Skip to main content

Fundamentals of Robust Representations

  • Chapter
  • First Online:
  • 1136 Accesses

Part of the book series: Advanced Information and Knowledge Processing ((AI&KP))

Abstract

This chapter presents the fundamentals of robust representations. In particular, we provide a brief overview of existing representation learning and robust representation methods. The advantages and disadvantages of these existing methods are also discussed.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

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

    Article  Google Scholar 

  2. Bach, F.: Consistency of trace norm minimization. J. Mach. Learn. Res. 9, 1019–1048 (2008)

    MathSciNet  MATH  Google Scholar 

  3. Bellhumeur, P.N., Hespanha, J.P., Kriegeman, D.J.: Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans. Pattern Anal. Mach. Intell. 19(7), 711–720 (1997)

    Google Scholar 

  4. Cai, D., He, X., Han, J.: Semi-supervised discriminant analysis. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 1–7. IEEE (2007)

    Google Scholar 

  5. Cai, D., He, X., Zhou, K., Han, J., Bao, H.: Locality sensitive discriminant analysis. In: Proceedings of the 20th International Joint Conference on Artificial Intelligence, pp. 708–713 (2007)

    Google Scholar 

  6. Candès, E.J., Li, X., Ma, Y., Wright, J.: Robust principal component analysis? J. ACM 58(3), 11 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Chen, C., Wei, C., Wang, Y.: Low-rank matrix recovery with structural incoherence for robust face recognition. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 2618–2625 (2012)

    Google Scholar 

  8. Chen, C.Y., Cai, J.F., Lin, W.S., Shi, G.M.: Surveillance video coding via low-rank and sparse decomposition. In: Proceedings of the 20th ACM International Conference on Multimedia, pp. 713–716 (2012)

    Google Scholar 

  9. Christoforou, C., Haralick, R., Sajda, P., Parra, L.C.: Second-order bilinear discriminant analysis. J. Mach. Learn. Res. 11, 665–685 (2010)

    MATH  Google Scholar 

  10. Cong, Y., Liu, J., Yuan, J., Luo, J.: Self-supervised online metric learning with low rank constraint for scene categorization. IEEE Trans. Image Process. 22(8), 3179–3191 (2013)

    Article  Google Scholar 

  11. Deng Y., Dai, Q., Liu, R., Zhang, Z., Hu, S.: Low-rank structure learning via nonconvex heuristic recovery. IEEE Trans. Neural Netw. Learn. Syst. 24(3), 383–396 (2013)

    Article  Google Scholar 

  12. Dyrholm, M., Christoforou, C., Parra, L.C.: Bilinear discriminant component analysis. J. Mach. Learn. Res. 8, 1097–1111 (2007)

    Google Scholar 

  13. Elhamifar, E., Vidal, R.: Sparse subspace clustering. In: CVPR, pp. 2790–2797 (2009)

    Google Scholar 

  14. Fisher, R.A.: The statistical utilization of multiple measurements. Ann. Eugen. 8(4), 376–386 (1938)

    Article  MATH  Google Scholar 

  15. Gu, S., Zhang, L., Zuo, W., Feng, X.: Projective dictionary pair learning for pattern classification. In: Proceedings of the Annual Conference on Neural Information Processing Systems, pp. 793–801 (2014)

    Google Scholar 

  16. Günnemann, S., Färber, I., Rüdiger, M., Seidl, T.: SMVC: semi-supervised multi-view clustering in subspace projections. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 253–262. ACM (2014)

    Google Scholar 

  17. Guo, H., Jiang, Z., Davis, L.S.: Discriminative dictionary learning with pairwise constraints. In: Proceedings of the Asian Conference on Computer Vision, pp. 328–342. Springer (2013)

    Google Scholar 

  18. Guo, Y.: Convex subspace representation learning from multi-view data. In: Proceedings of the 27th AAAI Conference on Artificial Intelligence, vol. 1, p. 2 (2013)

    Google Scholar 

  19. He, X., Niyogi, P.: Locality preserving projections. In: Advances in Neural Information Processing Systems, pp. 153–160 (2004)

    Google Scholar 

  20. Hotelling, H.: Relations between two sets of variates. Biometrika 28(3/4), 321–377 (1936)

    Article  MATH  Google Scholar 

  21. Hu, H., Lin, Z., Feng, J., Zhou, J.: Smooth representation clustering. In: CVPR (2014)

    Book  Google Scholar 

  22. Jing, X.-Y., Li, S., Zhang, D., Yang, J., Yang, J.-Y.: Supervised and unsupervised parallel subspace learning for large-scale image recognition. IEEE Trans. Circuits Syst. Video Technol. 22(10), 1497–1511 (2012)

