An Inexact Implementation of Smoothing Homotopy Method for Semi-Supervised Support Vector Machines

Show more

References

[1] A. Astorino and A. Fuduli, “Nonsmooth Optimization Techniques for Semi-Supervised Classification,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 29, No. 12, 2007, pp. 2135-2142.
doi:10.1109/TPAMI.2007.1102

[2] C. J. C. Burges, “A Tutorial on Support Vector Machines for Pattern Recognition, “Data Mining and Knowledge Discovery, Vol. 2, No. 2, 1998, pp. 121-167.
doi:10.1023/A:1009715923555

[3] E. L. Allgower and K. Georg, “Numerical Continuation Methods: An Introduction,” Springer-Vergal, Berlin, 1990.
doi:10.1007/978-3-642-61257-2

[4] E. Polak, J. O. Royset and R. S. Womersley, “Algorithms with Adaptive Smoothing for Finite Minimax Problems,” Journal of Optimization Theory and Application, Vol. 119, No. 3, 2003, pp. 459-484.
doi:10.1023/B:JOTA.0000006685.60019.3e

[5] G. Fung and O. Mangasarian, “Semi-Supervised Support Vector Machines for Unlabeled Data Classification,” Optimization Methods and Software, Vol. 15, No. 1, 2001, pp. 29-44. doi:10.1080/10556780108805809

[6] G. X., Liu, “Aggregate Homotopy Methods for Solving Sequential Max-Min Problems, Complementarity Problems and Variational Inequalities,” PhD Thesis, Jilin University, Jilin, 2003.

[7] K. Bennett and A. Demiriz, “Semi-Supervised Support Vector Machines,” In: M. S. Kearns, S. A. Solla and D. A. Cohn, Eds, Advances in Neural Information Processing Systems, MIT Press, Vol. 10, 1998, pp. 368-374.

[8] L. T. Watson, S. C. Billups and A. P. Morgan, “Algorithm 652 Hompack: A Suite of Codes for Globally Convergent Homotopy Algorithms,” ACM Transactions on Mathematical Software, Vol. 13, No. 3, 1987, pp. 281-310. doi:10.1145/29380.214343

[9] M. M. Mkela and P. Neittaanmki, “Nonsmooth Optimizatin: Analysis and Algorithms with Application to Optimal Control,” Utopia Press, Singapore, 1992.

[10] P. M. Murphy and D. W. Aha, “UCI Repository of Machine Learning Databases.
http://www.ics.uci.edu/ mlearn/MLRepository.html.

[11] O. Chapelle, V. Sindhwani and S. S. Keerthi, “Optimization Techniques for Semi-Supervised Support Vector Machines,” Journal of Machine Learning Research, Vol. 9, 2008, pp. 203-233.

[12] O. Chapelle, M. Chi and A. Zien, “A Continuation Method for Semi-Supervised SVMs,” ACM International Conference Proceeding Series, Proceedings of the 23rd international conference on Machine learning, Vol. 148, 2006, pp. 185-192.

[13] O. Chapelle and A. Zien, “Semi-Supervised Classification by Low Density Separation,” Proceedings of the Tenth International Workshop on Artificial Intelligence and Statistics, Vol. 1, 2005, pp. 57-64.

[14] O. Chapelle, V. Sindwani and S. Keerthi, “Branch and Bound for Semi-Supervised Support Vector Machines,” Advances in Neural Information Processing Systems 19, Proceedings of the 2006 Conference, MIT Press, Cambridge, 2007, pp. 217-224.

[15] O. L. Mangasarian and D. R. Musicant, “Lagrangian Support Vector Machines,” Journal of Machine Learning Research, Vol. 1, 2001, pp. 161-177.

[16] S. Birbil, S. C. Fang and J. Han, “Entropic Regularization Approach for Mathematical Programs with Equilibrium Constraints,” Technical Report, Industrial Engineering and Operations Research, Carolina, 2002.

[17] T. D. Bie, N. Cristianini, “Semi-Supervised Learning Using Semi-Definite Programming,” In: O. Chapelle, B. Scholkopf and A. Zien, Eds., Semi-Supervised Learning, MIT Press, Cambridge, 2006.

[18] X. J. Zhu, “Semi-Supervised Learning Literature Survey,” Technical Report 1530, Computer Science, University of Wisconsin-Madison, 2005.

[19] X. S. Li and S. C. Fang, “On the Entropic Regularization Method for Solving Min-Max Problems with Applications,” Mathematical Methods and Operations Research, Vol. 46, No. 1, 1997, pp. 119-130.
doi:10.1007/BF01199466

[20] Y. Xiao, H. J. Xiong and B. Yu, “Truncated Aggregate Homotopy Method for Nonconvex Nonlinear Programming,” Optimization Methods and Software, 2012, pp. 1- 18.

[21] H. J. Xiong and B. Yu, “Aggregate Homotopy Method for Semi-Supervised SVMs,” 2011 International Conference on Electric Information and Control Engineering, pp. 1147-1150.