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Spatially Correlated Nonnegative Matrix Factorization for Image Analysis

  • Conference paper
Book cover Intelligent Science and Intelligent Data Engineering (IScIDE 2012)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7751))

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Abstract

Low rank approximation of matrices has been frequently applied in information processing tasks, and in recent years, Nonnegative Matrix Factorization (NMF) has received considerable attentions for its straightforward interpretability and superior performance. When applied to image processing, ordinary NMF merely views a p 1×p 2 image as a vector in p 1×p 2-dimensional space and the pixels of the image are considered as independent. It fails to consider the fact that an image displayed in the plane is intrinsically a matrix, and pixels spatially close to each other may probably be correlated. Even though we have p 1×p 2 pixels per image, this spatial correlation suggests the real number of freedom is far less. In this paper, we introduce a Spatially Correlated Nonnegative Matrix Factorization algorithm, which explicitly models the spatial correlation between neighboring pixels in the parts-based image representation. A multiplicative updating algorithm is also proposed to solve the corresponding optimization problem. Experimental results on benchmark image data sets demonstrate the effectiveness of the proposed method.

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References

  1. Bishop, C.M.: Pattern recognition and machine learning, vol. 4. Springer, New York (2006)

    MATH  Google Scholar 

  2. Boutsidis, C., Gallopoulos, E.: Svd based initialization: A head start for nonnegative matrix factorization. Pattern Recognition 41(4), 1350–1362 (2008)

    Article  MATH  Google Scholar 

  3. Cai, D., He, X., Han, J., Huang, T.: Graph regularized non-negative matrix factorization for data representation. IEEE TPAMI 33(8), 1548–1560 (2011)

    Article  Google Scholar 

  4. Cai, D., He, X., Hu, Y., Han, J., Huang, T.: Learning a spatially smooth subspace for face recognition. In: CVPR. IEEE (2007)

    Google Scholar 

  5. Cai, D., He, X., Wu, X., Han, J.: Non-negative matrix factorization on manifold. In: ICDM, pp. 63–72. IEEE (2008)

    Google Scholar 

  6. Chen, X., Tong, Z., Liu, H., Cai, D.: Metric learning with two-dimensional smoothness for visual analysis. In: CVPR, pp. 2533–2538. IEEE (2012)

    Google Scholar 

  7. Ding, C., He, X., Simon, H.D.: On the equivalence of nonnegative matrix factorization and spectral clustering. In: SDM, vol. 4, pp. 606–610 (2005)

    Google Scholar 

  8. Gillis, N.: Nonnegative Matrix Factorization: Complexity, Algorithms and Applications. PhD thesis, University of Waterloo, Canada (2011)

    Google Scholar 

  9. Gu, Q., Ding, C.H.Q., Han, J.: On trivial solution and scale transfer problems in graph regularized nmf. In: IJCAI, pp. 1288–1293 (2011)

    Google Scholar 

  10. Guillamet, D., Vitrià, J.: Non-negative matrix factorization for face recognition. In: Topics in Artificial Intelligence, pp. 336–344 (2002)

    Google Scholar 

  11. Horn, R., Johnson, C.: Topics in Matrix Analysis. Cambridge University Press (1991)

    Google Scholar 

  12. Hoyer, P.O.: Non-negative matrix factorization with sparseness constraints. JMLR 5, 1457–1469 (2004)

    MathSciNet  MATH  Google Scholar 

  13. Jost, J.: Riemannian Geometry and Geometric Analysis. Springer (2002)

    Google Scholar 

  14. Kim, J., Park, H.: Toward faster nonnegative matrix factorization: A new algorithm and comparisons. In: ICDM, pp. 353–362. IEEE (2008)

    Google Scholar 

  15. Land, S.R., Friedman, J.H.: Variable fusion: A new adaptive signal regression method. Technical report, Technical Report 656, Department of Statistics, Carnegie Mellon University Pittsburgh (1997)

    Google Scholar 

  16. Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. In: NIPS, vol. 13. MIT Press (2001)

    Google Scholar 

  17. Lee, D.D., Seung, H.S., et al.: Learning the parts of objects by non-negative matrix factorization. Nature 401(6755), 788–791 (1999)

    Article  Google Scholar 

  18. Li, S.Z., Hou, X.W., Zhang, H.J., Cheng, Q.S.: Learning spatially localized, parts-based representation. In: CVPR. IEEE (2001)

