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Enhanced Similarity Measure for Sparse Subspace Clustering Method

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Advances in Computational Intelligence (IWANN 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10305))

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Abstract

Trying to find clusters in high dimensional data is one of the most challenging issues in machine learning. Within this context, subspace clustering methods have showed interesting results especially when applied in computer vision tasks. The key idea of these methods is to uncover groups of data that are embedding in multiple underlying subspaces. In this spirit, numerous subspace clustering algorithms have been proposed. One of them is Sparse Subspace Clustering (SSC) which has presented notable clustering accuracy. In this paper, the problem of similarity measure used in the affinity matrix construction in the SSC method is discussed. Assessment on motion segmentation and face clustering highlights the increase of the clustering accuracy brought by the enhanced SSC compared to other state-of-the-art subspace clustering methods.

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References

  1. Aggarwal, C.C., Reddy, C.K. (eds.): Data Clustering: Algorithms and Applications. Chapman and Hall/CRC, Boca Raton (2013)

    Google Scholar 

  2. Kriegel, H.P., Kröger, P., Zimek, A.: Clustering high-dimensional data: a survey on subspace clustering, pattern-based clustering, and correlation clustering. ACM Trans. Knowl. Discov. Data (TKDD) 3(1), 1 (2009)

    Article  Google Scholar 

  3. Vidal, R., Tron, R., Hartley, R.: Multiframe motion segmentation with missing data using PowerFactorization and GPCA. Int. J. Comput. Vis. 79(1), 85–105 (2008)

    Article  Google Scholar 

  4. Rao, A., Noushath, S.: Subspace methods for face recognition. Comput. Sci. Rev. 4(1), 1–17 (2010)

    Article  Google Scholar 

  5. Vidal, R.: Subspace clustering. IEEE Sig. Process. Mag. 28(2), 52–68 (2011)

    Article  Google Scholar 

  6. Yan, J., Pollefeys, M.: A general framework for motion segmentation: independent, articulated, rigid, non-rigid, degenerate and non-degenerate. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3954, pp. 94–106. Springer, Heidelberg (2006). doi:10.1007/11744085_8

    Chapter  Google Scholar 

  7. Zhang, T., Szlam, A., Wang, Y., Lerman, G.: Hybrid linear modeling via local best-fit flats. Int. J. Comput. Vis. 100(3), 217–240 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: analysis and an algorithm. In: NIPS, vol. 14, no. 2, pp. 849–856 (2001)

    Google Scholar 

  9. Elhamifar, E., Vidal, R.: Clustering disjoint subspaces via sparse representation. In: IEEE International Conference on Acoustics Speech and Signal Processing ICASSP 2010, pp. 1926–1929 (2010)

    Google Scholar 

  10. Elhamifar, E., Vidal, R.: Sparse subspace clustering: algorithm, theory, and applications. IEEE Trans. Pattern Anal. Mach. Intell. 35(11), 2765–2781 (2013)

    Article  Google Scholar 

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

    Google Scholar 

  12. 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 

  13. Donoho, D.L.: For most large underdetermined systems of linear equations the minimal l1-norm solution is also the sparsest solution. Commun. Pure Appl. Math. 59(6), 797–829 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. Tron, R., Vidal, R.: A benchmark for the comparison of 3-D motion segmentation algorithms. In: IEEE Conference on Computer Vision and Pattern Recognition CVPR 2007, pp. 1–8 (2007)

    Google Scholar 

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

    Article  Google Scholar 

  16. Chen, G., Lerman, G.: Motion segmentation by SCC on the Hopkins 155 database. In: the 12th International Conference on Computer Vision Workshops (ICCV Workshops), pp. 759–764 (2009)

    Google Scholar 

  17. Yin, M., Fang, X., Xie, S.: Semi-supervised sparse subspace clustering on symmetric positive definite manifolds. In: Tan, T., Li, X., Chen, X., Zhou, J., Yang, J., Cheng, H. (eds.) CCPR 2016. CCIS, vol. 662, pp. 601–611. Springer, Singapore (2016). doi:10.1007/978-981-10-3002-4_49

    Chapter  Google Scholar 

  18. Alok, A.K., Saha, S., Ekbal, A.: Development of an external cluster validity index using probabilistic approach and min-max distance. IJCISIM 6(1), 494–504 (2014)

    Google Scholar 

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Authors and Affiliations

  1. LIMTIC Laboratory, Higher Institute of Computer Science of Tunis, University of Tunis EL Manar, Abou Raihane Bayrouni, 2080, Ariana, Tunisia

    Sabra Hechmi, Abir Gallas & Ezzeddine Zagrouba

Authors
  1. Sabra Hechmi
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  2. Abir Gallas
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  3. Ezzeddine Zagrouba
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Corresponding author

Correspondence to Sabra Hechmi .

Editor information

Editors and Affiliations

  1. Universidad de Granada , Granada, Spain

    Ignacio Rojas

  2. University of Malaga , Malaga, Spain

    Gonzalo Joya

  3. Polytechnic University of Catalonia, Vilanova i la Geltrú, Barcelona, Spain

    Andreu Catala

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Hechmi, S., Gallas, A., Zagrouba, E. (2017). Enhanced Similarity Measure for Sparse Subspace Clustering Method. In: Rojas, I., Joya, G., Catala, A. (eds) Advances in Computational Intelligence. IWANN 2017. Lecture Notes in Computer Science(), vol 10305. Springer, Cham. https://doi.org/10.1007/978-3-319-59153-7_26

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  • DOI: https://doi.org/10.1007/978-3-319-59153-7_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59152-0

  • Online ISBN: 978-3-319-59153-7

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