Graph Regularized Non-Negative Low-Rank Matrix Factorization for Image Clustering

IEEE Transactions on Cybernetics

Volumn 47, Issue 11, 2017, Pages 3840-3853

  Li, Xuelong ^a   Cui, Guosheng ^a,b   Dong, Yongsheng ^a,c  

^a XI AN INSTITUTE OF OPTICS AND PRECISION MECHANICS   (China)

^b INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^c HENAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Data representation; graph regularization; image clustering; low rank recovery; non negative matrix factorization (NMF)

Indexed keywords

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTER VISION; FACTORIZATION; ITERATIVE METHODS; LEARNING SYSTEMS; PRINCIPAL COMPONENT ANALYSIS;

DATA REPRESENTATIONS; HIGH-DIMENSIONAL IMAGES; ITERATIVE ALGORITHM; LOW-DIMENSIONAL REPRESENTATION; MANIFOLD STRUCTURES; NONNEGATIVE MATRIX FACTORIZATION; OBJECTIVE FUNCTIONS; ROBUST PRINCIPAL COMPONENT ANALYSIS;

MATRIX ALGEBRA;

ALGORITHM; ARTICLE; PRINCIPAL COMPONENT ANALYSIS;

EID: 84978827246     PISSN: 21682267     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCYB.2016.2585355     Document Type: Article

References (70)

