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Sparse factorial code representation using independent component analysis for face recognition

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Abstract

This paper presents a new face recognition method based on Independent Component Analysis (ICA), named Sparse Factorial Code Representation (SFCR). The SFCR employs the architecture II of ICA (ICAII) to achieve sparse facial codes, which seeks for a representation that generates encoding coefficients with the statistically independent property, i.e., factorial coding. In ICAII the coefficients of training samples are ‘natural’ sparse, but coefficients for test samples are not as sparse as that of training samples according to comprehensive experimental results. We believe that the generating process of the latter is contaminated by projection matrixes of the training samples which do not contain any information about the test samples, which makes the coefficients encoding non-consistency. As a result, the small values in the non-sparse encoding coefficients of a test sample, which are caused by noise and usually influence the representation of independent components, will increase the probability of misclassification in the recognition of facial patterns. To ensure the sparsity of the coefficients of test samples and encoding consistency, l1 -norm optimization based sparse constraint technology is employed in SFCR. The SFCR is evaluated on several public available datasets such as AR, ORL, Extended-Yale B, FERET, and LFW databases. The experimental results demonstrate the good performance of our method.

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References

  1. Aharon M, Elad M, Bruckstein A (2006) K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans Signal Process 54(11):4311–4322

    Article  MATH  Google Scholar 

  2. Allen Yang AG, Zhou Z. Fast l-1 minimization algorithms. UC Berkeley. URL: http://www.eecs.berkeley.edu/~yang/software/l1benchmark/

  3. Bartlett MS, Movellan JR, Sejnowski TJ (2002) Face recognition by independent component analysis. IEEE Trans Neural Netw 13(6):1450–1464

    Article  Google Scholar 

  4. Cevikalp H, Triggs B (2010) Face recognition based on image sets. IEEE conference on computer vision and pattern recognition, pp 2567–2573

  5. Chelali FZ, Djeradi A, Djeradi R (2009) Linear discriminant analysis for face recognition. International conference on multimedia computing and systems, pp 1–10

  6. Choi S, Lee O (2000) Factorial Code Representation of Faces for Recognition. In: Lee SW., Bülthoff HH, Poggio T (eds) Biologically Motivated Computer Vision. BMCV 2000. Lecture Notes in Computer Science, vol 1811. Springer, Berlin, Heidelberg

  7. Cover TM, Hart PE (1967) Nearest neighbor pattern classification. IEEE Trans Inf Theory 13(1):21–27

    Article  MATH  Google Scholar 

  8. Dhir CS, Lee S-Y (2011) Discriminant independent component analysis. IEEE Trans Neural Netw 22(6):845–857

    Article  Google Scholar 

  9. Donoho DL (2006) For most large underdetermined systems of linear equations the minimal. Commun Pure Appl Math 59(6):797–829

    Article  MathSciNet  MATH  Google Scholar 

  10. Donoho DL, Elad M (2003) Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization. Proc Natl Acad Sci 100(5):2197–2202

    Article  MathSciNet  MATH  Google Scholar 

  11. Donoho DL, Tsaig Y (2008) Fast solution of l1-norm minimization problems when the solution may be sparse. IEEE Trans Inf Theory 54(11):4789–4812

  12. Draper BA, Baek K, Bartlett MS, Beveridge JR (2003) Recognizing faces with PCA and ICA. Comput Vis Image Underst 91(1):115–137

    Article  Google Scholar 

  13. Ekenel HK, Sankur B (2004) Feature selection in the independent component subspace for face recognition. Pattern Recogn Lett 25(12):1377–1388

    Article  Google Scholar 

  14. Fu S, He H, Hou Z-G (2014) Learning race from face: a survey. IEEE Trans Pattern Anal Mach Intell 36(12):2483–2509

    Article  Google Scholar 

  15. Gao Q, Zhang L, Zhang D (2009) Sequential row–column independent component analysis for face recognition. Neurocomputing 72(4):1152–1159

