Discriminative projective dictionary pair based broad metric learning system: algorithm and its applications in pattern classification

Pattern classification plays a pivotal role in a wide range of domains, including computer vision and healthcare. The Broad Learning System (BLS) has attracted considerable attention for its competitive classification performance and computational efficiency. However, its reliance on randomly initialized parameters and lack of iterative updates often lead to performance instability. Directly applying backpropagation to refine these parameters may further result in overfitting. To address these limitations, this research propose a novel framework called the Discriminative Projective Dictionary Pair-based Broad Metric Learning System (D-BMLS). The foundation of this system is the Broad Metric Learning System (BMLS), which integrates a metric subsystem that employs iterative learning to reduce sensitivity to random initialization while leveraging the structural advantages of metric learning to suppress overfitting. Although this improves robustness, it can also introduce computational overhead and still struggle with nonlinear data modeling due to the dual-mapping structure of BLS. To overcome these challenges, D-BMLS incorporates Discriminative Projective Dictionary Pair Learning, which encodes input data into a low-dimensional, linearly separable space. This reduces the number of learnable parameters and enhances the model’s capacity to capture nonlinear relationships through linear transformations. Extensive experiments on five different tasks including image classification, signal recognition, and high-dimensional feature analysis demonstrate the superior performance of D-BMLS. Ablation studies on three benchmark datasets verify the contributions of each component, and results on a synthetic dataset highlight the metric subsystem’s effectiveness in mitigating overfitting.