1. C. Elkan, "Using the triangle inequality to accelerate k-means, " in Proc. 20th Int. Conf. Mach. Learn. (ICML), Washington, DC, USA, Aug. 2003, pp. 147-153.
2. J. Shi, J. Malik, "Normalized cuts, image segmentation, " IEEE Trans. Pattern Anal. Mach. Intell., vol. 22, no. 8, pp. 888-905, Aug. 2000.
3. Q. Huang, T. Wang, D. Tao, X. Li, "Biclustering learning of trading rules, " IEEE Trans. Cybern., vol. 45, no. 10, pp. 2287-2298, Oct. 2015.
4. C. Hou, F. Nie, D. Yi, D. Tao, "Discriminative embedded clustering: A framework for grouping high-dimensional data, " IEEE Trans. Neural Netw. Learn. Syst., vol. 26, no. 6, pp. 1287-1299, Jun. 2015.
5. D. Tao, L. Jin, W. Liu, X. Li, "Hessian regularized support vector machines for mobile image annotation on the cloud, " IEEE Trans. Multimedia, vol. 15, no. 4, pp. 833-844, Jun. 2013.
6. L. Chen, D. Xu, I. W. Tsang, X. Li, "Spectral embedded hashing for scalable image retrieval, " IEEE Trans. Cybern., vol. 44, no. 7, pp. 1180-1190, Jul. 2014.
7. B. Banerjee , et al., "A new self-training-based unsupervised satellite image classification technique using cluster ensemble strategy, " IEEE Geosci. Remote Sens. Lett., vol. 12, no. 4, pp. 741-745, Apr. 2015.
8. G. Liu, Y. Zhang, A. Wang, "Incorporating adaptive local information into fuzzy clustering for image segmentation, " IEEE Trans. Image Process., vol. 24, no. 11, pp. 3990-4000, Nov. 2015.
9. R. Datta, D. Joshi, J. Li, J. Z. Wang, "Image retrieval: Ideas, influences, and trends of the new age, " ACM Comput. Surv., vol. 40, no. 2, 2008, Art. no. 5.
10. X. Zhu, X. Li, S. Zhang, "Block-row sparse multiview multilabel learning for image classification, " IEEE Trans. Cybern., vol. 46, no. 2, pp. 450-461, Feb. 2016.
11. R. Ye, X. Li, "Compact structure hashing via sparse and similarity preserving embedding, " IEEE Trans. Cybern., vol. 46, no. 3, pp. 718-729, Mar. 2016.
12. H. Zhang, J. K. L. Ho, Q. M. J. Wu, Y. Ye, "Multidimensional latent semantic analysis using term spatial information, " IEEE Trans. Cybern., vol. 43, no. 6, pp. 1625-1640, Dec. 2013.
13. X. Li, S. Lin, S. Yan, D. Xu, "Discriminant locally linear embedding with high-order tensor data, " IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 38, no. 2, pp. 342-352, Apr. 2008.
14. L. Liu, L. Shao, X. Zhen, X. Li, "Learning discriminative key poses for action recognition, " IEEE Trans. Cybern., vol. 43, no. 6, pp. 1860-1870, Dec. 2013.
15. D. Tao, L. Jin, Z. Yang, X. Li, "Rank preserving sparse learning for Kinect based scene classification, " IEEE Trans. Cybern., vol. 43, no. 5, pp. 1406-1417, Oct. 2013.
16. Y. Yang, H. T. Shen, F. Nie, R. Ji, X. Zhou, "Nonnegative spectral clustering with discriminative regularization, " in Proc. 25th AAAI Conf. Artif. Intell., San Francisco, CA, USA, Aug. 2011, pp. 555-560.
17. X. Fang , et al., "Locality, similarity preserving embedding for feature selection, " Neurocomputing, vol. 128, pp. 304-315, Mar. 2014.
18. F. Nie, C. Ding, D. Luo, H. Huang, "Improved minmax cut graph clustering with nonnegative relaxation, " in Proc. Eur. Conf. Mach. Learn. Knowl. Disc. Databases ECML PKDD Part II, Barcelona, Spain, Sep. 2010, pp. 451-466.
19. F. Nie, Z. Zeng, I. W. Tsang, D. Xu, C. Zhang, "Spectral embedded clustering: A framework for in-sample, out-of-sample spectral clustering, " IEEE Trans. Neural Netw., vol. 22, no. 11, pp. 1796-1808, Nov. 2011.
20. M. Turk, A. Pentland, "Eigenfaces for recognition, " J. Cogn. Neurosci., vol. 3, no. 1, pp. 71-86, 1991.
21. J. Makhoul, S. Roucos, H. Gish, "Vector quantization in speech coding, " Proc. IEEE, vol. 73, no. 11, pp. 1551-1588, Nov. 1985.
22. D. D. Lee, H. S. Seung, "Learning the parts of objects by nonnegative matrix factorization, " Nature, vol. 401, no. 6755, pp. 788-791, 1999.
23. D. D. Lee, H. S. Seung, "Algorithms for non-negative matrix factorization, " in Proc. Adv. Neural Inf. Process. Syst. (NIPS), Denver, CO, USA, 2000, pp. 556-562.
24. N. K. Logothetis, D. L. Sheinberg, "Visual object recognition, " Annu. Rev. Neurosci., vol. 19, no. 1, pp. 577-621, 1996.
