In this paper,we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weightedℓ_(1)(OWL1)norm ball.In particular,an efficient semismooth Newton method is proposed f...In this paper,we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weightedℓ_(1)(OWL1)norm ball.In particular,an efficient semismooth Newton method is proposed for solving the dual of a reformulation of the original projection problem.Global and local quadratic convergence results,as well as the finite termination property,of the algorithm are proved.Numerical comparisons with the two best-known methods demonstrate the efficiency of our method.In addition,we derive the generalized Jacobian of the studied projector which,we believe,is crucial for the future designing of fast second-order nonsmooth methods for solving general OWL1 norm constrained problems.展开更多
文摘宽度学习系统(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.
基金supported by National Natural Science Foundation of China(Grant No.11901107)the Young Elite Scientists Sponsorship Program by CAST(Grant No.2019QNRC001)+1 种基金the Shanghai Sailing Program(Grant No.19YF1402600)the Science and Technology Commission of Shanghai Municipality Project(Grant No.19511120700).
文摘In this paper,we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weightedℓ_(1)(OWL1)norm ball.In particular,an efficient semismooth Newton method is proposed for solving the dual of a reformulation of the original projection problem.Global and local quadratic convergence results,as well as the finite termination property,of the algorithm are proved.Numerical comparisons with the two best-known methods demonstrate the efficiency of our method.In addition,we derive the generalized Jacobian of the studied projector which,we believe,is crucial for the future designing of fast second-order nonsmooth methods for solving general OWL1 norm constrained problems.