一种空间几何角度最大化的随机增量学习模型及应用  

A Stochastic Incremental Learning Model With Maximizing Spatial Geometry Angle and Its Application

作　　者：南静 代伟 袁冠[2] 周平 NAN Jing;DAI Wei;YUAN Guan;ZHOU Ping(School of Information and Control Engineering,China University of Mining and Technology,Xuzhou 221116;School of Computer Science&Technology,China University of Mining and Technology,Xuzhou 221116;State Key Laboratory of Synthetical Automation for Process Industries,Northeastern University,Shenyang 110819)

机构地区：[1]中国矿业大学信息与控制工程学院,徐州221116 [2]中国矿业大学计算机科学与技术学院,徐州221116 [3]东北大学流程工业综合自动化国家重点实验室,沈阳110819

出　　处：《自动化学报》2023年第6期1283-1294,共12页Acta Automatica Sinica

基　　金：国家自然科学基金(61973306);江苏省自然科学基金优秀青年项目(BK20200086);江苏省研究生科研与实践创新计划(KYCX22_2552);中国矿业大学未来杰出人才助力计划(2022WLKXJ077)资助。

摘　　要：针对随机权神经网络(Random weight neural networks,RWNNs)隐含层节点随机生成过程可解释性不足和节点随机生成而导致的网络结构不紧致等问题,提出了一种空间几何角度最大化随机增量学习模型(Stochastic incremental learning model with maximizing spatial geometry angle,SGA-SIM).首先,以空间几何视角深入分析随机增量学习过程,建立了具有可解释性的空间几何角度最大化约束,以改善隐含层节点质量,并证明该学习模型具有无限逼近特性;同时,引入格雷维尔迭代法优化学习模型输出权值计算方法,提高模型学习效率.在真实的分类和回归数据集以及数值模拟实例上的实验结果表明,所提增量学习模型在建模速度、模型精度和模型网络结构等多个方面具有明显优势.Aiming at the problems of insufficient interpretability and incompact network structure caused by random generation of hidden nodes in random weight neural networks(RWNNs),this paper proposes a stochastic incremental learning model with maximizing spatial geometry angle(SGA-SIM).Firstly,the random incremental learning process is deeply analyzed from the perspective of spatial geometry,then an interpretable spatial geometric angle maximization constraint is established to improve the quality of the hidden nodes,and the universal approximation property of this model is proved.Besides,the Grenville iteration method is introduced to optimize the output weight calculation,which improves the learning efficiency of the learning model.Experimental results on the real datasets and numerical simulation examples show that the proposed model has obvious advantages in modeling speed,model accuracy and model network structure.

关 键 词：随机权神经网络 增量学习 空间几何角度最大化约束 无限逼近性 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]