Using locally estimated geodesic distance to optimize neighborhood graph for isometric data embedding

Pattern Recognition

Volumn 41, Issue 7, 2008, Pages 2226-2236

  Wen, Guihua ^a   Jiang, Lijun ^a   Wen, Jun ^b  

^a SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

^b HUBEI UNIVERSITY FOR NATIONALITIES   (China)

Author keywords

Geodesic distance; Isometric data embedding; Manifold learning; Neighborhood graph; Nonlinear neighborhood

Indexed keywords

COMPUTATIONAL COMPLEXITY; DATA PROCESSING; DISTANCE MEASUREMENT; GRAPH THEORY;

GEODESIC DISTANCE; ISOMETRIC DATA EMBEDDING; MANIFOLD LEARNING; NEIGHBORHOOD GRAPH; NONLINEAR NEIGHBORHOOD;

GEODESY;

EID: 41549142718     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2007.12.015     Document Type: Article

References (19)

1. Roweis S.T., and Saul L.K. Nonlinear dimensionality reduction by locally linear embedding. Science 290 (2000) 2323-2326
2. Tenenbaum J.B., de Silva V., and Langford J.C. A global geometric framework for nonlinear dimensionality reduction. Science 290 (2000) 2319-2323
3. Silva V.D., and Tenenbaum J.B. Global versus local methods in nonlinear dimensionality reduction. Neural Inf. Process. Syst. 15 (2003) 705-712
4. Geng X., Zhan D.C., and Zhou Z.H. Supervised nonlinear dimensionality reduction for visualization and classification. IEEE Trans. Syst. Man Cybern. 35 (2005) 1098-1107
5. Law M.H.C., and Jain A.K. Incremental nonlinear dimensionality reduction by manifold learning. IEEE Trans. Pattern Anal. Mach. Intell. 28 (2006) 377-391
6. Yang L. Building k edge-disjoint spanning trees of minimum total length for isometric data embedding. IEEE Trans. Pattern Anal. Mach. Intell. 27 (2005) 1680-1683
7. L. Yang, k-Edge connected neighborhood graph for geodesic distance estimation and nonlinear data projection, in: Proceedings of the 17th International Conference on Pattern Recognition, vol. 1, August 2004, pp. 196-199.
8. Yang L. Building k-connected neighborhood graphs for isometric data embedding. IEEE Trans. Pattern Anal. Mach. Intell. 28 5 (2006) 827-831
9. A. Saxena, A. Gupta, A. Mukerjee, Non-linear dimensionality reduction by locally linear isomaps, Lecture Notes in Computer Science, vol. 3316, 2004, pp. 1038-1043.
10. O. Kouropteva, O. Okun, M. Pietikainen, Selection of the optimal parameter value for the locally linear embedding algorithm, in: Proceedings of 1st International Conference on Fuzzy Systems and Knowledge Discovery, Singapore, 2002, pp. 359-363.
11. G. Wen, L. Jiang, J. Wen, N.R. Shadbolt, Clustering-based nonlinear dimensionality reduction on manifold, Lecture Notes in Artificial Intelligence (LNAI), vol. 4099, 2006, pp. 444-453.
12. G. Wen, L. Jiang, Clustering-based locally linear embedding, in: Proceedings of 2006 IEEE International Conference on System, Man and Cybernetics, 2006, pp. 4192-4196.
13. G. Wen, L. Jiang, N.R. Shadbolt, Using graph algebra to optimize neighborhood for isometric mapping, in: 20th International Joint Conference on Artificial Intelligence (IJCAI-07), India, 2007, pp. 2398-2403.
14. G. Wen, L. Jiang, Globalizing local neighborhood for locally linear embedding, in: Proceedings of 2006 IEEE International Conference on System, Man and Cybernetics, 2006, pp. 3491-3496.
15. Corts J., Martnez S., and Bullo F. Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions. IEEE Trans. Autom. Control 51 8 (2006) 1289-1298
16. Y. Wu, K.L. Chan, L. Wang, Face recognition based on discriminative manifold learning, in: Proceedings of the 17th International Conference on Pattern Recognition, 2004, pp. 1038-1043.
17. Samko O., Marshall A.D., and Rosin P.L. Selection of the optimal parameter value for the Isomap algorithm. Pattern Recognition Lett. 27 (2006) 968-979
18. G. Wen, L. Jiang, J. Wen, N.R. Shadbolt, Performing locally linear embedding with adaptive neighborhood size on manifold, Lecture Notes in Artificial Intelligence (LNAI), vol. 4099, 2006, pp. 985-989.
19. Choi H., and Choi S. Robust kernel ISOMAP. Pattern Recognition 40 (2007) 853-862