    Article  Google Scholar 

  16. Ge T, He K, Sun J (2014) Product sparse coding. IEEE conference on computer vision and pattern recognition, pp 939–946

  17. Georghiades AS, Belhumeur PN, Kriegman DJ (2001) From few to many: Illumination cone models for face recognition under variable lighting and pose. IEEE Trans Pattern Anal Mach Intell 23(6):643–660

    Article  Google Scholar 

  18. He J-H (1999) Homotopy perturbation technique. Comput Methods Appl Mech Eng 178(3):257–262

    Article  MathSciNet  MATH  Google Scholar 

  19. He R, Zheng WS, Hu BG (2011) Maximum correntropy criterion for robust face recognition. IEEE Trans Pattern Anal Mach Intell 33(8):1561–1576

    Article  Google Scholar 

  20. He R, Zheng W-S, Tan T, Sun Z (2014) Half-quadratic-based iterative minimization for robust sparse representation. IEEE Trans Pattern Anal Mach Intell 36(2):261–275

    Article  Google Scholar 

  21. Hoyer PO, Hyvärinen A (2000) Independent component analysis applied to feature extraction from colour and stereo images. Netw Comput Neural Syst 11(3):191–210

    Article  MATH  Google Scholar 

  22. Jiang X, Lai J (2015) Sparse and dense hybrid representation via dictionary decomposition for face recognition. IEEE Trans Pattern Anal Mach Intell 37(5):1067–1079

    Article  Google Scholar 

  23. Jiang Z, Lin Z, Davis LS (2013) Label consistent K-SVD: learning a discriminative dictionary for recognition. IEEE Trans Pattern Anal Mach Intell 35(11):2651–2664

    Article  Google Scholar 

  24. Karimi MM, Soltanian-Zadeh H (2012) Face recognition: a sparse representation-based classification using independent component analysis. 2012 sixth international symposium on telecommunications (IST), pp 1170–1174

  25. Kim J, Choi J, Yi J, Turk M (2005) Effective representation using ICA for face recognition robust to local distortion and partial occlusion. IEEE Trans Pattern Anal Mach Intell 27(12):1977–1981

    Article  Google Scholar 

  26. Koldovsky Z, Tichavsky P, Oja E (2006) Efficient variant of algorithm fastica for independent component analysis attaining the cramÉr-rao lower bound. IEEE Trans Neural Netw 17(5):1265–1277

    Article  MATH  Google Scholar 

  27. Koldovský Z, Málek J, Tichavský P, Deville Y, Hosseini S (2008) Extension of EFICA algorithm for blind separation of piecewise stationary non Gaussian sources. IEEE international conference on acoustics, speech and signal processing, pp 1913–1916

  28. Kviatkovsky I, Gabel M, Rivlin E, Shimshoni I (2017) On the equivalence of the LC-KSVD and the D-KSVD algorithms. IEEE Trans Pattern Anal Mach Intell 39(2):411–416

    Article  Google Scholar 

  29. Kwak K-C, Pedrycz W (2007) Face recognition using an enhanced independent component analysis approach. IEEE Trans Neural Netw 18(2):530–541

    Article  Google Scholar 

  30. Lee K-C, Ho J, Kriegman DJ (2005) Acquiring linear subspaces for face recognition under variable lighting. IEEE Trans Pattern Anal Mach Intell 27(5):684–698

    Article  Google Scholar 

  31. Li SZ, Lu X, Hou X, Peng X, Cheng Q (2005) Learning multiview face subspaces and facial pose estimation using independent component analysis. IEEE Trans Image Process 14(6):705–712

    Article  Google Scholar 

  32. Liu C, Wechsler H (1999) Comparative assessment of independent component analysis (ICA) for face recognition. International conference on audio and video based biometric person authentication, pp 886–897

  33. Liu C, Wechsler H (2000) Learning the face space-representation and recognition. Proceedings 15th international conference on pattern recognition, pp 249–256

