Advertisement

A regularized approach for supervised multi-view multi-manifold learning from unlabeled data

  • Faraein Aeini
  • Amir Masoud Eftekhari MoghadamEmail author
  • Fariborz Mahmoudi
Article
  • 18 Downloads

Abstract

In this paper, we combined two steps in a new multi-view multi-manifold learning algorithm that are essential for recognition tasks in the absence of class label information; first, we emphasize the first step of graph-based multi-view multi-manifold learning methods, i.e., select class-consistent neighbors from all available views. In multi-manifold space, the ideal neighborhood set is unidentified, and selection of a proper neighborhood set is not an easy task, especially if manifolds have some intersections. We describe each class of objects with continuous varying of pose angle as a relatively independent object-manifold. To find the object-manifolds, we utilize the transitivity of the similarity in the objects and use the TV-regularization to describe each object in a weighted sum of its class-consistent neighbors under different views. The proposed method aims to make a distinction between some objects with the same class and some objects with different classes that have similar views. The proposed method can be efficiently solved by an ADMM method. Second, we propose a regularized approach for supervised dimension reduction via discovering the discriminating information hidden in the data structure. Neighborhood selection and recognition accuracy experiments on COIL-20, CAS-PEAL, FEI, and ORL multi-view datasets have shown the excellent performance of our novel approach.

Keywords

Multi-view multi-manifold learning Supervised manifold learning Unlabeled data Neighborhood graph construction Object recognition Out-of-sample extension problem 

