文献类型：期刊文献

英文题名：Incorporating Linear Regression Problems Into an Adaptive Framework With Feasible Optimizations

作者：Zhang, Hengmin[1,2];Qian, Feng[1,3];Zhang, Bob[2];Du, Wenli[1,3];Qian, Jianjun[4,5];Yang, Jian[5]

机构：[1]East China Univ Sci & Technol, Sch Informat Sci & Engn, Key Lab Smart Mfg Energy Chem Proc, Minist Educ, Shanghai 200237, Peoples R China;[2]Univ Macau, Dept Comp & Informat Sci, Pattern Recognit & Machine Intelligence PAMI Res, Fac Sci & Technol, Macau 999078, Peoples R China;[3]Tongji Univ, Shanghai Inst Intelligent Sci & Technol, Shanghai 200092, Peoples R China;[4]PCA Lab, Guangzhou, Peoples R China;[5]Nanjing Univ Sci & Technol, Key Lab Intelligent Percept & Syst High Dimens In, Minist Educ, Sch Comp Sci & Engn, Nanjing 210094, Peoples R China

年份：2023

卷号：25

起止页码：4041

外文期刊名：IEEE TRANSACTIONS ON MULTIMEDIA

收录：;EI(收录号：20221912092078);WOS:【SCI-EXPANDED(收录号:WOS:001144015500037)】；

基金：This work was supported in part by the National Natural Science Foundation of China for the Distinguished Young Scholars under Grant 61725301, and in part General and Youth Programs under Grants 61906067, 62176124, and 61876083, and in part by the China Postdoctoral Science Foundation under Grants 2019M651415 and 2020T130191, and in part by UM Macao Talent Programme under Grant UMMTP-2020-01.

语种：英文

外文关键词：Linear regression; Optimization; Loss measurement; Adaptation models; Matrices; Sparse matrices; Convergence; Linear regression; convex vector and matrix norm; iteratively re-weighted algorithm; convergence analysis

摘要：Accompanied with the increasing popularity of linear regression approaches, most of the existing minimization problems are related with several convex measurements, e.g., l(1)/l(2) /l(2,1) norm of a vector and L-1/L-2,L-1/Frobenius/nuclear norm of amatrix, where the regularized function and the loss function are usually studied for two objective terms case by case, respectively. To address this issue, this work combines these linear regression problems into a unified expression framework by employing an adaptive and flexible function, in which we need to choose different variable elements and adjust an inner parameter, properly. Besides this, they are equipped with some corresponding relationships and their interesting properties. Intuitively speaking, the proposed framework can generalize several traditional linear regression formulations and even more complex ones into an extended representation. For further optimizations, an iteratively re-weighted penalty solution (IRwPS) is devised without any inner loops, making the iteration programming easy to perform. Meanwhile, the theoretical results are provided for guaranteeing that themathematical convergence analysis is solid andmeaningful. Finally, by performing real-world applications in supervised, unsupervised, and semi-supervised tasks, numerical experiments are conducted to validate the theoretical properties and the superiority over some of the state-of-the-art.