  34. Liu C, Wechsler H (2003) Independent component analysis of Gabor features for face recognition. IEEE Trans Neural Netw 14(4):919–928

    Article  Google Scholar 

  35. Lu J, Plataniotis K, Venetsanopoulos A (2001) Face recognition using feature optimization and ν-support vector learning. Neural networks for signal processing, proceedings of the 2001 I.E. signal processing society workshop, pp 373–382

  36. Martinez AM (1998) The AR face database. CVC Technical Report, vol. 24

  37. Martiriggiano T, Leo M, D’Orazio T, Distante A (2005) Face recognition by kernel independent component analysis. Innovations in applied artificial intelligence, pp 55–58, Springer

  38. Meng Y, Zhang L, Yang J, Zhang D (2012) Regularized robust coding for face recognition. IEEE Trans Image Process 22(5):1753–1766

    MathSciNet  MATH  Google Scholar 

  39. Mi J-X (2014) A novel algorithm for independent component analysis with reference and methods for its applications. PLoS One 9(5):e93984

    Article  Google Scholar 

  40. Mi J-X, Xu Y (2014) A comparative study and improvement of two ICA using reference signal methods. Neurocomputing 137:157–164

    Article  Google Scholar 

  41. Mi J-X, Yang Y (2012) A comparative study of two independent component analysis using reference signal methods. Emerging intelligent computing technology and applications, pp 93–99, Springer

  42. Naseem I, Togneri R, Bennamoun M (2010) Linear regression for face recognition. IEEE Trans Pattern Anal Mach Intell 32(11):2106–2112

    Article  Google Scholar 

  43. Ortiz EG, Wright A, Shah M (2013) Face recognition in movie trailers via mean sequence sparse representation-based classification. IEEE conference on computer vision and pattern recognition, pp 3531–3538

  44. Perlibakas V (2004) Distance measures for PCA-based face recognition. Pattern Recogn Lett 25(6):711–724

    Article  Google Scholar 

  45. Phillips PJ, Wechsler H, Huang J, Rauss PJ (1998) The FERET database and evaluation procedure for face-recognition algorithms. Image Vis Comput 16(5):295–306

    Article  Google Scholar 

  46. Rubinstein R, Bruckstein AM, Elad M (2010) Dictionaries for sparse representation modeling. Proc IEEE 98(6):1045–1057

    Article  Google Scholar 

  47. Rubinstein R, Zibulevsky M, Elad M (2010) Double sparsity: learning sparse dictionaries for sparse signal approximation. IEEE Trans Signal Process 58(3):1553–1564

    Article  MathSciNet  MATH  Google Scholar 

  48. Sharon Y, Wright J, Ma Y (2007) Computation and relaxation of conditions for equivalence between l1 and l0 minimization. IEEE Trans Inf Theory 5

  49. Simonyan K, Zisserman A (2015) Very deep convolutional networks for large-scale image recognition. ICLR 2015

  50. Sinha P, Balas B, Ostrovsky Y, Russell R (2006) Face recognition by humans: nineteen results all computer vision researchers should know about. Proc IEEE 94(11):1948–1962

    Article  Google Scholar 

  51. Tan H, Zhang X, Guan N, Tao D, Huang X, Luo Z (2004) Two-dimensional euler PCA for face recognition. IEEE transactions on pattern analysis and machine intelligence, pp 548–559

  52. Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc Ser B Methodol 58(1):267–288

    MathSciNet  MATH  Google Scholar 

  53. Turk M, Pentland A (1991) Eigenfaces for recognition. J Cogn Neurosci 3(1):71–86

    Article  Google Scholar 

  54. Wagner A, Wright J, Ganesh A, Zhou Z, Mobahi H, Ma Y (2012) Toward a practical face recognition system: robust alignment and illumination by sparse representation. IEEE Trans Pattern Anal Mach Intell 34(2):372–386

