Skip to main content
Erschienen in: Pattern Analysis and Applications 3/2018

07.02.2017 | Theoretical Advances

Matrix-based subspace analysis with the general norm for image feature extraction

verfasst von: Zhizheng Liang

Erschienen in: Pattern Analysis and Applications | Ausgabe 3/2018

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Classical matrix-based subspace analysis tries to exploit the structured information (rows or columns) of images for extracting image features. However, it is not robust in dealing with contaminated data. In this paper, novel models for matrix-based subspace analysis with robust objective functions and general norms are developed to address this problem. In the proposed models, general vector norms are employed to control the sparsity of projection vectors and the alternative optimization technique is utilized to solve the proposed models due to the characteristics of the models. Nonnegative constraints are also imposed on projection vectors to encourage their sparsity in the proposed models. A deflation scheme for image data is devised to achieve arbitrary pairs of projection vectors. A series of experiments on some face data sets are conducted to demonstrate that the proposed models are more effective than previous methods in handling contaminated data.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

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!

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!

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!

Literatur
1.
Zurück zum Zitat Averbuch A, Rabin N, Schclar A et al (2012) Dimensionality reduction for detection of moving vehicles. Pattern Anal Appl 15(1):19–27MathSciNetCrossRef Averbuch A, Rabin N, Schclar A et al (2012) Dimensionality reduction for detection of moving vehicles. Pattern Anal Appl 15(1):19–27MathSciNetCrossRef
2.
Zurück zum Zitat Koren Y, Carmel L (2004) Robust linear dimensionality reduction. IEEE Trans Vis Comput Graph 10(4):459–470CrossRef Koren Y, Carmel L (2004) Robust linear dimensionality reduction. IEEE Trans Vis Comput Graph 10(4):459–470CrossRef
3.
Zurück zum Zitat 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 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
4.
Zurück zum Zitat Martinez AM, Kak AC (2001) PCA versus LDA. IEEE Trans Pattern Anal Mach Intell 23(2):228–233CrossRef Martinez AM, Kak AC (2001) PCA versus LDA. IEEE Trans Pattern Anal Mach Intell 23(2):228–233CrossRef
5.
Zurück zum Zitat Liu K, Cheng YQ, Yang JY (1993) Algebraic feature extraction for image recognition based on an optimal discriminant criterion. Pattern Recogn 26(6):903–911CrossRef Liu K, Cheng YQ, Yang JY (1993) Algebraic feature extraction for image recognition based on an optimal discriminant criterion. Pattern Recogn 26(6):903–911CrossRef
6.
Zurück zum Zitat Yang J, Zhang D, Frangi AF, Yang JY (2004) Two-dimensional PCA: a new approach to appearance-based face representation and recognition. IEEE Trans PAMI 26(1):131–137CrossRef Yang J, Zhang D, Frangi AF, Yang JY (2004) Two-dimensional PCA: a new approach to appearance-based face representation and recognition. IEEE Trans PAMI 26(1):131–137CrossRef
7.
Zurück zum Zitat Ye J (2005) Generalized low rank approximations of matrices. Mach Learn 61(1–3):167–191CrossRefMATH Ye J (2005) Generalized low rank approximations of matrices. Mach Learn 61(1–3):167–191CrossRefMATH
8.
Zurück zum Zitat Liang Z, Zhang D, Shi P (2005) The theoretical analysis of GLRAM and its applications. Pattern Recogn 40(3):1032–1041CrossRefMATH Liang Z, Zhang D, Shi P (2005) The theoretical analysis of GLRAM and its applications. Pattern Recogn 40(3):1032–1041CrossRefMATH
9.
Zurück zum Zitat Ding C, Ye J (2005) Two-dimensional singular value decomposition for 2d maps and images. In: SIAM int’l Conference data ming, pp 32–43 Ding C, Ye J (2005) Two-dimensional singular value decomposition for 2d maps and images. In: SIAM int’l Conference data ming, pp 32–43