Notes

References

  1. 1.
    Suliman A, Omarov BS (2018) Applying Bayesian Regularization for Acceleration of Levenberg-Marquardt based Neural Network Training. International Journal of Interactive Multimedia and Artificial Intelligence 5(1):68–72CrossRefGoogle Scholar
  2. 2.
    Magdin M, Prikler F (2018) Real-Time Facial Expression Recognition Using Webcam and SDK Affectiva. International Journal of Interactive Multimedia and Artificial Intelligence 5(1):7–15CrossRefGoogle Scholar
  3. 3.
    Zhang Y, Ye D, Liu Y (2018) Robust locally linear embedding algorithm for machinery fault diagnosis. Neurocomputing 273(17):323–332CrossRefGoogle Scholar
  4. 4.
    Ren S et al (2018) An iterative paradigm of joint feature extraction and labeling for semi-supervised discriminant analysis. Neurocomputing 273(17):466–480CrossRefGoogle Scholar
  5. 5.
    Hu MW, Sun Z, Zhao S (2018) Kernel collaboration representation-based manifold regularized model for unconstrained face recognition. SIViP 12(5):925–932CrossRefGoogle Scholar
  6. 6.
    Yang M et al (2017) Joint regularized nearest points for image set based face recognition. Image Vis Comput 58:47–60CrossRefGoogle Scholar
  7. 7.
    Zhang Z, Mao J (2016) Jointly sparse neighborhood graph for multi-view manifold clustering. Neurocomputing 216(5):28–38CrossRefGoogle Scholar
  8. 8.
    Lai Z, Wan M, Jin Z (2011) Locality preserving embedding for face and handwriting digital recognition. Neural Comput & Applic 20:565–573CrossRefGoogle Scholar
  9. 9.
    Yan H et al (2014) Multi-feature multi-manifold learning for single-sample face recognition. Neurocomputing 143(2):134–143CrossRefGoogle Scholar
  10. 10.
    Chen W-J et al (2014) Manifold proximal support vector machine for semi-supervised classification. Appl Intell 40(4):623–638CrossRefGoogle Scholar
  11. 11.
    Belkin M, Niyogi P (2000) Laplacian eigenmaps for dimensional reduction and data representation. Neural Comput 15:1373–1396CrossRefzbMATHGoogle Scholar
  12. 12.
    Zhang Z, Zha H (2002) Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment. SIAM Journal of Scientific Computing 26(1):313–338CrossRefzbMATHGoogle Scholar
  13. 13.
    Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290:2323–2326CrossRefGoogle Scholar
  14. 14.
    Tenenbaum J, Silva V, Langford J (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5500):2319–2323CrossRefGoogle Scholar
  15. 15.
    Vlachos M, et al (2002) Non-linear dimensionality reduction techniques for classification and visualization. In: Proceedings of ACM Int. Conf. Knowl. Discovery Data Mining. ACM New York pp. 645–651Google Scholar
  16. 16.
    Belkin M, Niyogi P (2002) Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Neural Information Processing Systems, pp. 585–591Google Scholar
  17. 17.
    Hettiarachchi R, Peters JF (2015) Multi-manifold LLE learning in pattern recognition. Pattern Recogn 48(9):2947–2960CrossRefzbMATHGoogle Scholar
  18. 18.
    Lee C-S, Elgammal A, Torki M (2016) Learning representations from multiple manifolds. Pattern Recogn 50:74–87CrossRefGoogle Scholar
  19. 19.
    Fan M et al (2016) Efficient isometric multi-manifold learning based on the self-organizing method. Inf Sci 345:325–339CrossRefGoogle Scholar
  20. 20.
    Yang B, Xiang M, Zhang Y (2016) Multi-manifold discriminant Isomap for visualization and classification. Pattern Recogn 55:215–230CrossRefGoogle Scholar
  21. 21.
    Li B, Li J, Zhang X-P (2015) Nonparametric discriminant multi-manifold learning for dimensionality reduction. Neurocomputing 152(25):121–126CrossRefGoogle Scholar
  22. 22.
    Li J et al (2016) Multi-manifold Sparse Graph Embedding for Multi-modal Image Classification. Neurocomputing 173(3):501–510CrossRefGoogle Scholar
  23. 23.
    Sun S (2013) A survey of multi-view machine learning. Neural Comput & Applic 23:2031–2038CrossRefGoogle Scholar
  24. 24.
    Li Y et al (2016) Manifold regularized multi-view feature selection for social image annotation. Neurocomputing 204(5):135–141CrossRefGoogle Scholar
  25. 25.
    Nane SA, Nayar SK, Murase H (1996) Columbia object image library (COIL-20). Department of Computer Science: Columbia UniversityGoogle Scholar
  26. 26.
    Gao W, Cao B, Shan S (2008) The CAS-PEAL Large-Scale Chinese Face Database and Baseline Evaluations. IEEE Transactions on Systems, Man, and Cybernetics—Part A: Systems and Humans 38(1)Google Scholar
  27. 27.
    Gao W et al (2008) The CAS-PEAL Large-Scale Chinese Face Database and Baseline Evaluations. IEEE Transactions on Systems, Man, and Cybernetics—Part A: Systems And Humans 38(1):149–161CrossRefGoogle Scholar
  28. 28.
    Wang L, Zhang Y, Feng J (2005) On the Euclidean distance of images. IEEE Trans Pattern Anal Mach Intell 27(8):1334–1339CrossRefGoogle Scholar
  29. 29.
    Geng X, Zhan DC, Zhou ZH (2005) Supervised Nonlinear Dimensionality Reduction for Visualization and Classification. IEEE Transactions On Systems, Man, And Cybernetics—Part B: Cybernetics 35(6):1098–1107CrossRefGoogle Scholar
  30. 30.
    Raducanu B, Dornaika F (2012) A supervised non-linear dimensionality reduction approach for manifold learning. Pattern Recogn 45:2432–2444CrossRefzbMATHGoogle Scholar
  31. 31.
    Aeini F, Eftekhari Moghadam AM, Mahmoudi F (2014) Non linear dimensional reduction method based on supervised neighborhood graph. In: 7th International Symposium on Telecommunications (IST'2014). IEEE: Tehran. p. 35–40Google Scholar
  32. 32.
    Ridder DD, et al (2003) Supervised locally linear embedding. In: Artificial Neural Networks and Neural Information Processing-ICANN/ICONIP 2003. 2003, Springer. p. 333–341Google Scholar
  33. 33.
    Zhang Z, Chow TWS, Zhao M (2013) M-Isomap: Orthogonal Constrained Marginal Isomap for Nonlinear Dimensionality Reduction. IEEE Transactions on Cybernetics 43(1):180–191CrossRefGoogle Scholar
