On kernels, margins, and low-dimensional mappings

Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science)

Volumn 3244, Issue , 2004, Pages 194-205

  Balcan, Maria Florina ^a   Blum, Avrim ^a   Vempala, Santosh ^b  

^a Carnegie Mellon University ^*  (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; ERROR ANALYSIS; FUNCTIONS; LEARNING ALGORITHMS; MAPPING; POLYNOMIALS; PROBABILITY; THEOREM PROVING; ARTIFICIAL INTELLIGENCE; COMPUTERS;

KERNEL FUNCTION; LEARNING THEORY; POLYNOMIAL KERNEL; UNDERLYING DISTRIBUTION; HIGH DIMENSIONAL SPACES; JOHNSON-LINDENSTRAUSS LEMMATA; LINEARLY SEPARABLE; LOW-DIMENSIONAL SPACES; POLYNOMIAL KERNELS; STANDARD KERNELS;

LEARNING SYSTEMS; MAPPING;

EID: 22944491769     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-540-30215-5_16     Document Type: Conference Paper

References (15)

1. D. Achlioptas, "Database-friendly Random Projections", Symposium on Principles of Database Systems, 2001.
2. R. I. Arriaga, S. Vempala, "An algorithmic theory of learning, Robust concepts and random projection", Proc. of the 40th Foundations of Computer Science, 616 - 623, 1999.
3. P. Bartlett, J. Shawe-Taylor, "Generalization Performance of Support Vector Machines and Other Pattern Classifiers", Advances in Kernel Methods: Support Vector Learning, MIT Press, 1999.
4. S. Ben-David, N. Eiron, H.U. Simon, "Limitations of Learning Via Embeddings in Euclidean Half-Spaces", Journal of Machine Learning Research 3: 441-461, 2002.
5. S. Ben-David, "A Priori Generalization Bounds for Kernel Based Learning", NIPS 2001 Workshop on Kernel Based Learning.
6. B. E. Boser, I. M. Guyon, V. N. Vapnik, "A Training Algorithm for Optimal Margin Classifiers", Proceedings of the Fifth Annual Workshop on Computational Learning Theory, 1992.
7. C. Cortes, V. Vapnik, "Support-Vector Networks", Machine Learning, Volume 20(3): 273 - 297, 1995.
8. S. Dasgupta, A. Gupta, "An elementary proof of the Johnson-Lindenstrauss Lemma", Tech Report, UC Berkeley, 1999.
9. Y. Freund, R. E. Schapire, "Large Margin Classification Using the Perceptron Algorithm", Machine Learning, Volume 37, No. 3, 277-296, 1999.
10. W. B. Johnson, J. Lindenstrauss, "Extensions of Lipschitz mappings into a Hilbert space", Conference in modern analysis and probability, 189-206, 1984.
11. K. R. Muller, S. Mika, G. Ratsch, K. Tsuda, B. Scholkopf, "An Introduction to kernel-based learning algorithms", IEEE Transactions on Neural Networks, Vol. 12, pp. 181-201, 2001.
12. J. Shawe-Taylor, P. L. Bartlett, R. C. Williamson, M. Anthony, "Structural Risk Minimization over Data-Dependent Hierarchies", IEEE Trans. on Information Theory, 44(5): 1926-1940, 1998.
13. A. J. Smola, P. Bartlett, B. Scholkopf, D. Schuurmans (Eds.), "Advances in Large Margin Classifiers", MIT Press, 2000.
14. B. Scholkopf, A. J. Smola , "Learning with kernels. Support Vector Machines, Regularization, Optimization, and Beyond", MIT University Press, Cambridge, 2002.
15. V. N. Vapnik, "Statistical Learning Theory", John Wiley and Sons Inc., New York, 1998.