10.
Zurück zum Zitat Tao D, Li X, Wu Maybank S (2007) General tensor discriminant analysis and gabor features for gait recognition. IEEE Trans Pattern Anal Mach Intell 29(10):1700–1715CrossRef Tao D, Li X, Wu Maybank S (2007) General tensor discriminant analysis and gabor features for gait recognition. IEEE Trans Pattern Anal Mach Intell 29(10):1700–1715CrossRef
11.
Zurück zum Zitat Xu S, Yan SC, Zhang L, Zhang HJ, Liu ZK, Shum HY (2005) Concurrent subspace analysis. In: Proceedings of CVPR, pp 203–208 Xu S, Yan SC, Zhang L, Zhang HJ, Liu ZK, Shum HY (2005) Concurrent subspace analysis. In: Proceedings of CVPR, pp 203–208
12.
Zurück zum Zitat Ye J, Janardan R, Li Q (2004) Two-dimensional linear discriminant analysis. In: Advances in neural information processing systems, pp 1–8 Ye J, Janardan R, Li Q (2004) Two-dimensional linear discriminant analysis. In: Advances in neural information processing systems, pp 1–8
13.
Zurück zum Zitat Baccini A, Besse P, Falguerolles AD (1996) A L1-norm PCA and a heuristic approach. Ord Symb Data Anal 1(1):359–368CrossRefMATH Baccini A, Besse P, Falguerolles AD (1996) A L1-norm PCA and a heuristic approach. Ord Symb Data Anal 1(1):359–368CrossRefMATH
14.
Zurück zum Zitat Ding C, Zhou D, He X, Zha H (2006) R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization. In: Proceedings of 23rd int’l conference machine learning, June, pp 231–238 Ding C, Zhou D, He X, Zha H (2006) R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization. In: Proceedings of 23rd int’l conference machine learning, June, pp 231–238
15.
Zurück zum Zitat Kwak N (2008) Principal component analysis based on L1-norm maximization. IEEE Trans on Pattern Anal Mach Intell 30(9):1672–1680CrossRef Kwak N (2008) Principal component analysis based on L1-norm maximization. IEEE Trans on Pattern Anal Mach Intell 30(9):1672–1680CrossRef
16.
Zurück zum Zitat De la Torre Fernando J, Black Michael (2001) Robust principal component analysis for computer vision. In: Proceedings of ICCV, pp 362–369 De la Torre Fernando J, Black Michael (2001) Robust principal component analysis for computer vision. In: Proceedings of ICCV, pp 362–369
17.
Zurück zum Zitat Liang Z, Li Y (2010) A regularization framework for robust dimensionality reduction with applications to image reconstruction and feature extraction. Pattern Recogn 43(4):1269–1281MathSciNetCrossRefMATH Liang Z, Li Y (2010) A regularization framework for robust dimensionality reduction with applications to image reconstruction and feature extraction. Pattern Recogn 43(4):1269–1281MathSciNetCrossRefMATH
18.
Zurück zum Zitat Li X, Pang Y, Yuan Y (2009) L1-norm based 2DPCA. IEEE Trans Syst Man Cybern Part B 40(2):1170–1175 Li X, Pang Y, Yuan Y (2009) L1-norm based 2DPCA. IEEE Trans Syst Man Cybern Part B 40(2):1170–1175
19.
Zurück zum Zitat Pang Y, Li X, Yuan Y (2010) Robust tensor analysis with L1 norm. IEEE Trans Circuits Syst Video Technol 20(2):172–178CrossRef Pang Y, Li X, Yuan Y (2010) Robust tensor analysis with L1 norm. IEEE Trans Circuits Syst Video Technol 20(2):172–178CrossRef
20.
Zurück zum Zitat Huang H, Ding C (2008) Robust tensor factorization using R1 norm. In: Proceedings of computer vision and pattern recognition, pp 1–8 Huang H, Ding C (2008) Robust tensor factorization using R1 norm. In: Proceedings of computer vision and pattern recognition, pp 1–8
21.
Zurück zum Zitat Liwicki S, Tzimiropoulos G, Zafeiriou S, Pantic M (2013) Euler principal component analysis. Int J Comput Vis 101(3):498–518MathSciNetCrossRefMATH Liwicki S, Tzimiropoulos G, Zafeiriou S, Pantic M (2013) Euler principal component analysis. Int J Comput Vis 101(3):498–518MathSciNetCrossRefMATH
22.
Zurück zum Zitat Zhang T,Ghanem B, Liu S, Xu C, Ahuja N (2013) Low-rank sparse coding for image classification. In: IEEE international conference on computer vision, pp 281–288 Zhang T,Ghanem B, Liu S, Xu C, Ahuja N (2013) Low-rank sparse coding for image classification. In: IEEE international conference on computer vision, pp 281–288
