[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Graph-based local concept coordinate factorization

  • Regular Paper
  • Published:
Knowledge and Information Systems Aims and scope Submit manuscript

Abstract

Ubiquitous data are increasingly expanding in large volumes due to human activities, and grouping them into appropriate clusters is an important and yet challenging problem. Existing matrix factorization techniques have shown their significant power in solving this problem, e.g., nonnegative matrix factorization, concept factorization. Recently, one state-of-the-art method called locality-constrained concept factorization is put forward, but its locality constraint does not well reveal the intrinsic data structure since it only requires the concept to be as close to the original data points as possible. To address this issue, we present a graph-based local concept coordinate factorization (GLCF) method, which respects the intrinsic structure of the data through manifold kernel learning in the warped Reproducing Kernel Hilbert Space. Besides, a generalized update algorithm is developed to handle data matrices containing both positive and negative entries. Since GLCF is essentially based on the local coordinate coding and concept factorization, it inherits many advantageous properties, such as the locality and sparsity of the data representation. Moreover, it can better encode the locally geometrical structure via graph Laplacian in the manifold adaptive kernel. Therefore, a more compact and better structured representation can be obtained in the low-dimensional data space. Extensive experiments on several image and gene expression databases suggest the superiority of the proposed method in comparison with some alternatives.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Notes

  1. http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html.

  2. http://cvc.yale.edu/projects/yalefaces/yalefaces.html.

  3. http://www.vision.caltech.edu/Image-Datasets/Caltech101/.

  4. http://appsrv.cse.cuhk.edu.hk/~jkzhu/felib.html.

References

  1. Abdi H, Williams LJ (2010) Principal component analysis. Wiley Interdiscip Rev: Comput Stat 2(4):433–459

    Article  Google Scholar 

  2. Belkin M, Niyogi P (2002) Laplacian eigenmaps and spectral techniques for embedding and clustering. Adv Neural Inf Process Syst 2:585–592

    Google Scholar 

  3. Belkin M, Niyogi P, Sindhwani V (2006) Manifold regularization: a geometric framework for learning from labeled and unlabeled examples. J Mach Learn Res 7:2399–2434

    MATH  MathSciNet  Google Scholar 

  4. Bouguila N, Ziou D (2012) A countably infinite mixture model for clustering and feature selection. Knowl Inf Syst 33(2):351–370

    Article  Google Scholar 

  5. Cai D, He X, Han J (2011) Locally consistent concept factorization for document clustering. IEEE Trans Knowl Data Eng 23(7):902–913

    Article  Google Scholar 

  6. Cai D, He X, Han J, Huang TS (2011) Graph regularized nonnegative matrix factorization for data representation. IEEE Trans Pattern Anal Mach Intell 33(8):1548–1560

    Article  Google Scholar 

  7. Cai D, He X (2012) Manifold adaptive experimental design for text categorization. IEEE Trans Knowl Data Eng 24(4):707–719

    Article  Google Scholar 

  8. Cai D, Bao H, He X (2011) Sparse concept coding for visual analysis. In: Proceedings of the 24th IEEE conference on computer vision and pattern recognition, pp 2905–2910

  9. Cai D, He X, Wang X, Bao H, Han J (2009) Locality preserving nonnegative matrix factorization. In: Proceedings of the 21st international joint conference on artificial intelligence, pp 1010–1015

  10. Cheng X, Du P, Guo J, Zhu X, Chen Y (2013) Ranking on data manifold with sink points. IEEE Trans Knowl Data Eng 25(1):177–191

    Article  Google Scholar 

  11. Ding C, Li T, Peng W, Park H (2006) Orthogonal nonnegative matrix t-factorizations for clustering. In: Proceedings of the 12th ACM international conference on knowledge discovery and data mining, pp 126–135

  12. Gong P, Zhang C (2012) Efficient nonnegative matrix factorization via projected Newton method. Pattern Recognit 45(9):3557–3565

    Article  MATH  Google Scholar 

  13. Guan N, Tao D, Luo Z, Yuan B (2012) NeNMF: An optimal gradient method for nonnegative matrix factorization. IEEE Trans Signal Process 45(9):3557–3565

    MathSciNet  Google Scholar 

  14. Hadsell R, Chopra S, LeCun Y (2006) Dimensionality reduction by learning an invariant mapping. In: Proceedings of the 19th IEEE conference on computer vision and pattern recognition 2:1735–1742

  15. Hastie T, Tibshirani R, Friedman J, Franklin J (2009) The elements of statistical learning: data mining, inference, and prediction

  16. Hoyer PO, Dayan P (2004) Non-negative matrix factorization with sparseness constraints. J Mach Learn Res 5:1457–1469

    MATH  Google Scholar 

  17. Hua W, He X (2011) Discriminative concept factorization for data representation. Neurocomputing 74(18):3800–3807

    Article  Google Scholar 

  18. Kim Y, Chung C, Lee SG, Kim D (2011) Distance approximation techniques to reduce the dimensionality for multimedia databases. Knowl Inf Syst 28(1):227–248

    Article  Google Scholar 

  19. Lee DD, Seung HS (1999) Learning the parts of objects by non-negative matrix factorization. Nature 401(6755):788–791

    Article  Google Scholar 

  20. Li Z, Wu X, Peng H (2010) Nonnegative matrix factorization on orthogonal subspace. Pattern Recognit Lett 31(9):905–911

