Block Principle Component Analysis with Lp-norm for Robust and Sparse Modelling

doi:10.1007/s12204-018-1955-4

sa ›› 2018, Vol. 23 ›› Issue (3): 398-.doi: 10.1007/s12204-018-1955-4

Block Principle Component Analysis with Lp-norm for Robust and Sparse Modelling

TANG Ganyi (唐肝翌), LU Guifu (卢桂馥)

(School of Computer and Information, Anhui Polytechnic University, Wuhu 241000, Anhui, China)

出版日期:2018-05-31 发布日期:2018-06-17
通讯作者: TANG Ganyi (唐肝翌) E-mail:tangganyi.tony@qq.com

Block Principle Component Analysis with Lp-norm for Robust and Sparse Modelling

TANG Ganyi (唐肝翌), LU Guifu (卢桂馥)

(School of Computer and Information, Anhui Polytechnic University, Wuhu 241000, Anhui, China)

Online:2018-05-31 Published:2018-06-17
Contact: TANG Ganyi (唐肝翌) E-mail:tangganyi.tony@qq.com

摘要/Abstract

摘要： Block principle component analysis (BPCA) is a recently developed technique in computer vision and pattern classiˉcation. In this paper, we propose a robust and sparse BPCA with Lp-norm, referred to as BPCALp-S, which inherits the robustness of BPCA-L1 due to the employment of adjustable Lp-norm. In order to perform a sparse modelling, the elastic net is integrated into the objective function. An iterative algorithm which extracts feature vectors one by one greedily is elaborately designed. The monotonicity of the proposed iterative procedure is theoretically guaranteed. Experiments of image classiˉcation and reconstruction on several benchmark sets show the e?ectiveness of the proposed approach.

关键词: block principle component analysis (BPCA), Lp-norm, robust modelling, sparse modelling

Abstract: Block principle component analysis (BPCA) is a recently developed technique in computer vision and pattern classiˉcation. In this paper, we propose a robust and sparse BPCA with Lp-norm, referred to as BPCALp-S, which inherits the robustness of BPCA-L1 due to the employment of adjustable Lp-norm. In order to perform a sparse modelling, the elastic net is integrated into the objective function. An iterative algorithm which extracts feature vectors one by one greedily is elaborately designed. The monotonicity of the proposed iterative procedure is theoretically guaranteed. Experiments of image classiˉcation and reconstruction on several benchmark sets show the e?ectiveness of the proposed approach.

Key words: block principle component analysis (BPCA), Lp-norm, robust modelling, sparse modelling

中图分类号:

TP 391

TANG Ganyi (唐肝翌), LU Guifu (卢桂馥). Block Principle Component Analysis with Lp-norm for Robust and Sparse Modelling[J]. sa, 2018, 23(3): 398-.

TANG Ganyi (唐肝翌), LU Guifu (卢桂馥). Block Principle Component Analysis with Lp-norm for Robust and Sparse Modelling[J]. Journal of Shanghai Jiao Tong University (Science), 2018, 23(3): 398-.

