Sets of approximating functions with finite Vapnik-Chervonenkis dimension for nearest-neighbors algorithms

Pattern Recognition Letters

Volumn 32, Issue 14, 2011, Pages 1882-1893

  Klsk, P ^a   Korzen M ^a  

^a WEST POMERANIAN UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Complexity selection; Generalization; k Nearest neighbors; Statistical learning theory; Structural risk minimization; Vapnik Chervonenkis dimension

Indexed keywords

COMPLEXITY SELECTION; GENERALIZATION; K-NEAREST NEIGHBORS; STATISTICAL LEARNING THEORY; STRUCTURAL RISK MINIMIZATION; VAPNIK-CHERVONENKIS DIMENSIONS;

ELECTROMAGNETIC WAVE EMISSION;

ALGORITHMS;

EID: 80052561333     PISSN: 01678655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patrec.2011.07.012     Document Type: Article

References (25)

1. M. Anthony, and P. Bartlett Neural Network Learning: Theoretical Foundations 2009 Cambridge University Press Cambridge, UK
2. F. Aurenhammer, and R. Klein Voronoi Diagrams 2000 North-Holland Netherlands Chapter 5, pp. 201-209
3. P. Bartlett, and S. Mendelson Rademacher and gaussian complexities: risk bounds and structural results J. Mach. Learn. Res. 3 2002 463 482
4. J. Bentley Multidimensional binary search trees used for associative searching Commun. ACM 18 1975
5. V. Cherkassky, and F. Mulier Learning From Data Adaptive and Learning Systems for Signal Processing, Communications and Control 1998 John Wiley and Sons, Inc
6. L. Devroye, L. Gyorfi, and G. Lugosi A Probabilistic Theory of Pattern Recognition 1996 Springer-Verlag, Inc New York
7. J. Friedman An algorithm for finding best matches in logarithmic expected time ACM Trans. Math. Softw. 3 1977 209 226
8. J. Friedman The Elements of Statistical Learning 2009 Springer
9. R. Graham, D. Knuth, and O. Patashik Concrete Mathematics. A foundation for Computer Science 2002 Wydawnictwo Naukowe PWN SA Warsaw, Poland
10. M. Hellman, and J. Raviv Probability of error, equivocation and the Chernoff bound IEEE Trans. Inform. Theor. IT-16 1970 368 372
11. J. Hjorth Computer Intensive Statistical Methods Validation, Model Selection, and Bootstrap 1994 Chapman and Hall London
12. Holden, S., 1996. Cross-validation and the PAC learning model. Technical Report. Research Note, RN/96/64. Department of CS, University College, London.
13. B. Jahne Practical Handbook on Image Processing for Scientific and Technical Application 2004 CRC Press LLC
14. M. Kearns, and D. Ron Algorithmic stability and sanity-check bounds for leave-one-out cross-validation Neural Comput. 11 1999 1427 1453
15. T. Kohonen The self-organizing map Proc. IEEE 78 1990 1464 1479
16. Kohonen, T., 1992. Clustering, taxonomy, and topological maps of patterns. In: Proc. 6th Internat. Conf. on Pattern Recognition, Munich, Germany, pp. 114-128.
17. M. Korzeń, and P. Klsk Maximal margin estimation with perceptron-like algorithm L. Rutkowski, R. Tadeusiewicz, L.A. Zadeh, J.M. Zurada, Lecture Notes in Computer Science vol. 5097 2008 Springer 597 608
18. Lloyd, S.P., 1957. Least squares quantization in PCM's. Technical Report. Bell Telephone Laboratories, Murray Hill, New Jersey.
19. S. Roweis, and L. Saul Nonlinear dimensionality reduction by locally linear embedding Science 290 2000 2323 2326 (Pubitemid 32041578)
20. Shawe-Taylor, J., et al., 1996. A framework for structural risk minimization. In: COLT, ACM Press, pp. 68-76, ISBN 0-89791-811-8. Available from: < http://www.ecs.soton.ac.uk/people/jst/publications/creators-name >.
21. P. Simard, Y. LeCun, J. Denker, and B. Victorri Transformation invariance in pattern recognition: Tangent distance and propagation International Journal of Imaging Systems and Technology vol. 11 2000 Springer pp. 181-197
22. V. Vapnik The Nature of Statistical Learning Theory 1995 Springer-Verlag New York
23. V. Vapnik Statistical Learning Theory: Inference from Small Samples 1995 Wiley New York
24. Vapnik, V., Chervonenkis, A., 1989. The necessary and sufficient conditions for the consistency of the method of empirical risk minimization. In: Yearbook of the Academy of Sciences of the USSR on Recognition, Classification and Forecasting, vol. 2, pp. 217-249.
25. P. Vincent, and Y. Bengio K-local hyperplane and convex distance nearest neighbors algorithms Adv. Neural Inform. Process. Syst. 2001 985 992