On numerical optimization theory of infinite kernel learning

Journal of Global Optimization

Volumn 48, Issue 2, 2010, Pages 215-239

  Ozogur Akyuz, S ^a   Weber, G W ^b,c  

^a BAHCESEHIR UNIVERSITY   (Turkey)

^b MIDDLE EAST TECHNICAL UNIVERSITY   (Turkey)

^c UNIVERSITY OF SIEGEN   (Germany)

Author keywords

Conceptual reduction; Continuous optimization; Discretization; Exchange method; Infinite kernel learning; Infinite programming; Machine learning; Semi infinite optimization; Support vector machines; Triangulation

Indexed keywords

CONCEPTUAL REDUCTION; CONTINUOUS OPTIMIZATION; DISCRETIZATIONS; EXCHANGE METHOD; INFINITE PROGRAMMING; KERNEL LEARNING; MACHINE-LEARNING; SEMI-INFINITE OPTIMIZATION; SUPPORT VECTOR;

CONVERGENCE OF NUMERICAL METHODS; OPTIMIZATION; SITE SELECTION; SUPPORT VECTOR MACHINES; TRIANGULATION;

LEARNING ALGORITHMS;

EID: 77957865414     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-009-9488-x     Document Type: Article

References (25)

1. Anderson E.J., Nash P.: Linear Programming in Infinite-Dimensional Spaces. Wiley, New York (1987)
2. Apostol T.M.: Mathematical Analysis: A Modern Approach to Advanced Calculus. Addison Wesley, Reading (1974)
3. Argyriou, A., Hauser, R., Micchelli, C., Pontil, M.: A dc-programming algorithm for kernel selection. In: Proceedings of the 23rd International Conference on Machine Learning, Pittsburgh, PA (2006)
4. Bach, F.R., Lanckriet, G.R.G.: Multiple kernel learning, conic duality, and the smo algorithm. In: Proceedings of the 21st International Conference on Machine Learning (2004)
5. Chang, C.-C., Lin, C.-J.: Libsvm: a library for support vector machines. http://www.csie.ntu.edu.tw/cjlin/libsvm (2001)
6. Hettich R., Jongen H.Th.: Semi-infinite programming: conditions of optimality and applications. In: Stoer, J. (eds) Optimization Techniques 2. Lecture notes in control and Information Science, Springer, Berlin, Heidelberg, New York (1978)
7. R. Hettich O. Kortanek 1993 Semi-infinite programming: theory, methods and applications SIAM Rev. 35 3 380 429 10.1137/1035089
8. Hettich R., Zencke P.: Numerische Methoden der Approximation und semi-infiniten Optimierung. Tuebner, Stuttgart (1982)
9. Jongen H.Th., Jonker P., Twilt F.: Nonlinear Optimization in Finite Dimensions-Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects. Springer, New York (2000)
10. Ozan Y.: Scientific discussion with YIldIray Ozan. Department of Mathematics, METU, Ankara (2008)
11. Özöǧür-Akyüz, S.: A Mathematical Contribution of Statistical Learning and Continuous Optimization Using Infinite and Semi-Infinite Programming, to Computational Statistics (submitted). PhD thesis, Middle East Technical University, Insitiute of Applied Mathematics, Department of Scientific Computing, February (2009)
12. Özöǧür-Akyüz, S., Weber, G.W.: Modelling of kernel machines by infinite and semi-infinite programming. In: Hakim, A.H., Vasant, P., Barsoum, N. (eds.) Proceedings of the Second Global Conference on Power Control and Optimization, AIP Conference Proceedings, Bali, Indonesia. Mathematical and Statistical Physics, pp. 306-313. ISBN 978-0-7354-0696-4 (August 2009), 1-3 June (2009)
13. Özöǧür-Akyüz, S., Weber, G.-W.: Learning with infinitely many kernels via infinite and semi-infinite programming. Accepted to Optimization Methods and Software
14. Özöǧür-Akyüz, S., Hussain, Z., Shawe-Taylor, J.: Prediction with the SVM using test point margins. In: R. Sharda, S.V.B (eds) Special issue on Data Mining of Journal of (German B) In Annals of Information Systems. Springer Book Series (2009) (in press)
15. S. Özöǧür-Akyüz J. Shawe-Taylor G.-W. Weber Z.B. Ögel 2009 Pattern analysis for the prediction of eukoryatic pro-peptide cleavage sites Discret. Appl. Math. 157 10 2388 2394 10.1016/j.dam.2008.06.043
16. Özöǧür-Akyüz, S., Weber, G.-W.: Learning with infinitely many kernels via semi-infinite programming. In: Continuous Optimization and Knowledge Based Technologies, 20th EURO Mini conference, Lithunia, pp. 342-348 (2008)
17. Pardalos, P.M., Hansen, P. (eds.): Data Mining andMathematical Programming, volume CRM 45. American Mathematical Society, Providence (2008)
18. J.-J. Rückmann G.-W. Weber 1998 Semi-infinite optimization: Excisional stability of noncompact feasible sets Sibir. Math. Z. 39 129 145
19. Seref, O., Kundakcioglu, O.E., Pardalos, P.M. (eds.): Data Mining, Systems Analysis, and Optimization in Biomedicine. Springer, New York (2007)
20. Shiryaev A.N.: Probability. Springer, New York (1995)
21. S. Sonnenburg G. Räetsch C. Schafer B. Schölkopf 2006 Large scale multiple kernel learning J. Mach. Learn. Res. 7 1531 1565
22. Still, G.: Semi-infinite programming: An introduction, preliminary version. Technical report, University of Twente Department of Applied Mathematics, Enschede, The Netherlands (2004)
23. Vaz, A.I.F., Fernandes, E.M.G.P., Gomes, M.P.S.F.: Discretization methods for semi-infinite programming. Investigaç ǎo Operacional 21(1), (2001)
24. Weber G.-W.: Generalized Semi-Infinite Optimization and Related Topics, volume 29 of Research and Exposition in Mathematics. Heldermann, Berlin (2003)
25. Yershova, A., LaVelle, S.M.: Deterministic sampling methods for spheres and so(3). In: IEEE International Conference on Robotics and Automation (ICRA) (2004)