Inner Product Laplacian Embedding Based on Semidefinite Programming

References

[1] J. Tenenbaum, V. D. Silva and J. Langford, “A Global Geometric Framework for Nonlinear Dimensionality Reduction,” Science, Vol. 290, No. 5500, 2000, pp. 2319-2323. doi:10.1126/science.290.5500.2319

[2]
M. Belkin and P. Niyogi, “Laplacian Eigenmaps for Dimensionality Reduction and Data Representation,” Technical Report, University of Chicago, Chicago, 2001.

[3]
K. Q. Weinberger and L. K. Saul, “An Introduction to Nonlinear Dimensionality Reduction by Maximum Variance Unfolding,” AAAI Press, Boston, 2006.

[4]
H. Choi and S. Choi, “Kernel Isomap,” Electronics Letters, Vol. 40, No. 25, 2005, pp. 1612-1613.
doi:10.1049/el:20046791

[5]
M. Belkin, “Problems of Learning on Manifolds,” Ph.D. Dissertation, University of Chicago, Chicago, 2003.

[6]
K. Q. Weinberger, “Metric Learning with Convex Optimization,” Ph.D. Dissertation, University of Pennsylvania, Philadephia, 2007.

[7]
K. Q. Weinberger, F. Sha and L. K. Saul, “Learning a Kernel Matrix for Nonlinear Dimensionality Reduction,” Proceedings of the 21st International Conference on Machine Learning, Banff, 4-8 July 2004, pp. 839-846.

[8]
K. Q. Weinberger, B. D. Packer and L. K. Saul, “Nonlinear Dimensionality Reduction by Semidefinite Programming and Kernel Matrix Factorization,” Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics, Barbados, 6-8 January 2005, pp. 381-388.

[9]
K. Q. Weinberger and L. K. Saul, “An Introduction to Nonlinear Dimensionality Reduction by Maximum Variance Unfolding,” AAAI Press, Boston, 2006.

[10]
L. F. Sha and K. Saul, “Analysis and Extension of Spectral Methods for Nonlinear Dimensionality Reduction,” Proceedings of the 22nd International Conference on Machine Learning, Bonn, Vol. 15, 7-11 August 2005, pp. 721-728.
doi:10.1145/1102351.1102450

[11]
L. Yang, “Building k Edge-Disjoint Spanning Trees of Minimum Total Length for Isometric Data Embedding,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 27, No. 10, 2005, pp. 1680-1683.
doi:10.1109/TPAMI.2005.192

[12]
M. Belkin and P. Niyogi. “Semi-Supervised Learning on Riemannian Manifolds,” Machine Learning Journal, Vol. 56, No. 1-3, 2004, pp. 209-239.
doi:10.1023/B:MACH.0000033120.25363.1e

[13]
E. W. Dijkstra, “A Note on Two Problems in Connexion with Graphs,” Numerische MathematiK, Vol. 1, No. 1, 1959, pp. 269-271. doi:10.1007/BF01386390

[14]
USPS Handwritten Digit Dataset, 2010.
http://cs.nyu.edu/~roweis/data.html

[15]
COILT20 Database, 2010.
http://www1.cs.columbia.edu/CAVE/software/softlib/coil-20.php

[16]
B. Borchers, “CSDP, a C Library for Semidefinite Programming,” Optimization Methods and Software, Vol. 11-2, No. 1-4, 1999, pp. 613-623.
doi:10.1080/10556789908805765

[17]
Z. H. Zhou and J. Wang, “Machine Learning and Its Application2007,” Tsinghua University Press, Beijing, 2007.

[18]
Z. Y. Zhang, H. Y. Zha and M. Zhang, “Spectral Methods for Semi-Supervised Manifold Learning,” IEEE Conference on Computer Vision and Pattern Recognition, Anchorage, 24-26 June 2008, pp. 1-6.

[19]
X. H. Zeng, L. Gan and J. Wang, “A Semidefinite Programming Embedding Framework for Local Preserving Manifold Learning,” Chinese Conference on Pattern Recognition, Chongqing, 21-23 October 2010, pp. 257-261. doi:10.1109/CCPR.2010.5659162

[20]
O. Arandjelovic, “Unfolding a Face: From Singular to Manifold,” 9th Asian Conference on Computer Vision, Xi’an, 23-27 September 2009, pp. 203-213.

[21]
E. L. Hu, S. C. Chen and X. S. Yin, “Manifold Contraction for Semi-Supervised Classification,” Science in China, Vol. 53, No. 6, 2010, pp. 1170-1187.

[22]
D. Zhao and L. Yang, “Incremental Isometric Embedding of High Dimensional Data Using Connected Neighborhood Graphs,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 31, No. 1, 2009, pp. 86-98.
doi:10.1109/TPAMI.2008.34

[23]
M. H. C. Law and A. K. Jain, “Incremental Nonlinear Dimensionality Reduction by Manifold Learning,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 28, No. 3, 2006, pp. 377-391.
doi:10.1109/TPAMI.2006.56