    Article  Google Scholar 

  21. Li P, Chen C, Bu J (2012) Clustering analysis using manifold kernel concept factorization. Neurocomputing 87:120–131

    Article  Google Scholar 

  22. Li P, Bu J, Chen C, Wang C, Cai D (2013) Subspace learning via locally constrained A-optimal nonnegative projection. Neurocomputing 115:49–62

    Article  Google Scholar 

  23. Li P, Bu J, Chen C, He Z, Cai D (2013) Relational multi-manifold co-clustering. IEEE Trans Cybern. 43(6):1871–1881

    Google Scholar 

  24. Liu H, Wu Z, Cai D, Huang TS (2012) Constrained nonnegative matrix factorization for image representation. IEEE Trans Pattern Anal Mach Intell 34(7):1299–1311

    Article  Google Scholar 

  25. Liu H, Yang Z, Wu Z (2011) Locality-constrained concept factorization. In: Proceedings of the 22nd international joint conference on artificial intelligence, pp 1378–1383

  26. Lovász L, Plummer M (1986) Matching theory. In: North Holland, Akadémiai Kiadó

  27. Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500):2323–2326

    Article  Google Scholar 

  28. Seung D, Lee L (2001) Algorithms for non-negative matrix factorization. Adv Neural Inf Process Syst 13:556–562

    Google Scholar 

  29. Sha F, Lin Y, Saul LK, Lee DD (2007) Multiplicative updates for nonnegative quadratic programming. Neural Comput, MIT Press 19(8):2004–2031

    Google Scholar 

  30. Sindhwani V, Niyogi P, elkin M (2005) Beyond the point cloud: from transductive to semi-supervised learning. In: Proceedings of the 22nd international conference on machine learning, pp 824–831

  31. Tenenbaum JB, De Silva V, Langford JC, Bauckhage C (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5500):2319–2323

    Article  Google Scholar 

  32. Thurau C, Kersting K, Wahabzada M, Bauckhage C (2011) Convex non-negative matrix factorization for massive datasets. Knowl Inf Syst 29(2):457–478

    Article  Google Scholar 

  33. Tzimiropoulos G, Zafeiriou S, Pantic M (2012) Subspace learning from image gradient orientations. IEEE Trans Pattern Anal Mach Intell 34(12):2454–2466

    Article  Google Scholar 

  34. Xu B, Bu J, Chen C, Cai D (2012) A Bregman divergence optimization framework for ranking on data manifold and its new extensions. In: Proceedings of the 26th AAAI conference on artificial intelligence, pp 1190–1196

  35. Xu W, Gong Y (2004) Document clustering by concept factorization. In: Proceedings of the 27th annual international ACM SIGIR conference on research and development in information retrieval, pp 202–209

  36. Xu W, Liu X, Gong Y (2003) Document clustering based on non-negative matrix factorization. In: Proceedings of the 26th annual international ACM SIGIR conference on research and development in information retrieval, pp 267–273

  37. Yang Z, Oja E (2012) Quadratic nonnegative matrix factorization. Pattern Recognit 45(4):1500–1510

    Article  MATH  Google Scholar 

  38. Yu K, Zhang T, Gong Y (2009) Nonlinear learning using local coordinate coding. Adv Neural Inf Process Syst 22:2223–2231

    Google Scholar 

  39. Zhang L, Chen Z, Zheng M, He X (2011) Robust non-negative matrix factorization. Frontiers Electr Electron Eng China 6(2):192–200

    Article  Google Scholar 

  40. Zhang Z, Wang J, Zha H (2012) Adaptive manifold learning. IEEE Trans Pattern Anal Mach Intell 34(2):253–265

    Article  Google Scholar 

  41. Zhu S, Wang D, Yu K, Li T, Gong Y (2010) Feature selection for gene expression using model-based entropy. IEEE/ACM Trans Comput Biol Bioinform 7(1):25–36

    Article  Google Scholar 

  42. Zhu J, Hoi SCH, Lyu MR, Yan S (2008) Near-duplicate keyframe retrieval by nonrigid image matching. In: Proceedings of the 16th ACM international conference on multimedia, pp 41–50

Download references

Acknowledgments

We thank the anonymous reviewers for their valuable comments and suggestions which greatly improve the quality of the paper. This work was supported in part by National Natural Science Foundation of China under Grants 91120302, 61222207, 61173185, and 61173186, National Basic Research Program of China (973 Program) under Grant 2013CB336500, the Fundamental Research Funds for the Central Universities under Grant 2012FZA5017, and the Zhejiang Province Key S&T Innovation Group Project under Grant 2009R50009.

Author information

Authors and Affiliations

  1. Zhejiang Provincial Key Laboratory of Service Robot, College of Computer Science, Zhejiang University, Hangzhou, 310027, China

    Ping Li, Jiajun Bu & Chun Chen

  2. Department of Computer Science and Engineering, Michigan State University, East Lansing, MI, 48824, USA

    Lijun Zhang

Authors
  1. Ping Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiajun Bu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lijun Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chun Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ping Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, P., Bu, J., Zhang, L. et al. Graph-based local concept coordinate factorization. Knowl Inf Syst 43, 103–126 (2015). https://doi.org/10.1007/s10115-013-0715-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10115-013-0715-x

Keywords

Search

Navigation