ECA-BLS：一种高效的复增广宽学习系统
ECA-BLS: An Efficient Complex-Augmented Broad Learning System
- Indian Institute of Technology Indore（印度印多尔印度理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出ECA-BLS，通过将复增广BLS转换为实域形式降低计算成本，在26个基准数据集上表现优于经典BLS及先进随机神经网络，为BLS研究补充了增广二阶建模维度。
AI中文摘要：
宽学习系统（Broad Learning System, BLS）是深度架构的高效替代方案，具有训练快速、解析学习、在有限数据下泛化能力强等优势。但现有BLS变体局限于实值表示，限制了其捕捉现实数据中固有的非线性交互和二阶统计依赖的能力。值得注意的是，此前没有BLS模型充分利用数据嵌入复域时自然产生的完整二阶统计信息。为解决这一局限，本文提出首个复增广宽学习系统（Complex Augmented Broad Learning System, CA-BLS），该系统将实值输入转换为相位编码的复表示，并采用广线性建模，通过复共轭增广联合利用协方差和伪协方差信息，从而有效建模传统BLS公式无法触及的潜在非线性、相干结构和二阶依赖。为缓解复增广带来的额外计算成本，本文进一步开发了高效复增广BLS（Efficient Complex Augmented BLS, ECA-BLS），在完全保留CA-BLS精确决策函数的前提下，将其重新表述为实域形式，实现乘法运算减少多达75%，加法运算减少超过60%。严格的理论分析证明了CA-BLS与ECA-BLS之间的数学等价性，确保零理论损失。在来自UCI和KEEL仓库的26个基准数据集上开展的大量实验表明，ECA-BLS在准确率、平均排名和统计显著性方面始终优于经典BLS和近期最先进的随机神经网络，确立了增广二阶建模是BLS研究中关键且此前缺失的维度。
英文摘要：
Broad Learning System (BLS) is an efficient alternative to deep architectures due to its fast training, analytical learning, and strong generalization under limited data. However, existing BLS variants are confined to real-valued representations, restricting their ability to capture nonlinear interactions and second-order statistical dependencies inherent in real-world data. Notably, no prior BLS model fully exploits the complete second-order statistics that naturally emerge when data are embedded in the complex domain. To address this limitation, this paper introduces the first complex augmented Broad Learning System (CA-BLS), which transforms real-valued inputs into phase-encoded complex representations and adopts widely linear modeling to jointly leverage covariance and pseudo-covariance information via complex conjugate augmentation. This enables effective modeling of latent nonlinearities, coherence structures, and second-order dependencies inaccessible to conventional BLS formulations. To mitigate the additional computational cost of complex augmentation, an Efficient Complex Augmented BLS (ECA-BLS) is further developed, reformulating CA-BLS entirely in the real domain while preserving its exact decision function, achieving up to 75\% fewer multiplications and over 60\% fewer additions. A rigorous theoretical analysis proves the mathematical equivalence between CA-BLS and ECA-BLS, ensuring zero theoretical loss. Extensive experiments on 26 benchmark datasets from the UCI and KEEL repositories demonstrate that ECA-BLS consistently outperforms classical BLS and recent state-of-the-art randomized neural networks in accuracy, average rank, and statistical significance, establishing augmented second-order modeling as a critical and previously missing dimension of BLS research.