    Article  Google Scholar 

  23. Jolliffe, I.T.: Principal component analysis and factor analysis. In: Principal Component Analysis, pp. 150–166. Springer, Berlin/London (2002)

    Google Scholar 

  24. Kan, M., Shan, S., Zhang, H., Lao, S., Chen, X.: Multi-view discriminant analysis. IEEE Trans. Pattern Anal. Mach. Intell. 38(1), 188–194 (2016)

    Article  Google Scholar 

  25. Lan, C., Huan, J.: Reducing the unlabeled sample complexity of semi-supervised multi-view learning. In: Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 627–634. ACM (2015)

    Google Scholar 

  26. Li, L., Li, S., Fu, Y.: Learning low-rank and discriminative dictionary for image classification. Image Vis. Comput. 32(10), 814–823 (2014)

    Article  Google Scholar 

  27. Li, S., Fu, Y.: Robust subspace discovery through supervised low-rank constraints. In: Proceedings of the SIAM International Conference on Data Mining, pp. 163–171 (2014)

    Google Scholar 

  28. Li, S., Fu, Y.: Learning balanced and unbalanced graphs via low-rank coding. IEEE Trans. Knowl. Data Eng. 27(5), 1274–1287 (2015)

    Article  Google Scholar 

  29. Li, S., Fu, Y.: Learning robust and discriminative subspace with low-rank constraints. IEEE Trans. Neural Netw. Learn. Syst. 27(11), 2160–2173 (2016)

    Article  MathSciNet  Google Scholar 

  30. Li, S., Shao, M., Fu, Y.: Cross-view projective dictionary learning for person re-identification. In: Proceedings of the 24th International Conference on Artificial Intelligence, pp. 2155–2161 (2015)

    Google Scholar 

  31. Li, S., Shao, M., Fu, Y.: Multi-view low-rank analysis for outlier detection. In: Proceedings of the SIAM International Conference on Data Mining, pp. 748–756. SIAM (2015)

    Google Scholar 

  32. Li, Y., Nie, F., Huang, H., Huang, J.: Large-scale multi-view spectral clustering via bipartite graph. In: Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence, pp. 2750–2756 (2015)

    Google Scholar 

  33. Liu, G., Lin, Z., Yan, S., Sun, J., Yu, Y., Ma, Y.: Robust recovery of subspace structures by low-rank representation. IEEE Trans. Pattern Anal. Mach. Intell. 35(1), 171–184 (2013)

    Article  Google Scholar 

  34. Liu, G., Yan, S.: Latent low-rank representation for subspace segmentation and feature extraction. In: Proceedings of the 13th IEEE International Conference on Computer Vision, pp. 1615–1622 (2011)

    Google Scholar 

  35. Liu, G., Yan, S.: Active subspace: toward scalable low-rank learning. Neural Comput. 24(12), 3371–3394 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  36. Liu, G.C., Lin, Z.C., Yu, Y.: Robust subspace segmentation by low-rank representation. In: Proceedings of the 27th International Conference on Machine Learning, pp. 663–670 (2010)

    Google Scholar 

  37. Liu, X., Xu, Q., Ma, J., Jin, H., Zhang, Y.: MsLRR: a unified multiscale low-rank representation for image segmentation. IEEE Trans. Image Process. 23(5), 2159–2167 (2014)

    Article  MathSciNet  Google Scholar 

  38. Lu, C., Min, H., Zhao, Z., Zhu, L., Huang, D., Yan, S.: Robust and efficient subspace segmentation via least squares regression. In: ECCV, pp. 347–360 (2012)

    Google Scholar 

  39. Ma, L., Wang, C., Xiao, B., Zhou, W.: Sparse representation for face recognition based on discriminative low-rank dictionary learning. In: Proceedings of the 25th IEEE Conference on Computer Vision and Pattern Recognition, pp. 2586–2593 (2012)

    Google Scholar 

  40. Mairal, J., Bach, F., Ponce, J.: Task-driven dictionary learning. IEEE Trans. Pattern Anal. Mach. Intell. 34(4), 791–804 (2012)

