[1]唐肝翌,卢桂馥,王 勇,等.基于L1-范数和弹性网约束的鲁棒稀疏块PCA[J].南京师大学报(自然科学版),2022,45(04):102-109.[doi:10.3969/j.issn.1001-4616.2022.04.014]
　Tang Ganyi,Lu Guifu,Wang Yong,et al.Robust and Sparse BPCA with the Constraints of L1-norm and the Elastic Net[J].Journal of Nanjing Normal University(Natural Science Edition),2022,45(04):102-109.[doi:10.3969/j.issn.1001-4616.2022.04.014]
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基于L1-范数和弹性网约束的鲁棒稀疏块PCA()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第45卷
期数:
2022年04期
页码:
102-109
栏目:
计算机科学与技术
出版日期:
2022-12-15

文章信息/Info

Title:
Robust and Sparse BPCA with the Constraints of L1-norm and the Elastic Net
文章编号:
1001-4616(2022)04-0102-08
作者:
唐肝翌1; 卢桂馥1; 王 勇1; 2; 范莉莉1; 杜扬帆1
(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)
Author(s):
Tang Ganyi1; Lu Guifu1; Wang Yong1; 2; Fan Lili1; Du Yangfan1
(1.School of Computer and Information,Anhui Polytechnic University,Wuhu 241000,China)
(2.State Key Laboratory for Novel Software Technology,Nanjing University,Nanjing 210023,China)
关键词:
块主成份分析; L1-范数; 弹性网; 稀疏建模; 子空间学习
Keywords:
BPCA; L1-norm; elastic net; sparse modelling; subspace learning
分类号:
TP391
DOI:
10.3969/j.issn.1001-4616.2022.04.014
文献标志码:
A
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.
Abstract:
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.

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备注/Memo

备注/Memo:
收稿日期:2022-04-16.
基金项目: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).
通讯作者:唐肝翌,硕士,副教授,研究方向:
更新日期/Last Update: 2022-12-15