Neural Computing and Applications

, Volume 31, Issue 12, pp 8727–8736 | Cite as

Superpixels for large dataset subspace clustering

  • Kewei TangEmail author
  • Zhixun Su
  • Wei Jiang
  • Jie ZhangEmail author
Original Article


Due to the numerous applications in computer vision, subspace clustering has been extensively studied in the past two decades. Most research puts emphasis on the spectral clustering-based methods in the recent years. This kind of methods usually extracts the affinity by the self-representation of the data points. Although they achieve the state-of-the-art results, the computation time will be unbearable when the number of the data points is large enough. In addition, the self-representation only considers the information provided by each single data point. In this paper, inspired by the idea of the superpixels in image segmentation, we first propose superpixels for subspace clustering with the large dataset. Then, we provide the strategy for the popular spectral clustering-based methods using these superpixels. Experimental results confirm that our superpixel-based subspace clustering methods can improve the computation speed dramatically. In addition, since the superpixels can consider the information provided by the group of data points, these methods can also improve the performance to some extent.


Superpixels Large dataset Subspace clustering Spectral clustering-based methods 



The work of K. Tang was supported by the National Natural Science Foundation of China (No. 61702243) and the Educational Commission of Liaoning Province, China (No. L201683662). The work of Z. Su was supported by the High-tech Ship Research Program Support Project and the National Natural Science Foundation of China (No. 61572099). The work of W. Jiang was supported by the National Natural Science Foundation of China (No. 61771229). The work of J. Zhang was supported by National Natural Science Foundation of China (No. 61702245) and the Educational Commission of Liaoning Province, China (No. L201683663).

Compliance with ethical standards

Conflict of interest

The authors declared that they have no conflict of interest to this work.


