Optimizing multi-view broad learning systems via graph embedding and adaptive membership functions

Abstract

Randomized neural networks (RNNs) have emerged as efficient alternatives to traditional deep learning models by replacing iterative backpropagation with random feature projections and closed-form solutions. RNNs includes random vector functional link (RVFL) networks which o↵er faster training while maintaining competitive performance. However, their shallow architectures often limit feature representation capability. The broad learning system (BLS) addresses this limitation through a flat, incremental network structure that expands horizontally via randomly generated feature and enhancement nodes. Unlike deep networks, BLS computes output weights analytically in broader manner using pseudo-inverse methods, achieving remarkable efficiency. While successful in applications ranging from medical diagnosis to industrial fault detection, standard BLS su↵ers from some drawbacks, including sensitivity to outliers, poor handling of class imbalance as all samples contribute equally, limited data understanding from single-view processing, and inability to capture geometric properties of data. Limited understanding of the BLS causes not capturing the complex relationships within the datasets, resulting in poor generalization performance and less reliability on the traditional BLS. Furthermore, Noise and imbalanced classes are common challenges in real-world datasets. To overcome these limitations of BLS, this thesis makes three fundamental contributions: the class probability-based generalized bell-shaped broad learning system (CPBS-BLS); its multi-view extension, the class probability based generalized bell-shaped multi-view broad learning system (CPBS-MvBLS); and the graph embedded multi-view broad learning system (GrMv-BLS). First, the proposed CPBS-BLS enhances robustness through an integrated framework that combines generalized bell-shaped membership functions with class probability density estimation, enabling adaptive sample weighting that automatically suppresses outliers while emphasizing high-confidence regions near class centroids. Second, the proposed multi-view extension CPBS-MvBLS ex-tends this capability to multi-view data sources by incorporating view-specific membership weighting that simultaneously understands the correlation between the views and addresses class imbalance across multiple feature spaces. Finally, the graph embedded multi-view BLS (GrMv-BLS) introduces a comprehensive architecture that unifies multi-view learning with graph regularized broad learning, incorporating both intrinsic and penalty graph embeddings for topological structure preservation and local fisher discriminant analysis (LFDA) weighted subspace learning for optimal discriminative projection. By addressing BLS’s core limitations while preserving its efficiency advantages, these advances enable more reliable deployment in real-world scenarios involving imperfect, imbalanced, and multi-view data. The proposed frameworks establish new state-of-the-art performance while maintaining the simplicity that makes BLS practically valuable.