Estimating the optimal margins of embeddings in Euclidean half spaces

Machine Learning

Volumn 51, Issue 3, 2003, Pages 263-281

  Forster, Jürgen ^a   Schmitt, Niels ^a   Simon, Hans Ulrich ^a   Suttorp, Thorsten ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

Euclidean half spaces; Maximal margins; Singular value decomposition

Indexed keywords

BOOLEAN FUNCTIONS; EIGENVALUES AND EIGENFUNCTIONS; OPTIMIZATION; SET THEORY; THEOREM PROVING; VECTORS;

EUCLIDEAN HALF SPACES; OPTIMAL MARGINS; SINGULAR VALUE DECOMPOSITION;

MATRIX ALGEBRA;

EID: 0038629051     PISSN: 08856125     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022905618164     Document Type: Article

References (13)

1. Ben-David, S. (2000). Personal Communication.
2. Ben-David, S., Eiron, N., & Simon, H. U., (2001). Limitations of learning via embeddings in Euclidean half-spaces. To appear in the Journal of Machine Learning Research. A preliminary version appeared in the Proceedings of the 14th Annual Conference on Computational Learning Theory (pp. 385-401). Berlin: Springer.
3. Blumer, A., Ehrenfeucht, A., Haussler, D., & Warmuth, M. K. (1989). Learnability and the Vapnik-Chervonenkis dimension. Journal of the ACM, 100, 157-184.
4. Cristianini, N., & Shawe-Taylor, J. (2000). An Introduction to Support Vector Machines. Cambridge, United Kingdom: Cambridge University Press.
5. Forster, J. (2001). A linear lower bound on the unbounded error probabilistic communication complexity. In Proceedings of the 16th Annual IEEE Conference on Computational Complexity (pp. 100-106). IEEE Computer Society Press.
6. Forster, J., Krause, M., Lokam, S. V., Mubarakzjanov, R., Schmitt, N., & Simon, H. U., (2001). Relations between communication complexity, linear arrangements and computational complexity. In Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science (pp. 171-182). Berlin: Springer.
7. Horn, R. A., & Johnson, C. R. (1985). Matrix Analysis. Cambridge, United Kingdom: Cambridge University Press.
8. Kearns, M. J., & Vazirani, U. V. (1994). An Introduction to Computational Learning Theory. Cambridge, Massachusetts: Massachusetts Institute of Technology.
9. Krause, M. (1996). Geometric arguments yield better bounds for threshold circuits and distributed computing. Theoretical Computer Science, 156, 99-117.
10. Maass, W., & Turan, G. (1992). Lower bound methods and separation results for on-line learning models. Journal of Machine Learning, 9, 107-145.
11. Novikoff, A. B. (1962). On convergence proofs on perceptrons. Symposium on the Mathematical Theory of Automata, 12 (pp. 615-622). Polytechnic Institute of Brooklyn.
12. Vapnik, V. (1998). Statistical Learning Theory. New York: John Wiley & Sons, Inc.
13. Vapnik, V. N., & Chervonenkis, A. Y. (1971). On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probability and its Applications, 16, 264-280.