25. S. E. Palmer, "Hierarchical structure in perceptual representation, " Cogn. Psychol., vol. 9, no. 4, pp. 441-474, 1977.
26. E. Wachsmuth, M. Oram, D. Perrett, "Recognition of objects and their component parts: Responses of single units in the temporal cortex of the macaque, " Cereb. Cortex, vol. 4, no. 5, pp. 509-522, 1994.
27. W. Xu, X. Liu, Y. Gong, "Document clustering based on nonnegative matrix factorization, " in Proc. 26th Annu. Int. ACM SIGIR Conf. Res. Develop. Inf. Retr., Toronto, ON, Canada, Jul. 2003, pp. 267-273.
28. S. Z. Li, X. W. Hou, H. J. Zhang, Q. S. Cheng, "Learning spatially localized, parts-based representation, " in Proc. IEEE Int. Conf. Comput. Vis. Pattern Recognit., vol. 1. Kauai, HI, USA, Dec. 2001, pp. 207-212.
29. P. O. Hoyer, "Non-negative sparse coding, " in Proc. IEEE Workshop Neural Netw. Signal Process., Martigny, Switzerland, 2002, pp. 557-565.
30. D. Cai, X. He, J. Han, T. S. Huang, "Graph regularized nonnegative matrix factorization for data representation, " IEEE Trans. Pattern Anal. Mach. Intell., vol. 33, no. 8, pp. 1548-1560, Aug. 2011.
31. K. Zeng, J. Yu, C. Li, J. You, T. Jin, "Image clustering by hypergraph regularized non-negative matrix factorization, " Neurocomputing, vol. 138, pp. 209-217, Aug. 2014.
32. S. Zafeiriou, A. Tefas, I. Buciu, I. Pitas, "Exploiting discriminant information in nonnegative matrix factorization with application to frontal face verification, " IEEE Trans. Neural Netw., vol. 17, no. 3, pp. 683-695, May 2006.
33. J. Wright, A. Ganesh, S. Rao, Y. Peng, Y. Ma, "Robust principal component analysis: Exact recovery of corrupted low-rank matrices via convex optimization, " in Proc. Adv. Neural Inf. Process. Syst. (NIPS), Vancouver, BC, Canada, 2009, pp. 2080-2088.
34. E. J. Candès, X. Li, Y. Ma, J. Wright, "Robust principal component analysis?" J. ACM, vol. 58, no. 3, 2011, Art. no. 11.
35. J. Wright, A. Y. Yang, A. Ganesh, S. S. Sastry, Y. Ma, "Robust face recognition via sparse representation, " IEEE Trans. Pattern Anal. Mach. Intell., vol. 31, no. 2, pp. 210-227, Feb. 2009.
36. F. Nie, J. Yuan, H. Huang, "Optimal mean robust principal component analysis, " in Proc. 31st Int. Conf. Mach. Learn. (ICML), Beijing, China, Jun. 2014, pp. 1062-1070.
37. C. H. Papadimitriou, H. Tamaki, P. Raghavan, S. Vempala, "Latent semantic indexing: A probabilistic analysis, " in Proc. 17th ACM SIGACT SIGMOD SIGART Symp. Principles Database Syst., Seattle, WA, USA, Jun. 1998, pp. 159-168.
38. H. Liu, Z. Wu, X. Li, D. Cai, T. S. Huang, "Constrained nonnegative matrix factorization for image representation, " IEEE Trans. Pattern Anal. Mach. Intell., vol. 34, no. 7, pp. 1299-1311, Jul. 2012.
39. Z. Li, J. Liu, H. Lu, "Structure preserving non-negative matrix factorization for dimensionality reduction, " Comput. Vis. Image Understanding, vol. 117, no. 9, pp. 1175-1189, Sep. 2013.
40. P. O. Hoyer, "Non-negative matrix factorization with sparseness constraints, " J. Mach. Learn. Res., vol. 5, no. 11, pp. 1457-1469, 2004.
41. L.-X. Li, L. Wu, H.-S. Zhang, F.-X. Wu, "A fast algorithm for nonnegative matrix factorization, its convergence, " IEEE Trans. Neural Netw. Learn. Syst., vol. 25, no. 10, pp. 1855-1863, Oct. 2014.
42. N. Guan, D. Tao, Z. Luo, B. Yuan, "Online nonnegative matrix factorization with robust stochastic approximation, " IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 7, pp. 1087-1099, Jul. 2012.
43. Y. Chen, J. Zhang, D. Cai, W. Liu, X. He, "Nonnegative local coordinate factorization for image representation, " IEEE Trans. Image Process., vol. 22, no. 3, pp. 969-979, Mar. 2013.
44. B. Gao, W. L. Woo, S. S. Dlay, "Variational regularized 2-D nonnegative matrix factorization, " IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 5, pp. 703-716, May 2012.
45. L. Wei, N. Guan, X. Zhang, Z. Luo, D. Tao, "Orthogonal nonnegative locally linear embedding, " in Proc. IEEE Int. Conf. Syst. Man Cybern. (SMC), Manchester, U.K., Oct. 2013, pp. 2134-2139.
46. Y. Yuan, X. Li, Y. Pang, X. Lu, D. Tao, "Binary sparse nonnegative matrix factorization, " IEEE Trans. Circuits Syst. Video Technol., vol. 19, no. 5, pp. 772-777, May 2009.