    Article  Google Scholar 

  41. Peng, X., Zhang, L., Yi, Z.: Scalable sparse subspace clustering. In: Proceedings of the 26th IEEE Conference on Computer Vision and Pattern Recognition, pp. 430–437 (2013)

    Google Scholar 

  42. Qiu, Q., Patel, V.M., Chellappa, R.: Information-theoretic dictionary learning for image classification. IEEE Trans. Pattern Anal. Mach. Intell. 36(11), 2173–2184 (2014)

    Article  Google Scholar 

  43. Rupnik, J., Shawe-Taylor, J.: Multi-view canonical correlation analysis. In: Conference on Data Mining and Data Warehouses, pp. 1–4 (2010)

    Google Scholar 

  44. Sugiyama, M.: Dimensionality reduction of multimodal labeled data by local Fisher discriminant analysis. J. Mach. Learn. Res. 8, 1027–1061 (2007)

    MATH  Google Scholar 

  45. Talwalkar, A., Mackey, L.W., Mu, Y., Chang, S., Jordan, M.I.: Distributed low-rank subspace segmentation. In: ICCV, pp. 3543–3550 (2013)

    Google Scholar 

  46. Talwalkar, A., Mackey, L.W., Mu, Y., Chang, S.-F., Jordan, M.I.: Distributed low-rank subspace segmentation. In: International Conference on Computer Vision (ICCV), pp. 3543–3550 (2013)

    Google Scholar 

  47. Wang, S., Tu, B., Xu, C., Zhang, Z.: Exact subspace clustering in linear time. In: AAAI, pp. 2113–2120 (2014)

    Google Scholar 

  48. Wang, W., Arora, R., Livescu, K., Bilmes, J.: On deep multi-view representation learning. In: Proceedings of the 32nd International Conference on Machine Learning, pp. 1083–1092 (2015)

    Google Scholar 

  49. Xu, C., Tao, D., Xu, C.: A survey on multi-view learning. arXiv preprint arXiv:1304.5634 (2013)

    Google Scholar 

  50. Yuan, X., Li, P.: Sparse additive subspace clustering. In: ECCV, pp. 644–659 (2014)

    Google Scholar 

  51. Zhang, N., Yang, J.: Low-rank representation based discriminative projection for robust feature extraction. Neurocomputing 111, 13–20 (2013)

    Article  Google Scholar 

  52. Zhang, Q., Li, B.: Discriminative k-SVD for dictionary learning in face recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2691–2698 (2010)

    Google Scholar 

  53. Zhang, Y., Jiang, Z., Davis, L.S.: Learning structured low-rank representations for image classification. In: Proceedings of the 26th IEEE Conference on Computer Vision and Pattern Recognition, pp. 676–683 (2013)

    Google Scholar 

  54. Zhang, Z., Ganesh, A., Liang, X., Ma, Y.: TILT: transform invariant low-rank textures. Int. J. Comput. Vis. 99(1), 1–24 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  55. Zheng, J., Jiang, Z., Phillips, P.J., Chellappa, R.: Cross-view action recognition via a transferable dictionary pair. In: BMVC, vol. 1, pp. 1–11 (2012)

    Google Scholar 

  56. Zheng, Z., Zhang, H., Jia, J., Zhao, J., Guo, L., Fu, F., Yu, M.: Low-rank matrix recovery with discriminant regularization. In: Proceedings of the 17th Pacific-Asia Conference on Advances in Knowledge Discovery and Data Mining II, pp. 437–448 (2013)

    Google Scholar 

  57. Zhou, X., Yang, C., Yu, W.: Moving object detection by detecting contiguous outliers in the low-rank representation. IEEE Trans. Pattern Anal. Mach. Intell. 35(3), 597–610 (2013)

    Article  Google Scholar 

  58. Zhu, M., Martínez, A.M.: Subclass discriminant analysis. IEEE Trans. Pattern Anal. Mach. Intell. 28(8), 1274–1286 (2006)

    Article  Google Scholar 

  59. Zografos, V., Ellis, L., Mester, R.: Discriminative subspace clustering. In: Proceedings of the 26th IEEE Conference on Computer Vision and Pattern Recognition, pp. 2107–2114 (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Li, S., Fu, Y. (2017). Fundamentals of Robust Representations. In: Robust Representation for Data Analytics. Advanced Information and Knowledge Processing. Springer, Cham. https://doi.org/10.1007/978-3-319-60176-2_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-60176-2_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60175-5

  • Online ISBN: 978-3-319-60176-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics