基于L1-范数和弹性网约束的鲁棒稀疏块PCA  

Robust and Sparse BPCA with the Constraints of L1-norm and the Elastic Net

作　　者：唐肝翌 卢桂馥 王勇 范莉莉[1] 杜扬帆 Tang Ganyi;Lu Guifu;Wang Yong;Fan Lili;Du Yangfan(School of Computer and Information,Anhui Polytechnic University,Wuhu 241000,China;State Key Laboratory for Novel Software Technology,Nanjing University,Nanjing 210023,China)

机构地区：[1]安徽工程大学计算机与信息学院,安徽芜湖241000 [2]计算机软件国家重点实验室(南京大学),江苏南京210023

出　　处：《南京师大学报（自然科学版）》2022年第4期102-109,共8页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(61976005);安徽省自然科学基金项目(1908085MF183);安徽高校自然科学研究项目重点项目(KJ2020A0363);安徽工程大学“中青年拔尖人才培养计划”(201812);计算机软件新技术国家重点实验室(南京大学)开放基金项目(KFKT2019B23);安徽省高等教育提升计划项目(TSKJ2016B01);安徽省高等学校省级质量工程项目(2019jyxm1183).

摘　　要：块主成份分析(block principal component analysis,BPCA)是一种重要的子空间学习方法,能充分利用图像矩阵的部分关联.基于L1-范数的BPCA是近年来发展起来的鲁棒降维的有效方法.本研究提出了一种新的鲁棒稀疏BPCA方法,称之为BPCAL1-S.该方法相对于传统的基于L2-范数的PCA对噪声更加鲁棒.为了建立稀疏模型,优化过程中引入弹性网,联合使用Lasso与Ridge惩罚因子进行约束.提出了一种贪心算法逐个提取特征向量,对迭代过程的收敛性做了理论证明.将BPCAL1-S应用于图像分类与图像重构,实验结果验证了该方法的有效性.Block principal component analysis(BPCA),which can utilize part correlation of image matrix sufficiently,is an important subspace learning approach.L1-norm based BPCA is an effective technique for robust learning in dimensionality reduction developed recently.We propose a novel robust and sparse BPCA method referred to as BPCAL1-S.The approach is more robust to outliers than the traditional L2-norm based PCA.To develop a model with sparsity,the elastic net constraint which combining ridge and lasso penalty,is integrated into the optimization procedure.We present a greedy algorithm to extract basic feature vectors one by one,and proposed theoretical analysis to guarantee the convergence of the iterative process.The proposed BPCAL1-S is applied to the analysis of image classification and image reconstruction,and the experimental results verify its effectiveness.

关 键 词：块主成份分析 L1-范数 弹性网 稀疏建模 子空间学习 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]