Improved Sample Complexity in Sparse Subspace Clustering with Noisy and Missing Observations

  • Bin Shi
  • S. S. Iyengar


In this chapter, we show the results of the new CoCoSSC algorithm. The content is organized as follows: The main results concerning CoCoSSC algorithm are shown in Sect. 9.1. Following Sect. 9.1, we show the full proofs in Sect. 9.2. In Sect. 9.3, we show the performance for CoCoSSC algorithm and some related algorithms numerically. Finally, we conclude this work with some future directions.


CoCoSSC algorithm Gaussian noise model Spectral clustering Inner-subspace incoherence Self-similarity matrix Inter-subspace incoherence 


  1. [CJW17]
    Z. Charles, A. Jalali, R. Willett, Sparse subspace clustering with missing and corrupted data. arXiv preprint: arXiv:1707.02461 (2017)Google Scholar
  2. [CR09]
    E.J. Candès, B. Recht, Exact matrix completion via convex optimization. Found. Comput. Math. 9(6), 717–772 (2009)MathSciNetCrossRefGoogle Scholar
  3. [FM83]
    E.B. Fowlkes, C.L. Mallows, A method for comparing two hierarchical clusterings. J. Am. Stat. Assoc. 78(383), 553–569 (1983)CrossRefGoogle Scholar
  4. [HB15]
    R. Heckel, H. Bölcskei, Robust subspace clustering via thresholding. IEEE Trans. Inf. Theory 61(11), 6320–6342 (2015)MathSciNetCrossRefGoogle Scholar
  5. [KMO10]
    R.H. Keshavan, A. Montanari, S. Oh, Matrix completion from a few entries. IEEE Trans. Inf. Theory 56(6), 2980–2998 (2010)MathSciNetCrossRefGoogle Scholar
  6. [NH11]
    B. Nasihatkon, R. Hartley, Graph connectivity in sparse subspace clustering, in CVPR (IEEE, Piscataway, 2011)Google Scholar
  7. [PCS14]
    D. Park, C. Caramanis, S. Sanghavi, Greedy subspace clustering, in Advances in Neural Information Processing Systems (2014), pp. 2753–2761Google Scholar
  8. [Rec11]
    B. Recht, A simpler approach to matrix completion. J. Mach. Learn. Res. 12, 3413–3430 (2011)MathSciNetzbMATHGoogle Scholar
  9. [SC12]
    M. Soltanolkotabi, E.J. Candes, A geometric analysis of subspace clustering with outliers. Ann. Stat. 40(4), 2195–2238 (2012)MathSciNetCrossRefGoogle Scholar
  10. [SEC14]
    M. Soltanolkotabi, E. Elhamifar, E.J. Candes, Robust subspace clustering. Ann. Stat. 42(2), 669–699 (2014)MathSciNetCrossRefGoogle Scholar
  11. [WWBS17]
    Y. Wang, J. Wang, S. Balakrishnan, A. Singh, Rate optimal estimation and confidence intervals for high-dimensional regression with missing covariates. arXiv preprint arXiv:1702.02686 (2017)Google Scholar
  12. [WWS15a]
    Y. Wang, Y.-X. Wang, A. Singh, A deterministic analysis of noisy sparse subspace clustering for dimensionality-reduced data, in International Conference on Machine Learning (2015), pp. 1422–1431Google Scholar
  13. [WWS16]
    Y. Wang, Y.-X. Wang, A. Singh, Graph connectivity in noisy sparse subspace clustering, in Artificial Intelligence and Statistics (2016), pp. 538–546Google Scholar
  14. [WX16]
    Y.-X. Wang, H. Xu, Noisy sparse subspace clustering. J. Mach. Learn. Res. 17(12), 1–41 (2016)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Bin Shi
    • 1
  • S. S. Iyengar
    • 2
  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.Florida International UniversityMiamiUSA

Personalised recommendations