基于Frobenius和L_(2,1)范数的多输出宽度学习系统  

Multi-output broad learning system based on Frobenius and L_(2,1)norm

作　　者：褚菲[1,2] 卢新宇 苏嘉铭 王雪松 马小平 CHU Fei;LU Xin-yu;SU Jia-ming;WANG Xue-song;MA Xiao-ping(Artificial Intelligence Research Institute,China University of Mining and Technology,Xuzhou 221116,China;School of Information and Control Engineering,China University of Mining and Technology,Xuzhou 221116,China)

机构地区：[1]中国矿业大学人工智能研究院,江苏徐州221116 [2]中国矿业大学信息与控制工程学院,江苏徐州221116

出　　处：《控制与决策》2023年第10期2919-2924,共6页Control and Decision

基　　金：国家自然科学基金项目(61973304,61873049,62073060);江苏省自然科学基金项目(BK20191339);江苏省第十六届“六大人才高峰”高层次人才选拔培养项目(DZXX-045);中国矿业大学研究生创新计划项目(2022WLJCRCZL109);中央高校基本科研业务费专项资金项目(2019XKQYMS64)。

摘　　要：宽度学习系统(broad learning system,BLS)因其特征提取能力强、计算效率高而被广泛应用于众多领域.然而,目前BLS主要用于单输出回归,当BLS存在多个输出时,BLS无法有效发掘多个输出权重之间的相关性,会导致模型预测性能的下降.鉴于此,通过Frobenius和L_(2,1)矩阵范数的联合约束,提出多输出宽度学习系统(multi-output broad learning system,MOBLS).首先,在原有BLS的基础上构建新的目标函数,将L2损失函数替换为L_(2,1)形式,L_(2)正则化项替换为Frobenius和L_(2,1)两项;然后,利用交替方向乘子法(alternating direction method of multipliers,ADMM)对新目标函数BLS的输出权重优化求解.利用11个公共数据集和1个实际过程数据集验证了所提系统的有效性.Broad learning systems(BLS)have been widely used in many fields because of its strong feature extraction ability and high computational efficiency.However,the BLS is mainly used for single-output regression at present,When the BLS has multi-outputs,it cannot effectively explore the correlation between multi-output weights,which will lead to the degradation of model prediction performance.Therefore,by introducing the Frobenius and L_(2,1) matrix norm,this paper proposes a multi-output broad learning system(MOBLS).Firstly,a new objective function is constructed on the basis of the original BLS.The L_(2)-loss function is replaced by the L_(2,1) form,and the L_(2) regularization term is replaced by the Frobenius and L_(2,1) two terms.Then,alternating direction method of multipliers(ADMM)is used to optimize the output weight of the BLS with the new objective function.Finally,11 public datasets and 1 actual process dataset are used to verify its effectiveness.

关 键 词：宽度学习系统 多输出回归 FROBENIUS范数 L_(2 1)范数 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]