参考文献 18

[1]	JOLLIFFE I T. Principal component analysis [M].New York, USA: Springer, 2002.
[2]	YANG J, ZHANG D, FRANGI A F, et al. Two-dimensional PCA: A new approach to appearance-based face representation and recognition [J]. IEEETransaction on Pattern Analysis and Machine Intel-ligence, 2004, 26(1): 131-137.
[3]	KE Q F, KANADE T. Robust L1-norm factorizationin the presence of outliers and missing data by al-ternative convex programming [C]//Proceedings of the2005 Computer Society Conference on Computer Vi-sion and Pattern Recognition. San Diego, USA: IEEE,2005: 739-746.
[4]	DING C, ZHOU D, HE X F, et al. R1-PCA: Rota-tional invariant L1-norm principal component analysisfor robust subspace factorization [C]//Proceedings ofthe 23rd International Conference on Machine Learn-ing. Pittsburgh, USA: ACM, 2006: 281-288.
[5]	KWAK N. Principal component analysis based on L1-norm maximization [J]. IEEE Transaction on PatternAnalysis and Machine Intelligence, 2008, 30(9): 1672-1680.
[6]	NIE F P, HUANG H, DING C, et al. Robust principalcomponent analysis with non-greedy L1-norm maxi-mization [C]//Proceedings of the Twenty-Second In-ternational Joint Conference on Artiˉcial Intelligence.Barcelona, Spain: [s.n.], 2011: 1433-1438.
[7]	LI X L, PANG Y W, YUAN Y. L1-norm-based 2DPCA[J]. IEEE Transactions on Systems, Man, and Cyber-netics Part B: Cybernetics, 2009, 40(4): 1170-1175.
[8]	WANG R, NIE F P, YANG X J, et al. Robust2DPCA with non-greedy L1-norm maximization forimage analysis [J]. IEEE Transactions on Cybernetics,2015, 45(5): 1108-1112.
[9]	KWAK N. Principal component analysis by Lp-normmaximization [J]. IEEE Transactions on Cybernetics,2014, 44(5): 594-609.
[10]	GAO Q X. Is two-dimensional PCA equivalent to aspecial case of modular PCA? [J]. Pattern RecognitionLetters, 2007, 28(10): 1250-1251.
[11]	KONG H, WANG L, TEOH E K, et al. Generalized2D principal component analysis for face image representation and recognition [J]. Neural Networks, 2005,18(5/6): 585-594.
[12]	WANG L W,WANG X, ZHANG X R, et al. The equivalence of two-dimensional PCA to line-based PCA [J].Pattern Recognition Letters, 2005, 26(1): 57-60.
[13]	GOTTUMUKKAL R, ASARI V K. An improved facerecognition technique based on modular PCA approach [J]. Pattern Recognition Letters, 2004, 25(4):429-436.
[14]	KIM C, CHOI C H. Image covariance-based subspacemethod for face recognition [J]. Pattern Recognition,2007, 40(5): 1592-1604.
[15]	WANG H X. Block principal component analysis withL1-norm for image analysis [J]. Pattern RecognitionLetters, 2012, 33(5): 537-542.
[16]	WANG H X, WANG J. 2DPCA with L1-norm for simultaneously robust and sparse modelling [J]. NeuralNetworks, 2013, 46: 190-198.
[17]	WANG J. Generalized 2-D principal component analysis by Lp-norm for image analysis [J]. IEEE Transactions on Cybernetics, 2015, 46(3): 792-803.
[18]	JENATTON R, OBOZINSKI G, BACH F. Structuredsparse principal component analysis [C]//Proceedingsof the 13th International Conference on Artiˉcial Intelligence and Statistics. Chia Laguna Resort, Italy:[s.n.], 2010: 366-373.

相关文章 15

[1]	蒋祖华1, 周宏明2, 陶宁蓉3, 李柏鹤1. 基于知识的船舶曲面分段建造调度及应用[J]. J Shanghai Jiaotong Univ Sci, 2024, 29(5): 759-765.
[2]	于佳琪1，王殊轶1，王浴屺1，谢华2，吴张檑1，付小妮1，马邦峰1. 基于增强现实技术的新型经皮肾穿刺训练可视化工具[J]. J Shanghai Jiaotong Univ Sci, 2023, 28(4): 517-.
[3]	姜锐1，朱瑞祥1，蔡萧萃1，苏虎2. 具有增强注意力的前景分割网络[J]. J Shanghai Jiaotong Univ Sci, 2023, 28(3): 360-369.
[4]	祝楷, 熊柏青, 闫宏伟, 张永安, 李志辉, 李锡武, 刘红伟, 温凯, 闫丽珍, . 辊道传送速度对大规格铝合金厚板应力分布及演变影响的数值模拟研究[J]. J Shanghai Jiaotong Univ Sci, 2023, 28(2): 255-263.
[5]	. [J]. J Shanghai Jiaotong Univ Sci, 2022, 27(6): 757-767.
[6]	. [J]. J Shanghai Jiaotong Univ Sci, 2022, 27(2): 190-201.
[7]	. [J]. J Shanghai Jiaotong Univ Sci, 2022, 27(2): 240-249.
[8]	. [J]. J Shanghai Jiaotong Univ Sci, 2022, 27(1): 7-14.
[9]	. [J]. J Shanghai Jiaotong Univ Sci, 2022, 27(1): 24-35.
[10]	. [J]. J Shanghai Jiaotong Univ Sci, 2022, 27(1): 99-111.
[11]	. [J]. J Shanghai Jiaotong Univ Sci, 2022, 27(1): 121-136.
[12]	. [J]. J Shanghai Jiaotong Univ Sci, 2021, 26(5): 577-586.
[13]	. [J]. J Shanghai Jiaotong Univ Sci, 2021, 26(5): 587-597.
[14]	. [J]. J Shanghai Jiaotong Univ Sci, 2021, 26(5): 670-679.
[15]	SHI Lianxing (石连星), WANG Zhiheng (王志恒), LI Xiaoyong (李小勇) . Novel Data Placement Algorithm for Distributed Storage System Based on Fault-Tolerant Domain[J]. J Shanghai Jiaotong Univ Sci, 2021, 26(4): 463-470.

Block Principle Component Analysis with Lp-norm for Robust and Sparse Modelling

Block Principle Component Analysis with Lp-norm for Robust and Sparse Modelling

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献 18

相关文章 15

编辑推荐

Metrics

本文评价