  34. 34.
    Aeini F, Eftekhari Moghadam AM, Mahmoud F (2018) Supervised hierarchical neighborhood graph construction for manifold learning. SIViP 12(4):799–807CrossRefGoogle Scholar
  35. 35.
    He X, Niyogi P (2004) Locality preserving projections. In: NIPS'03 Proceedings of the 16th International Conference on Neural Information Processing Systems. Whistler, British Columbia, Canada p. 153–160Google Scholar
  36. 36.
    Kokiopoulou E, Saad Y (2007) Orthogonal neighborhood preserving projections: A projection-based dimensionality reduction technique. IEEE Trans Pattern Anal Mach Intell 29(12):2143–2156CrossRefGoogle Scholar
  37. 37.
    Cheng J et al (2005) Supervised kernel locality-preserving projections for face recognition. Neurocomputing 67:443–449CrossRefGoogle Scholar
  38. 38.
    Fa X, et al (2011) Enhanced supervised locality preserving projections for face recognition, in International Conference on Machine Learning and CyberneticsGoogle Scholar
  39. 39.
    Fan M, et al (2012) Isometric multi-manifold learning for feature extraction. In: Proceedings of the Twelfth IEEE International Conference on Data Mining (ICDM). p. 241–250Google Scholar
  40. 40.
    Lu J, Tan Y-P, Wang G (2013) Discriminative Multimanifold Analysis for Face Recognition from a Single Training Sample per Person. IEEE Trans Pattern Anal Mach Intell 35(1):39–51CrossRefGoogle Scholar
  41. 41.
    Liu J, Li B, Zhang W-S (2012) Feature extraction using maximum variance sparse mapping. Neural Comput & Applic 21:1827–1833CrossRefGoogle Scholar
  42. 42.
    Feng P, Bresler Y (1996) Spectrum-blind minimum-rate sampling and reconstruction of multi-band signals. ICASSP3:1688–1691Google Scholar
  43. 43.
    Obozinski G, Taskar B, Jordan M (2010) Support union recovery in high-dimensional multi variate regression. Stat Comput 20(2):231–252MathSciNetCrossRefGoogle Scholar
  44. 44.
    Fornasier M, Pitolli F (2008) Adaptive iterative thresholding algorithms for magnetoence phalography (MEG). Comput Appl Math 211:386–395CrossRefzbMATHGoogle Scholar
  45. 45.
    Nie F et al (2010) Efficient and robust feature selection via joint ℓ2,1-norms minimization. Adv Neural Inf Proces Syst 2:1813–1821Google Scholar
  46. 46.
    Maaten LJPVD, Postma EO, Herik HJVD (2009) Dimensionality Reduction: A Comparative Review. Mach Learn Res 10(1–41):66–71Google Scholar
  47. 47.
    Aeini F, Eftekhari Moghadam AM, Mahmoudi F (2018) A regularized approach for unsupervisedmulti-viewmulti-manifold learning. Signal, Image and Video Processing 1–9Google Scholar
  48. 48.
    Xu Y et al (2010) LPP solution schemes for use with face recognition. Pattern Recogn 43:4165–4176CrossRefzbMATHGoogle Scholar
  49. 49.
    Evgeniou T et al (2002) Regularization and statistical learning theory for data analysis. Computational Statistics & Data Analysis 38(4):421–432MathSciNetCrossRefzbMATHGoogle Scholar
  50. 50.
    Belkin M, Niyogi P, Sindhwani V (2006) Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples. J Mach Learn Res 7:2399–2434MathSciNetzbMATHGoogle Scholar
  51. 51.
    Schölkopf B, Herbrich R, Smola AJ (2001) A Generalized Representer Theorem. COLT 2001: Computational Learning Theory, p. 416–426Google Scholar
  52. 52.
    Thomaz CE, Giraldi GA (2010) A new ranking method for Principal Components Analysis and its application to face image analysis. Image Vis Comput 28(6):902–913CrossRefGoogle Scholar
  53. 53.
    AT&T Laboratories Cambridge (2002) The ORL database of faces. "http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html. (Online;accessed 23.12.2014). Cambridge University Computer Laboratory
  54. 54.
    Tran L et al (2015) Adaptive graph construction for Isomap manifold learning. Article (PDF Available). Proceedings of SPIE - The International Society for Optical Engineering 1:1–7Google Scholar
  55. 55.
    Örnek C, Vural E (2019) Nonlinear supervised dimensionality reduction via smooth regular embeddings. Pattern Recogn 87:55–66CrossRefGoogle Scholar
  56. 56.
    Yan Y et al (2018) Face recognition algorithm using extended vector quantization histogram features. PLoS One 13(1)Google Scholar
  57. 57.
    Zhang Z, Song G, Wu J (2014) A Novel Two-Stage Illumination Estimation Framework for Expression Recognition. Sci World J 2014:1–12Google Scholar
  58. 58.
    Tsai Y-H et al (2018) Robust in-plane and out-of-plane face detection algorithm using frontal face detector and symmetry extension. Image Vis Comput 78:26–41CrossRefGoogle Scholar
  59. 59.
    Abhishree TM et al (2015) Face Recognition Using Gabor Filter Based Feature Extraction with Anisotropic Diffusion as a Pre-processing Technique. Procedia Computer Science 45:312–321CrossRefGoogle Scholar
  60. 60.
    Raducanu B, Dornaika F (2014) Embedding new observations via sparse-coding for non-linear manifold learning. Pattern Recogn 47(1)Google Scholar
  61. 61.
    Samaria F, Harter A (1994) Parameterisation of a Stochastic Model for Human Face Identification, in Proceedings of 2nd IEEE Workshop on Applications of Computer Vision, Sarasota FL. IEEE: SarasotaGoogle Scholar
  62. 62.
    Wasserman PD (1993) Advanced methods in nerual computing. Van Nostrand reinhold, New YorkGoogle Scholar
  63. 63.
    Nane, S.A., S.K. Nayar, and H. Murase (1996) Columbia object image library (coil-20). Technical Report CUCS-005-96Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer Engineering, Sari BranchIslamic Azad UniversitySariIran
  2. 2.Faculty of Computer and Information Technology Engineering, Qazvin BranchIslamic Azad UniversityQazvinIran
  3. 3.Data Scientist Advanced Analytics DepartmentGeneral MotorsWarrenUSA

Personalised recommendations