改进随机配置网络的评估机制，提升学习效率与可扩展性

Stochastic Configuration Networks (SCNs) are a class of randomized neural networks that integrate randomized algorithms within an incremental learning framework. A defining feature of SCNs is the supervisory mechanism, which adaptively adjusts the distribution to generate effective random basis functions, thereby enabling error-free learning. In this paper, we present a comprehensive analysis of the impact of the supervisory mechanism on the learning performance of SCNs. Our findings reveal that the current SCN framework evaluates the effectiveness of each random basis function in reducing residual errors using a lower bound on its error reduction potential, which constrains SCNs' overall learning efficiency. Specifically, SCNs may fail to consistently select the most effective random candidate as the new basis function during each training iteration. To overcome this problem, we propose a novel method for evaluating the hidden layer's output matrix, supported by a new supervisory mechanism that accurately assesses the error reduction potential of random basis functions without requiring the computation of the Moore-Penrose inverse of the output matrix. This approach enhances the selection of basis functions, reducing computational complexity and improving the overall scalability and learning capabilities of SCNs. We introduce a Recursive Moore-Penrose Inverse-SCN (RMPI-SCN) training scheme based on the new supervisory mechanism and demonstrate its effectiveness through simulations over some benchmark datasets. Experiments show that RMPI-SCN outperforms the conventional SCN in terms of learning capability, underscoring its potential to advance the SCN framework for large-scale data modeling applications.