23.
Zurück zum Zitat Sprechmann P, Bronstein AM, Sapiro G (2015) Learning efficient sparse and low rank models. IEEE Trans Pattern Anal Mach Intell 37(9):1821–1833CrossRef Sprechmann P, Bronstein AM, Sapiro G (2015) Learning efficient sparse and low rank models. IEEE Trans Pattern Anal Mach Intell 37(9):1821–1833CrossRef
24.
Zurück zum Zitat Dimitri B (1999) Nonlinear programming, 22nd edn. Athena Scientific, BelmontMATH Dimitri B (1999) Nonlinear programming, 22nd edn. Athena Scientific, BelmontMATH
25.
Zurück zum Zitat Grippo L, Sciandrone M (2000) On the convergence of the block nonlinear Gauss-Seidel method under convex constraints. Oper Res Lett 26:127–136MathSciNetCrossRefMATH Grippo L, Sciandrone M (2000) On the convergence of the block nonlinear Gauss-Seidel method under convex constraints. Oper Res Lett 26:127–136MathSciNetCrossRefMATH
26.
Zurück zum Zitat Liang ZZ, Xia S, Zhou Y, Zhang L, Li Y (2013) Feature extraction based on Lp norm generalized principal component analysis. Pattern Recogn Lett 34(9):1037–1045CrossRef Liang ZZ, Xia S, Zhou Y, Zhang L, Li Y (2013) Feature extraction based on Lp norm generalized principal component analysis. Pattern Recogn Lett 34(9):1037–1045CrossRef
27.
Zurück zum Zitat Razaviyayn M, Hong M, Luo ZQ (2013) A unified convergence analysis of block successive minimization methods for nonsmooth optimization. SIAM J Optim 23(2):1126–1153MathSciNetCrossRefMATH Razaviyayn M, Hong M, Luo ZQ (2013) A unified convergence analysis of block successive minimization methods for nonsmooth optimization. SIAM J Optim 23(2):1126–1153MathSciNetCrossRefMATH
28.
Zurück zum Zitat Journee M, Nesterov Y, Richtarik P, Sepulchre R (2010) Generalized power method for sparse principal component analysis. J Mach Learn Res 11:1055MathSciNetMATH Journee M, Nesterov Y, Richtarik P, Sepulchre R (2010) Generalized power method for sparse principal component analysis. J Mach Learn Res 11:1055MathSciNetMATH
29.
Zurück zum Zitat Bradely PS, Mangasarian OL (1998) Feature selection via concave minimization and support vector machine learning. In: Proceedings of the fifteenth international conference, pp 82–90 Bradely PS, Mangasarian OL (1998) Feature selection via concave minimization and support vector machine learning. In: Proceedings of the fifteenth international conference, pp 82–90
30.
Zurück zum Zitat Judice J, Faustino A (1992) Solution of the concave linear complementary problem. Recent advances in global optimization, pp 76–101 Judice J, Faustino A (1992) Solution of the concave linear complementary problem. Recent advances in global optimization, pp 76–101
31.
32.
Zurück zum Zitat Yang WH (1991) On generalized holder inequality. Nonlinear Anal Theory Appl 16(5):489–498CrossRefMATH Yang WH (1991) On generalized holder inequality. Nonlinear Anal Theory Appl 16(5):489–498CrossRefMATH
33.
Zurück zum Zitat Golub G, Loan CV (1996) Matrix computations. Johns Hopkins, BaltimoreMATH Golub G, Loan CV (1996) Matrix computations. Johns Hopkins, BaltimoreMATH
35.
Zurück zum Zitat Gao Q, Huang Y, Gao X et al (2015) A novel semi-supervised learning for face recognition. Neurocomputing 152:69–76CrossRef Gao Q, Huang Y, Gao X et al (2015) A novel semi-supervised learning for face recognition. Neurocomputing 152:69–76CrossRef
36.
Zurück zum Zitat Martines AM, Benavente R (1998) The AR face database, Technical Report, CVC Martines AM, Benavente R (1998) The AR face database, Technical Report, CVC
Metadaten
Titel
Matrix-based subspace analysis with the general norm for image feature extraction
verfasst von
Zhizheng Liang
Publikationsdatum
07.02.2017
Verlag
Springer London
Erschienen in
Pattern Analysis and Applications / Ausgabe 3/2018
Print ISSN: 1433-7541
Elektronische ISSN: 1433-755X
DOI
https://doi.org/10.1007/s10044-017-0603-1

Weitere Artikel der Ausgabe 3/2018

Pattern Analysis and Applications 3/2018 Zur Ausgabe