    Article  Google Scholar 

  55. Wang D, Kong S (2014) A classi_cation-oriented dictionary learning model: explicitly learning the particularity and commonality across categories. Pattern Recogn 47(2):885–898

    Article  MATH  Google Scholar 

  56. Wang J, Yang J, Yu K, Lv F, Huang T, Gong Y (2010) Locality-constrained linear coding for image classification. IEEE conference on computer vision and pattern recognition, pp 3360–3367

  57. Wright J, Yang AY, Ganesh A, Sastry SS, Ma Y (2009) Robust face recognition via sparse representation. IEEE Trans Pattern Anal Mach Intell 31(2):210–227

    Article  Google Scholar 

  58. Xu Y, Zhang D, Yang J, Yang J-Y (2011) A two-phase test sample sparse representation method for use with face recognition. IEEE Trans Circuits Syst Video Technol 21(9):1255–1262

    Article  MathSciNet  Google Scholar 

  59. Yang J, Zhang D, Frangi AF, Yang J-Y (2004) Two-dimensional PCA: a new approach to appearance-based face representation and recognition. IEEE Trans Pattern Anal Mach Intell 26(1):131–137

    Article  Google Scholar 

  60. Yang J, Gao X, Zhang D, Yang J-Y (2005) Kernel ICA: an alternative formulation and its application to face recognition. Pattern Recogn 38(10):1784–1787

    Article  MATH  Google Scholar 

  61. Yang J, Zhang D, Yang J-Y (2005) Is ICA significantly better than PCA for face recognition?. Tenth IEEE international conference on computer vision, pp 198–203

  62. Yang M, Zhang L, Yang J, Zhang D (2010) Metaface learning for sparse representation based face recognition. 17th IEEE international conference on image processing, pp 1601–1604

  63. Yang AY, Sastry SS, Ganesh A, Ma Y (2010) Fast ℓ 1-minimization algorithms and an application in robust face recognition: a review. IEEE international conference on image processing, pp 1849–1852

  64. Yuen PC, Lai J-H (2002) Face representation using independent component analysis. Pattern Recogn 35(6):1247–1257

    Article  MATH  Google Scholar 

  65. Zhang Q, Li B (2010) Discriminative K-SVD for dictionary learning in face recognition. IEEE conference on computer vision and pattern recognition, pp 2691–2698

  66. Zhang L, Yang M, Feng X (2011) Sparse representation or collaborative representation: which helps face recognition?. IEEE international conference on computer vision, pp. 471–478

  67. Zhang L, Yang M, Feng X, Ma Y, Zhang D (2012) Collaborative representation based classification for face recognition. arXiv preprint arXiv:1204.2358

  68. Zhao P, Yu B (2006) On model selection consistency of Lasso. J Mach Learn Res 7:2541–2563

    MathSciNet  MATH  Google Scholar 

  69. Zhuang L, Yang A, Zhou Z, Sastry S, Ma Y. Single-sample face recognition with image corruption and misalignment via sparse illumination transfer. In: 2013 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Portland, OR, USA, 23–28 June 2013

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Funding

This study was funded by the National Nature Science Foundation of China (Grant Nos. 61601070 and 61403053) and Chongqing Education Committee (Grant Nos. KJ1500402 and KJ1500417).

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Authors and Affiliations

  1. Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, China

    Chao Li & Jian-Xun Mi

  2. Key Laboratory of Machine Intelligence and Advanced Computing (Sun Yat-sen University), Ministry of Education, Guangzhou, China

    Jian-Xun Mi

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  1. Chao Li
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Correspondence to Jian-Xun Mi.

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Li, C., Mi, JX. Sparse factorial code representation using independent component analysis for face recognition. Multimed Tools Appl 77, 21371–21392 (2018). https://doi.org/10.1007/s11042-017-5542-8

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  • DOI: https://doi.org/10.1007/s11042-017-5542-8

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