Hybrid manifold embedding

IEEE Transactions on Neural Networks and Learning Systems

Volumn 25, Issue 12, 2014, Pages 2295-2302

  Liu, Yang ^a   Liu, Yan ^a   Chan, Keith C C ^a   Hua, Kien A ^b  

^a HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^b University of Central Florida   (United States)

Author keywords

Dimensionality reduction; geodesic clustering (GC); hybrid manifold embedding (HyME); locally conjugate discriminant projection (LCDP); supervised manifold learning.

Indexed keywords

GEODESY; MAPPING;

DIMENSIONALITY REDUCTION; GEODESIC CLUSTERING; HYBRID MANIFOLD EMBEDDING (HYME); LOCALLY CONJUGATE DISCRIMINANT PROJECTION (LCDP); SUPERVISED MANIFOLD LEARNING;

REDUCTION;

EID: 84913556325     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2014.2305760     Document Type: Article

References (42)

1. M. Belkin and P. Niyogi, "Laplacian eigenmaps and spectral techniques for embedding and clustering," in Proc. Adv. NIPS, 2001, pp. 585-591
2. C. Bregler and S. Omohundro, "Nonlinear manifold learning for visual speech recognition," in Proc. 5th ICCV, 1995, pp. 494-499
3. D. Cai, X. He, and J. Han, "Isometric projection," in Proc. AAAI, 2007, pp. 528-533
4. H.-T. Chen, H.-W. Chang, and T.-L. Liu, "Local discriminant embedding and its variants," in Proc. IEEE Comput. Soc. Conf. CVPR, Jun. 2005, pp. 846-853
5. J. Chen, Z. Ma, and Y. Liu, "Local coordinates alignment with global preservation for dimensionality reduction," IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 1, pp. 106-117, Jan. 2013
6. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, 3rd ed. Cambridge, MA, USA: MIT Press, 2009
7. Z. Fan, Y. Xu, and D. Zhang, "Local linear discriminant analysis framework using sample neighbors," IEEE Trans. Neural Netw., vol. 22, no. 7, pp. 1119-1132, Jul. 2011
8. H. R. Fang and Y. Saad, "Enhanced multilevel manifold learning," Dept. Comput. Sci. Eng., Univ. Minnesota, Minneapolis, MN, USA, Tech. Rep. ys-2012-2, 2012
9. H. R. Fang, S. Sakellaridi, and Y. Saad, "Multilevel manifold learning with application to spectral clustering," in Proc. 19th ACM CIKM, 2010, pp. 419-428
10. R. A. Fisher, "The use of multiple measurements in taxonomic problems," Ann. Eugenics, vol. 7, no. 2, pp. 179-188, 1936
11. B. Ge, Y. Shao, and Y. Shu, "Uncorrelated discriminant isometric projection for face recognition," in Proc. Inf. Comput. Appl., vol. 307. 2012, pp. 138-145
12. X. Geng, D.-C. Zhan, and Z.-H. Zhou, "Supervised nonlinear dimensionality reduction for visualization and classification," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 35, no. 6, pp. 1098-1107, Dec. 2005
13. T. F. Gonzalez, "Clustering to minimize the maximum intercluster distance," Theoretical Comput. Sci., vol. 38, pp. 293-306, 1985
14. D. B. Graham and N. M. Allinson, "Characterizing virtual eigensignatures for general purpose face recognition," in Proc. Face Recognit., From Theory Appl., NATO ASI Ser. F, Comput. Syst. Sci., vol. 163. 1998, pp. 446-456
15. X. He, D. Cai, S. Yan, and H.-J. Zhang, "Neighborhood preserving embedding," in Proc. 10th IEEE ICCV, Oct. 2005, pp. 1208-1213
16. X. He, S. Yan, Y. Hu, P. Niyogi, and H.-J. Zhang, "Face recognition using Laplacianfaces," IEEE Trans. Pattern Anal. Mach. Intell., vol. 27, no. 3, pp. 328-340, Mar. 2005
17. H. Hotelling, "Analysis of a complex of statistical variables into principal components," J. Educ. Psychol., vol. 24, no. 6, pp. 417-441, 1933
18. Y. Hou, P. Zhang, X. Xu, X. Zhang, and W. Li, "Nonlinear dimensionality reduction by locally linear inlaying," IEEE Trans. Neural Netw., vol. 20, no. 2, pp. 300-315, Feb. 2009
19. J. J. Hull, "A database for handwritten text recognition research," IEEE Trans. Pattern Anal. Mach. Intell., vol. 16, no. 5, pp. 550-554, May 1994
