization. This formulation allows the training process to be solved directly using matrix operations without iterative gradient based procedures. In addition, an incremental learning mechanism is introduced to enable efficient parameter updates when new samples or additional nodes are incorporated into the model. The presented formulation highlights how Broad Learning System combines nonlinear feature construction with computationally efficient closed form learning, providing a clear theoretical interpretation of the learning process.
Co-Authors Dimas Chaerul Ekty Saputra Futri, Irianna Pertiwi, Affifah Mutiara Pertiwi, Kharisma Monika Dian Rahmawati, Dyah Putri Safitri, Pima Hani Win, Thinzar Aung