F范数度量下的鲁棒张量低维表征  

Low-Dimensional Representation of Robust Tensor Under F-norm Metric

作　　者：王肖锋[1,2] 石乐岩 杨璐[1,2] 刘军[1,2] 周海波[1,2] WANG Xiao-Feng;SHI Le-Yan;YANG Lu;LIU Jun;ZHOU Hai-Bo(Tianjin Key Laboratory for Advanced Mechatronical System Design and Intelligent Control,Tianjin University of Technology,Tianjin 300384;National Demonstration Center for Experimental Mechanical and Electrical Engineering Education,Tianjin University of Technology,Tianjin 300384)

机构地区：[1]天津理工大学天津市先进机电系统设计与智能控制重点实验室,天津300384 [2]天津理工大学机电工程国家级实验教学示范中心,天津300384

出　　处：《自动化学报》2023年第8期1799-1812,共14页Acta Automatica Sinica

基　　金：国家重点研发计划(2018AAA0103004);天津市科技计划重大专项(20YFZCGX00550);国家自然科学基金(52005370)资助。

摘　　要：张量主成分分析(Tensor principal component analysis, TPCA)在彩色图像低维表征领域得到广泛深入研究,采用F范数平方作为低维投影的距离度量方式,表征含离群数据和噪声图像的鲁棒性较弱.L1范数能够抑制噪声的影响,但所获的低维投影数据缺乏重构误差约束,其局部表征能力也较弱.针对上述问题,利用F范数作为目标函数的距离度量方式,提出一种基于F范数的分块张量主成分分析算法(Block TPCA withF-norm,BlockTPCA-F),提高张量低维表征的鲁棒性.考虑到同时约束投影距离与重构误差,提出一种基于比例F范数的分块张量主成分分析算法(Block TPCA with proportional F-norm, BlockTPCA-PF),其最大化投影距离与最小化重构误差均得到了优化.然后,给出其贪婪的求解算法,并对其收敛性进行理论证明.最后,对包含不同噪声块和具有实际遮挡的彩色人脸数据集进行实验,结果表明,所提算法在平均重构误差、图像重构与分类率等方面均得到明显提升,在张量低维表征中具有较强的鲁棒性.Tensor principal component analysis(TPCA)has been widely and deeply studied in the field of low-dimensional representation of color images.Using the square F-norm as the distance metric of low-dimensional projection,the robustness of representing the images with outliers and noise is weak.can suppress the influence of noise,but the obtained low-dimensional projection data lacks the constraint of reconstruction errors,and the local representation ability is also weak.To solve the above problems,using F-norm as the distance metric of the objective function,a block TPCA with F-norm(BlockTPCA-F)algorithm is proposed to improve the robustness of tensor representation with low dimension.Considering the constraints of projection distances and reconstruction errors at the same time,a block TPCA with proportional F-norm(BlockTPCA-PF)algorithm is presented.The maximum projection distance and the minimum reconstruction error in the objective function are optimized.Then,the greedy algorithms for BlockTPCA-F and BlockTPCA-PF are given respectively,and the convergence is proved theoretically.Finally,experiments are carried out on color face datasets with different artificial noise blocks or actual occluded faces.The results show that the proposed algorithms have been significantly improved in the average reconstruction error,the image reconstruction and the classification rate,and they have strong robustness in tensor lowdimensional representation.

关 键 词：张量主成分分析 低维表征 特征提取 鲁棒性 重构误差 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]