Cauchy graph embedding

Proceedings of the 28th International Conference on Machine Learning, ICML 2011

Volumn , Issue , 2011, Pages 553-560

  Luo, Dijun ^a   Ding, Chris ^a   Nie, Feiping ^a   Huang, Heng ^a  

^a UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BENCHMARK DATA; EDGE WEIGHTS; GRAPH EMBEDDINGS; K-NEAREST NEIGHBORS; LAPLACIANS; LOCAL TOPOLOGY; LOW-DIMENSIONAL REPRESENTATION; MACHINE-LEARNING;

EMBEDDED SYSTEMS; LAPLACE TRANSFORMS; LEARNING SYSTEMS;

GRAPH THEORY;

EID: 80053449475     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (28)

1. Alpert, C.J. and Kahng, A.B. Recent directions in netlist partitioning: a survey. Integration, the VLSI Journal, 19:1-81, 1995.
2. Alter, O., Brown, P., and Botstein, D. Singular value decomposition for genome-wide expression data processing and modeling. PNAS, 97(18):10101-10106, 2000.
3. Ando, R. K. and Zhang, T. Learning on graph with laplacian regularization. In Advances in Neural Information Processing Systems 19, pp. 25-32.
4. Belkin, M. and Niyogi, P. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comp., 15(6):1373-1396, 2003. (Pubitemid 37049796)
5. Belkin, M. and Niyogi, P. Semi-supervised learning on riemannian manifolds. Machine Learning, pp. 209-239, 2004.
6. Bühler, T. and Hein, M. Spectral Clustering based on the graph p-Laplacian. In Proceedings of the 26th Annual International Conference on Machine Learning, pp. 81-88. ACM, 2009.
7. Cox, T. F. and Cox, M. A. A. Multidimensional scaling. Chapman and Hall, 2001.
8. Cun, Y. L. Le, Bottou, L., Bengio, Y., and Haffher, P. Gradient-based learning applied to document recognition. Proceedings of IEEE, 86(11):2278-2324, 1998.
9. Ding, C., He, X., Zha, H., Gu, M., and Simon, H. A min-max cut algorithm for graph partitioning and data clustering. Proc. IEEE Intl Conf. Data Mining (ICDM), pp. 107-114, 2001.
10. Fiedler, M. Algebraic connectivity of graphs. Czech. Math. J., 23:298-305, 1973.
11. Hall, K. M. R-dimensional quadratic placement algorithm. Management Science, 17:219-229, 1971.
12. Jolliffe, I.T. Principal Component Analysis. Springer, 2nd edition, 2002.
13. Luo, D., Ding, C., Huang, H., and Li, T. Non-negative Laplacian Embedding. In 2009 Ninth IEEE International Conference on Data Mining, pp. 337-346. IEEE, 2009.
14. Luo, D., Huang, H., Ding, C., and Nie, F. On the eigenvectors of p-Laplacian. Machine learning, 81(1):37-51, 2010. ISSN 0885-6125.
15. Nesterov, Y. Introductory lectures on convex optimization: A basic course. Kluwer Academic Publishers, 2003.
16. Ng, A. Y., Jordan, M. I., and Weiss, Y. On spectral clustering: Analysis and an algorithm. In Advances in Neural Information Processing Systems 14, Cambridge, MA, 2002. MIT Press.
17. Nie, F., Xu, D., Tsang, I., and Zhang, C. Flexible manifold embedding: A framework for semi-supervised and unsupervised dimension reduction. IEEE Transactions on Image Processing, 19(7):1921-1932, 2010.
18. Pothen, A., Simon, H. D., and Liou, K. P. Partitioning sparse matrices with egenvectors of graph. SIAM Journal of Matrix Anal. Appl., 11:430-452, 1990.
19. Roweis, S. and Saul, L. Nonlinear dimensionality reduction by locally linear embedding. Science, 290:2323-2326, 2000. (Pubitemid 32041578)
20. Shi, Jianbo and Malik, Jitendra. Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(8):888-905, 2000.
21. Simon, H. D. Partitioning of unstructured problems for parallel processing. Computing Systems in Engineering, 2(2/3):135-148, 1991.
22. Tenenbaum, J.B., De Silva, V., and Langford, J.C. A global geometric framework for nonlinear dimensionality reduction. Science, 290:2319-2323, 2000. (Pubitemid 32041577)
23. Turk, M. A. and Pentland, A. P. Face recognition using eigenfaces. In IEEE Conference on Computer Vision and Pattern Recognition, pp. 586-591, 1991.
24. Weinberger, K. Q., Sha, F., Zhu, Q., and Saul, L. K. Graph laplacian regularization for large-scale semidefinite programming. In NIPS, pp. 1489-1496.
25. Xiang, S., Nie, F., Zhang, C., and Zhang, C. Nonlinear dimensionality reduction with local spline embedding. IEEE Transactions on Knowledge and Data Engineering, 21(9):1285-1298, 2009.
26. Zhang, Z. and Zha, Z. Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM J. Scientific Computing, 26:313-338, 2004.
27. Zhou, D., Bousquet, O., Lal, T.N., Weston, J., and Schölkopf, B. Learning with local and global consistency. Proc. Neural Info. Processing Systems, 2003.
28. Zhu, X., Ghahramani, Z., and Lafferty, J. Semi-supervised learning using gaussian fields and harmonic functions. Proc. Int'l Conf. Machine Learning, 2003.