    Google Scholar 

  19. Li, T., Ding, C.: The relationships among various nonnegative matrix factorization methods for clustering. In: ICDM, pp. 362–371. IEEE (2006)

    Google Scholar 

  20. Lin, C.J.: Projected gradient methods for nonnegative matrix factorization. Neural Computation 19(10), 2756–2779 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. Liu, W., Zheng, N.: Non-negative matrix factorization based methods for object recognition. Pattern Recognition Letters 25(8), 893–897 (2004)

    Article  Google Scholar 

  22. Logothetis, N.K., Sheinberg, D.L.: Visual object recognition. Annual Review of Neuroscience 19(1), 577–621 (1996)

    Article  Google Scholar 

  23. Lovasz, L., Plummer, M.: Matching Theory. Akadémiai Kiadó. North Holland, Budapest (1986)

    Google Scholar 

  24. Monga, V., Mihcak, M.K.: Robust image hashing via non-negative matrix factorizations. In: ICASSP, vol. 2. IEEE (2006)

    Google Scholar 

  25. O’Sullivan, F.: Discretized laplacian smoothing by fourier methods. Journal of the American Statistical Association, 634–642 (1991)

    Google Scholar 

  26. Pauca, V.P., Piper, J., Plemmons, R.J.: Nonnegative matrix factorization for spectral data analysis. Linear Algebra and its Applications 416(1), 29–47 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  27. Sha, F., Lin, Y., Saul, L.K., Lee, D.D.: Multiplicative updates for nonnegative quadratic programming. Neural Computation 19(8), 2004–2031 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  28. Sra, S., Dhillon, I.S.: Nonnegative matrix approximation: Algorithms and applications. University of Texas at Austin (2006)

    Google Scholar 

  29. Srebro, N., Rennie, J.D.M., Jaakkola, T.: Maximum-margin matrix factorization. In: NIPS, vol. 17, pp. 1329–1336. MIT Press (2005)

    Google Scholar 

  30. Tibshirani, R., Saunders, M., Rosset, S., Zhu, J., Knight, K.: Sparsity and smoothness via the fused lasso. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 67(1), 91–108 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  31. Trefethen, L.N., Bau, D.: Numerical linear algebra. Society for Industrial Mathematics, vol. 50 (1997)

    Google Scholar 

  32. Turk, M.A., Pentland, A.P.: Face recognition using eigenfaces. In: CVPR, pp. 586–591. IEEE (1991)

    Google Scholar 

  33. Vasilescu, M.A.O., Terzopoulos, D.: Multilinear subspace analysis of image ensembles. In: CVPR. IEEE (2003)

    Google Scholar 

  34. Wold, S., Esbensen, K., Geladi, P.: Principal component analysis. Chemometrics and Intelligent Laboratory Systems 2(1-3), 37–52 (1987)

    Article  Google Scholar 

  35. Xu, W., Liu, X., Gong, Y.: Document clustering based on non-negative matrix factorization. In: SIGIR, pp. 267–273. ACM (2003)

    Google Scholar 

  36. Yang, J., Yang, S., Fu, Y., Li, X., Huang, T.: Non-negative graph embedding. In: CVPR, pp. 1–8. IEEE (2008)

    Google Scholar 

  37. Zdunek, R., Cichocki, A.: Non-negative Matrix Factorization with Quasi-Newton Optimization. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 870–879. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. State Key Lab of CAD&CG, College of Computer Science, Zhejiang University, China

    Xinlei Chen, Cheng Li & Deng Cai

Authors
  1. Xinlei Chen
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  2. Cheng Li
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  3. Deng Cai
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Editor information

Editors and Affiliations

  1. Nanjing University of Science & Technology, 210094, Nanjing, China

    Jian Yang

  2. Department of Psychology, Peking University, 100871, Beijing, China

    Fang Fang

  3. School of Automation, Southeast University, 210096, Nanjing, P.R. China

    Changyin Sun

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Chen, X., Li, C., Cai, D. (2013). Spatially Correlated Nonnegative Matrix Factorization for Image Analysis. In: Yang, J., Fang, F., Sun, C. (eds) Intelligent Science and Intelligent Data Engineering. IScIDE 2012. Lecture Notes in Computer Science, vol 7751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36669-7_19

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  • DOI: https://doi.org/10.1007/978-3-642-36669-7_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36668-0

  • Online ISBN: 978-3-642-36669-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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