Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
International Journal of Machine Learning and Cybernetics
Published in: International Journal of Machine Learning and Cybernetics 3/2020

23-08-2019 | Original Article

Flexible robust principal component analysis

Authors: Zinan He, Jigang Wu, Na Han

Published in: International Journal of Machine Learning and Cybernetics | Issue 3/2020

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The error correction problem is a very important topic in machine learning. However, existing methods only focus on data recovery and ignore data compact representation. In this paper, we propose a flexible robust principal component analysis (FRPCA) method in which two different matrices are used to perform error correction and the data compact representation can be obtained by using one of matrices. Moreover, FRPCA selects the most relevant features to guarantee that the recovered data can faithfully preserve the original data semantics. The learning is done by solving a nuclear-norm regularized minimization problem, which is convex and can be solved in polynomial time. Experiments were conducted on image sequences containing targets of interest in a variety of environments, e.g., offices, campuses. We also compare our method with existing method in recovering the face images from corruptions. Experimental results show that the proposed method achieves better performances and it is more practical than the existing approaches.
previous article Feature selection based on rough set approach, wrapper approach, and binary whale optimization algorithm
next article Unsupervised learning of monocular depth and ego-motion with space–temporal-centroid loss

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
Show more products
Literature
1.
Costeira JP, Kanade T (1998) A multibody factorization method for independently moving objects. Int J Comput Vis 29(3):159–179CrossRef
2.
Belhumeur P, Hespanha J, Kriegman D (2002) Eigenfaces versus fisherfaces: recognition using class specific linear projection. IEEE Trans Pattern Anal Mach Intell 19(7):711–720CrossRef
3.
De la Torre F, Black MJ (2001) Robust principal component analysis for computer vision. In: Proceedings 8th IEEE international conference on computer vision, ICCV 2001. IEEE, 2001, 1, Barcelona, Spain, pp 362–369
4.
Eldar YC, Mishali M (2009) Robust recovery of signals from a structured union of subspaces. IEEE Trans Inf Theory 55(11):5302–5316MathSciNetCrossRef
5.
Elhamifar E, Vidal R (2009) Sparse subspace clustering. In: Proceedings of the IEEE conference on computer vision and pattern recoginition, vol 2, pp 2790–2797
6.
Liu G, Lin Z, Yu Y (2010) Robust subspace segmentation by low-rank representation. In: Proceedings of the international conference on machine learning, pp 1–8
7.
Li S, Fu Y (2014) Robust subspace discovery through supervised low-rank constraints. In: Proceedings of the SIAM international conference on data mining, pp 163–171
8.
Guyon I, Elisseeff A (2003) An introduction to variable and feature selection. J Mach Learn Res 3:1157–1182MATH
9.
Kim E, Lee M, Oh S (2015) Elastic-net regularization of singular values for robust subspace learning. In: Proceedings of the IEEE conference of computer vision and pattern recognition, pp 915–923
10.
Wen J et al (2019) Robust sparse linear discriminant analysis. IEEE Trans Circ Syst Video Technol 29(2):390–403CrossRef
11.
12.
Fei L et al (2017) Low rank representation with adaptive distance penalty for semi-supervised subspace classification. Pattern Recogn 67(2017):252–262CrossRef
13.
Fang X, Han N, Jigang W, Xu Y, Yang J, Wong WK, Li X (2018) Approximate low-rank projection learning for feature extraction. IEEE Trans Neural Netw Learn Syst 29(11):5228–5241MathSciNetCrossRef
14.
Wen J, Han N, Fang X, Fei L, Yan K, Zhan S (2019) Low-rank preserving projection via graph regularized reconstruction. IEEE Trans Cybern 49(4):1279–1291CrossRef
15.
Pearson K (1901) On lines and planes of closest fit to systems of points in space. Philos Magn 2(6):559–572CrossRef
16.
Belhumeur PN, Hespanha JP, Kriegman DJ (1997) Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans Pattern Anal Mach Intell 19(7):711–720CrossRef
