A Greedy Interpretable Geometric Constructive Method for Industrial Data Analysis.

The interpretable geometric constructive neural network (IGCNet) has demonstrated significant potential for developing rapid learning models, making it particularly well-suited for data analysis tasks. However, its geometric control strategy is difficult to adapt to the dynamic transformation of network residuals, resulting in limited generalization ability. To address this issue, this article proposes a greedy variant of IGCNet, termed IGCNet-G, which enhances generalization. First, an adaptive relaxation parameter is constructed by analyzing the convergence behavior of network residuals within a function class. This approach eliminates the excessive computational cost associated with passive hyperparameter tuning. Second, the relaxed parameters and greedy theory are incorporated into the geometric control strategy of IGCNet, leading to the development of a relaxed greedy control strategy. This strategy enables the adaptive relaxation of constraints on candidate node parameters according to the convergence state of residuals, thereby accelerating residual convergence. Finally, the universal approximation property of IGCNet-G is substantiated through theoretical analysis. Experimental evaluations conducted on a nonlinear function example and a real coal flotation dataset confirm that IGCNet-G achieves a high level of predictive performance.