47. O. Zoidi, A. Tefas, I. Pitas, "Multiplicative update rules for concurrent nonnegative matrix factorization, maximum margin classification, " IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 3, pp. 422-434, Mar. 2013.
48. Y. Xiao , et al., "Topographic NMF for data representation, " IEEE Trans. Cybern., vol. 44, no. 10, pp. 1762-1771, Oct. 2014.
49. J. Huang, F. Nie, H. Huang, C. Ding, "Robust manifold nonnegative matrix factorization, " Trans. Knowl. Disc. Data, vol. 8, no. 3, 2014, Art. no. 11.
50. F. R. Chung, Spectral Graph Theory. Providence, RI, USA: Amer. Math. Soc., 1997.
51. F. Nie, X. Wang, M. I. Jordan, H. Huang, "The constrained Laplacian rank algorithm for graph-based clustering, " in Proc. 30th AAAI Conf. Artif. Intell., Phoenix, AZ, USA, Feb. 2016, pp. 1969-1976.
52. Y. Huang, Q. Liu, S. Zhang, D. N. Metaxas, "Image retrieval via probabilistic hypergraph ranking, " in Proc. IEEE Int. Conf. Comput. Vis. Pattern Recognit., San Francisco, CA, USA, Jun. 2010, pp. 3376-3383.
53. D. Zhou, J. Huang, B. Schölkopf, "Learning with hypergraphs: Clustering, classification, embedding, " in Proc. Adv. Neural Inf. Process. Syst. (NIPS), Vancouver, BC, Canada, Dec. 2006, pp. 1601-1608.
54. S. Agarwal, K. Branson, S. Belongie, "Higher order learning with graphs, " in Proc. 23rd Int. Conf. Mach. Learn. (ICML), Pittsburgh, PA, USA, Jun. 2006, pp. 17-24.
55. J. Yu, D. Tao, M. Wang, Y. Rui, "Learning to rank using user clicks and visual features for image retrieval, " IEEE Trans. Cybern., vol. 45, no. 4, pp. 767-779, Apr. 2015.
56. J. Yang, S. Yang, Y. Fu, X. Li, T. Huang, "Non-negative graph embedding, " in Proc. IEEE Int. Conf. Comput. Vis. Pattern Recognit., Anchorage, AK, USA, Jun. 2008, pp. 1-8.
57. S. An, J. Yoo, S. Choi, "Manifold-respecting discriminant nonnegative matrix factorization, " Pattern Recognit. Lett., vol. 32, no. 6, pp. 832-837, 2011.
58. V. P. Pauca, F. Shahnaz, M. W. Berry, R. J. Plemmons, "Text mining using non-negative matrix factorizations, " in Proc. SDM, Orlando, FL, USA, 2004, pp. 452-456.
59. N. Guan, D. Tao, Z. Luo, B. Yuan, "Manifold regularized discriminative nonnegative matrix factorization with fast gradient descent, " IEEE Trans. Image Process., vol. 20, no. 7, pp. 2030-2048, Jul. 2011.
60. T. Zhou, D. Tao, "GoDec: Randomized lowrank & sparse matrix decomposition in noisy case, " in Proc. 28th Int. Conf. Mach. Learn. (ICML), Bellevue, WA, USA, Jun. 2011, pp. 33-40.
61. M. Fazel, E. Candes, B. Recht, P. Parrilo, "Compressed sensing and robust recovery of low rank matrices, " in Proc. 42nd Asilomar Conf. Signals Syst. Comput., Pacific Grove, CA, USA, Oct. 2008, pp. 1043-1047.
62. S. Roweis, "EM algorithms for PCA, SPCA, " in Proc. Adv. Neural Inf. Process. Syst. (NIPS), Denver, CO, USA, 1997, pp. 626-632.
63. J. Kivinen, M. K. Warmuth, "Additive versus exponentiated gradient updates for linear prediction, " in Proc. 27th Annu. ACM Symp. Theory Comput., Las Vegas, NV, USA, May 1995, pp. 209-218.
64. L. Lovász, M. D. Plummer, Matching Theory, vol. 367. Providence, RI, USA: Amer. Math. Soc., 2009.
65. W. Xu, X. Liu, Y. Gong, "Document clustering based on nonnegative matrix factorization, " in Proc. 26th Annu. Int. ACM SIGIR Conf. Res. Develop. Inf. Retrieval, Toronto, ON, Canada, Jul. 2003, pp. 267-273.
66. F. Shahnaz, M. W. Berry, V. P. Pauca, R. J. Plemmons, "Document clustering using nonnegative matrix factorization, " Inf. Process. Manage., vol. 42, no. 2, pp. 373-386, 2006.
67. I. Jolliffe, Principal Component Analysis. New York, NY, USA: Wiley, 2005.
68. D. Cai, X. He, X. Wu, J. Han, "Non-negative matrix factorization on manifold, " in Proc. IEEE Int. Conf. Data Min., Pisa, Italy, Dec. 2008, pp. 63-72.
69. Y. Dong, D. Tao, X. Li, J. Ma, J. Pu, "Texture classification and retrieval using shearlets, linear regression, " IEEE Trans. Cybern., vol. 45, no. 3, pp. 358-369, Mar. 2015.
70. Y. Dong, D. Tao, X. Li, "Nonnegative multiresolution representation-based texture image classification, " ACM Trans. Intell. Syst. Technol., vol. 7, no. 1, 2015, Art. no. 4.