  1. 1.
    Achanta R, Shaji A, Smith K, Lucchi A, Fua P, Süsstrunk S (2012) SLIC superpixels compared to state-of-the-art superpixel methods. IEEE Trans Pattern Anal Mach Intell 34(11):2274–2282CrossRefGoogle Scholar
  2. 2.
    Basri R, Jacobs DW (2003) Lambertian reflectance and linear subspaces. IEEE Trans Pattern Anal Mach Intell 25(2):218–233CrossRefGoogle Scholar
  3. 3.
    Candès EJ, Li X, Ma Y, Wright J (2011) Robust principal component analysis? J ACM 58(3):1–37MathSciNetCrossRefGoogle Scholar
  4. 4.
    Costeira JP, Kanade T (1998) A multibody factorization method for independently moving objects. Int J Comput Vis 29(3):159–179CrossRefGoogle Scholar
  5. 5.
    Elhamifar E, Vidal R (2009) Sparse subspace clustering. In: CVPR, pp 2790–2797Google Scholar
  6. 6.
    Elhamifar E, Vidal R (2013) Sparse subspace clustering: algorithm, theory, and applications. IEEE Trans Pattern Anal Mach Intell 35(11):2765–2781CrossRefGoogle Scholar
  7. 7.
    Felzenszwalb PF, Huttenlocher DP (2004) Efficient graph-based image segmentation. Int J Comput Vis 59(2):167–181CrossRefGoogle Scholar
  8. 8.
    Golub GH, Loan CFV (1996) Matrix computations, 3rd edn. Johns Hopkins University Press, BaltimorezbMATHGoogle Scholar
  9. 9.
    Ham J, Lee DD (2008) Grassmann discriminant analysis: a unifying view on subspace-based learning. In: ICML, pp 376–383Google Scholar
  10. 10.
    Harris J (1992) Algebraic geometry. Springer, BerlinCrossRefGoogle Scholar
  11. 11.
    Haykin S, Kosko B (2009) Gradient based learning applied to document recognition. In: IEEE, pp 306–351Google Scholar
  12. 12.
    Ho J, Yang MH, Lim J, Lee KC, Kriegman DJ (2003) Clustering appearances of objects under varying illumination conditions. In: CVPR, pp 11–18Google Scholar
  13. 13.
    Lee K, Ho J, Kriegman DJ (2005) Acquiring linear subspaces for face recognition under variable lighting. IEEE Trans Pattern Anal Mach Intell 27(5):684–698CrossRefGoogle Scholar
  14. 14.
    Li Z, Chen J (2015) Superpixel segmentation using linear spectral clustering. In: CVPR, pp 1356–1363Google Scholar
  15. 15.
    Lin Z, Chen M, Wu L, Ma Y (2009) The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices. UIUC Technical Report, UILU-ENG-09-2215Google Scholar
  16. 16.
    Lin Z, Liu R, Su Z (2011) Linearized alternating direction method with adaptive penalty for low-rank representation. In: NIPS, pp 612–620Google Scholar
  17. 17.
    Liu G, Lin Z, Yan S, Sun J, Yu Y, Ma Y (2013) Robust recovery of subspace structures by low-rank representation. IEEE Trans Pattern Anal Mach Intell 35(1):171–184CrossRefGoogle Scholar
  18. 18.
    Liu G, Lin Z, Yu Y (2010) Robust subspace segmentation by low-rank representation. In: ICML, pp 663–670Google Scholar
  19. 19.
    Liu R, Lin Z, la Torre FD, Su Z (2012) Fixed-rank representation for unsupervised visual learning. In: CVPR, pp 598–605Google Scholar
  20. 20.
    Lowe DG (1999) Object recognition from local scale-invariant features. In: ICCV, pp 1150–1157Google Scholar
  21. 21.
    Nene SA, Nayar SK, Murase H (1996) Columbia object image library (coil-20). Technical Report, CUCS-005-96Google Scholar
  22. 22.
    Ojala T, Pietikäinen M, Mäenpää T (2000) Gray scale and rotation invariant texture classification with local binary patterns. In: ECCV, pp 404–420Google Scholar
  23. 23.
    Peng X, Zhang L, Yi Z (2013) Scalable sparse subspace clustering. In: CVPR, pp 430–437Google Scholar
  24. 24.
    Ren X, Malik J (2003) Learning a classification model for segmentation. In: ICCV, pp 10–17Google Scholar
  25. 25.
    Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8):888–905CrossRefGoogle Scholar
  26. 26.
    Soltanolkotabi M, Candès EJ (2012) A geometric analysis of subspace clustering with outliers. Ann Stat 40(4):2195–2238MathSciNetCrossRefGoogle Scholar
  27. 27.
    Tang K, Dunson DB, Su Z, Liu R, Zhang J, Dong J (2016) Subspace segmentation by dense block and sparse representation. Neural Netw 75:66–76CrossRefGoogle Scholar
  28. 28.
    Tang K, Liu R, Su Z, Zhang J (2014) Structure-constrained low-rank representation. IEEE Trans Neural Netw Learn Syst 25(12):2167–2179CrossRefGoogle Scholar
  29. 29.
    Tang K, Liu X, Su Z, Jiang W, Dong J (2016) Subspace learning based low-rank representation. In: ACCV, pp 416–431Google Scholar
  30. 30.
    Tang K, Su Z, Jiang W, Zhang J, Sun X, Luo X (2018) Robust subspace learning-based low-rank representation for manifold clustering. Neural Comput Appl. CrossRefGoogle Scholar
  31. 31.
    Tang K, Zhang J, Su Z, Dong J (2016) Bayesian low-rank and sparse nonlinear representation for manifold clustering. Neural Process Lett 44(3):719–733CrossRefGoogle Scholar
  32. 32.
    Vidal R (2011) Subspace clustering. IEEE Signal Process Mag 28(2):52–68CrossRefGoogle Scholar
  33. 33.
    Wang Y, Xu H, Leng C (2013) Provable subspace clustering: When LRR meets SSC. In: NIPS, pp 64–72Google Scholar
  34. 34.
    Yan J, Pollefeys M (2006) A general framework for motion segmentation: independent, articulated, rigid, non-rigid, degenerate and non-degenerate. In: ECCV, pp 94–106Google Scholar
  35. 35.
    You C, Robinson DP, Vidal R (2016) Scalable sparse subspace clustering by orthogonal matching pursuit. In: CVPR, pp 3918–3927Google Scholar
  36. 36.
    Zhang H, Wang S, Xu X, Chow T, Wu Q (2018) Tree2vector: learning a vectorial representation for tree-structured data. IEEE Trans Neural Netw Learn Syst 29(11):5304–5318MathSciNetCrossRefGoogle Scholar
  37. 37.
    Zhang H, Wang S, Zhao M, Xu X, Ye Y (2018) Locality reconstruction models for book representation. IEEE Trans Knowl Data Eng. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsLiaoning Normal UniversityDalianPeople’s Republic of China
  2. 2.School of Mathematical SciencesDalian University of TechnologyDalianPeople’s Republic of China
  3. 3.Guilin University of Electronic TechnologyGuilinPeople’s Republic of China

Personalised recommendations