20. Z. Jin, J.-Y. Yang, Z.-S. Hu, and Z. Lou, "Face recognition based on the uncorrelated discriminant transformation," Pattern Recognit., vol. 34, no. 7, pp. 1405-1416, 2001
21. T.-K. Kim and J. Kittler, "Locally linear discriminant analysis for multimodally distributed classes for face recognition with a single model image," IEEE Trans. Pattern Anal. Mach. Intell., vol. 27, no. 3, pp. 318-327, Mar. 2005
22. Y. Liu, Y. Liu, and K. C. C. Chan, "Ordinal regression via manifold learning," in Proc. 25th AAAI Conf. Artif. Intell., 2011, pp. 398-403
23. D. Luo, F. Nie, C. Ding, and H. Huang, "Multi-subspace representation and discovery," in Proc. ECML/PKDD, 2011, pp. 405-420
24. M. Mahajan, P. Nimbhorkar, and K. Varadarajan, "The planar k-means problem is NP-hard," Theoretical Comput. Sci., vol. 442, pp. 13-21, Jul. 2012
25. F. Nie, S. Xiang, and C. Zhang, "Neighborhood minmax projections," in Proc. 20th IJCAI, 2007, pp. 993-998
26. R. Pless, "Image spaces and video trajectories: Using isomap to explore video sequences," in Proc. 9th IEEE ICCV, Oct. 2003, pp. 1433-1440
27. A. Rahimi, B. Recht, and T. Darrell, "Learning appearance manifolds from video," in Proc. CVPR, 2005, pp. 868-875
28. S. Roweis and L. K. Saul, "Nonlinear dimensionality reduction by locally linear embedding," Science, vol. 290, no. 5500, pp. 2323-2326, 2000
29. T. Sim, S. Baker, and M. Bsat, "The CMU pose, illumination, and expression database," IEEE Trans. Pattern Anal. Mach. Intell., vol. 25, no. 1, pp. 1615-1618, Dec. 2003
30. M. Sun, J. Yang, C. Liu, and J. Yang, "Similarity preserving principal curve: An optimal 1-D feature extractor for data representation," IEEE Trans. Neural Netw., vol. 21, no. 9, pp. 1445-1456, Sep. 2010
31. J. B. Tenenbaum, V. De Silva, and J. C. Langford, "A global geometric framework for nonlinear dimensionality reduction," Science, vol. 290, no. 5500, pp. 2319-2323, 2000
32. M. Vlachos, C. Domeniconi, D. Gunopulos, G. Kollios, and N. Koudas, "Non-linear dimensionality reduction techniques for classification and visualization," in Proc. 8th ACM SIGKDD Int. Conf. Knowl. Discovery Data Mining, 2002, pp. 645-651
33. H. Wang, H. Huang, and C. H. Q. Ding, "Discriminant Laplacian embedding," in Proc. 24th AAAI, 2010, pp. 618-623
34. H. Wang, S. Chen, Z. Hu, and W. Zheng, "Locality-preserved maximum information projection," IEEE Trans. Neural Netw., vol. 19, no. 4, pp. 571-585, Apr. 2008
35. W. Wong and H. Zhao, "Supervised optimal locality preserving projection," Pattern Recognit., vol. 45, no. 1, pp. 186-197, 2012
36. S. Yan, Y. Hu, D. Xu, H.-J. Zhang, B. Zhang, and Q. Cheng, "Nonlinear discriminant analysis on embedded manifold," IEEE Trans. Circuits Syst. Video Technol., vol. 17, no. 4, pp. 468-477, Apr. 2007
37. J. Zhang, X. Wang, U. Krüger, and F.-Y. Wang, "Principal curve algorithms for partitioning high-dimensional data spaces," IEEE Trans. Neural Netw., vol. 22, no. 3, pp. 367-380, Mar. 2011
38. L. Zhang, L. Qiao, and S. Chen, "Graph-optimized locality preserving projections," Pattern Recognit., vol. 43, no. 6, pp. 1993-2002, 2010
39. T. Zhang, D. Tao, X. Li, and J. Yang, "Patch alignment for dimensionality reduction," IEEE Trans. Knowl. Data Eng., vol. 21, no. 9, pp. 1299-1313, Sep. 2009
40. Y. Zheng, B. Fang, Y. Y. Tang, T. Zhang, and R. Liu, "Learning orthogonal projections for isomap," Neurocomputing, vol. 103, pp. 149-154, Mar. 2013
41. T. Zhou and D. Tao, "Double shrinking sparse dimension reduction," IEEE Trans. Image Process., vol. 22, no. 1, pp. 244-257, Jan. 2013
42. T. Zhou, D. Tao, and X. Wu, "Manifold elastic net: A unified framework for sparse dimension reduction," Data Mining Knowl. Discovery, vol. 22, no. 3, pp. 340-371, 2011