17.
He X, Niyogi P (2004) Locality preserving projections. In: Advances in neural information processing systems pp 153–160
18.
He X et al (2005) Neighborhood preserving embedding. Computer Vision, 2005. ICCV 2005. In: 10th IEEE international conference on Vol 2, IEEE
19.
Yan S et al (2007) Graph embedding and extensions: a general framework for dimensionality reduction. IEEE Trans Pattern Anal Mach Intell 29(1):40–51CrossRef
20.
21.
Lai Z, Yong X, Yang J, Shen L, Zhang D (2017) Rotational invariant dimensionality reduction algorithms. IEEE Trans Cybern 47(11):3733–3746CrossRef
22.
Lai Z, Yong X, Yang J, Tang J, Zhang D (2013) Sparse tensor discriminant analysis. IEEE Trans Image Process 22(10):3904–3915MathSciNetCrossRef
23.
Cai D, He X, Han J (2007) Spectral regression: a unified approach for sparse subspace learning. In: 7th IEEE international conference on data mining (ICDM 2007). IEEE
24.
25.
26.
Devlin SJ, Gnanadesikan R, Kettenring JR (1981) Robust estimation of dispersion matrices and principal components. J Am Stat Assoc 76(374):354–362CrossRef
27.
Li G, Chen Z (1985) Projection-pursuit approach to robust dispersion matrices and principal components: primary theory and Monte Carlo. J Am Stat Assoc 80(391):759–766CrossRef
28.
Torre F, Black M (2001) Robust principal component analysis for computer vision. In: Proceedings of the international conference computer vision, Vancouver, BC, pp 362–369
29.
Wright J, Ganesh A, Rao S, Peng Y, Ma Y (2009) Robust principal component analysis: exact recovery of corrupted low-rank matrices via convex optimization. In: Proceedings of neural information processing system, pp 1–9
30.
Xu H, Caramanis C, Sanghavi S (2010) Robust PCA via outlier pursuit. In: Proceedings of advances in neural information processing system, pp 1–30
31.
Ma Y, Derksen H, Hong W, Wright J (2007) Segmentation of multivariate mixed data via lossy data coding and compression. IEEE Trans Pattern Anal Mach Intell 29(9):1546–1562CrossRef
32.
33.
Chung FRK (1997) Spectral graph theory. AMS, Providence, RIMATH
34.
Donoho DL (2006) For most large underdetermined systems of equations, the minimal \(\ell ^{1}\)-norm near-solution approximates the sparsest nearsolution. Commun Pure Appl Math 59(7):907–934CrossRef
35.
Lin Z, Chen M, Wu L, Ma Y (2009) The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices. Department of Electrical and Computer Engineering, UIUC, Urbana, Technical Report, UILU-ENG-09-2215
36.
Cai X, Ding C, Nie F, Huang H (2013) The equivalent of low-rank linear regressions and linear discriminant analysis based regressions. In: Proceedings of the 19th ACM SIGKDD conference knowledge discovery data mining, pp 1124–1132
37.
Fang X, Xu Y, Li X, Lai Z, Wong WK (2016) Robust semi-supervised subspace clustering via non-negative low-rank representation. IEEE Trans Cybern 46(8):1828–1838CrossRef
38.
Liu G, Lin Z, Yan S, Sun J, Yu Y, Ma Y (2013) Robust recovery of subspace structures by low-rank representation. IEEE Trans Pattern Anal Mach Intell 35(1):171–184CrossRef
Metadata
Title
Flexible robust principal component analysis
Authors
Zinan He
Jigang Wu
Na Han
Publication date
23-08-2019
Publisher
Springer Berlin Heidelberg
Published in
International Journal of Machine Learning and Cybernetics / Issue 3/2020
Print ISSN: 1868-8071
Electronic ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-019-00999-2

Other articles of this Issue 3/2020

International Journal of Machine Learning and Cybernetics 3/2020 Go to the issue

Original Article

Bibliometric analysis of support vector machines research trend: a case study in China

Original Article

Multi-view local linear KNN classification: theoretical and experimental studies on image classification

Original Article

An efficient clustering algorithm based on the k-nearest neighbors with an indexing ratio

Original Article

Clustering data with the presence of attribute noise: a study of noise completely at random and ensemble of multiple k-means clusterings

Original Article

An active multi-class classification using privileged information and belief function

Original Article

Granular matrix-based knowledge reductions of formal fuzzy contexts