Broad Learning System: A Derivation-Based Mathematical Formulation - Dimas Chaerul Ekty Saputra; Dyah Putri Rahmawati; Affifah Mutiara Pertiwi; Muhammad Ijaz Shafarin; Kharisma Monika Dian Pertiwi; Thinzar Aung Win; Irianna Futri; Pima Hani Safitri (Control Systems and Optimization Letters, 2026)
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.