Theory and Practice of Vector Quantizers Trained on Small Training Sets

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 16, Issue 1, 1994, Pages 54-65

  Ladner, Richard ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Image coding; learning theory; Vapnik Cher ; vonenkis dimension vector quantization

Indexed keywords

CODES (SYMBOLS); COMPUTATIONAL METHODS; DATA COMPRESSION; IMAGE ANALYSIS; IMAGE COMPRESSION; INFORMATION THEORY; LEARNING SYSTEMS; MATHEMATICAL MODELS; PERFORMANCE; RANDOM PROCESSES; VECTORS;

VAPNIK-CHERVONENKIS DIMENSION; VECTOR QUANTIZATION; VECTOR QUANTIZERS;

IMAGE CODING;

EID: 0028274388     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/34.273717     Document Type: Article

References (20)

1. A. Blumer, A. Ehrenfeucht, D. Haussler, and M. K. Warmuth, “Learnability and the Vapnik—Chervonenkis dimension,” J. Ass. Comput. Mach., vol. 36, no. 4, pp. 929-965, Oct. 1989.
2. D. Cohn and G. Tesauro, “How tight are the Vapnik—Chervonenkis bounds?” Neural Computation, vol. 4, no. 2, pp. 249-270, Mar. 1992.
3. D. Cohn, “Separating formal bounds from practical performance in learning systems,” Ph.D. dissertation, Dept. Comput. Sci. Eng., Univ. of Washington, Seattle, 1992.
4. P. Cosman, K. Perlmutter, S. Perlmutter, R. A. Olshen, and R. M. Gray, “Training sequence size and vector quantizer performance,” in Proc. 25th Asilomar Conf. Signals, Syst., Comput., Asilomar, CA, Nov. 1991, pp. 434-438.
5. J. Crutchfield and K. Young, Computation at the Onset of Chaos. Reading, MA: Addison-Wesley, 1990, pp. 223-269.
6. R. Floyd and L. Steinberg, “An adaptive algorithm for spatial grey scale,” in SID Int. Symp. Dig. Tech. Papers, 1975, pp. 36-37.
7. A. Gersho and R. M. Gray, Vector Quantization and Signal Compression. Boston: Kluwer Academic, 1992.
8. R. M. Gray, “Vector quantization,” IEEE ASSP Mag., vol. 1, pp. 4-29, Apr. 1984.
9. D. Haussler, M. Kearns, and R. Schapire, “Unifying bounds on the sample complexity of Bayesian learning theory using information theory and the VC dimension,” in Proc. 4th Annual Workshop Computational Learning Theory. San Mateo, CA: Morgan Kaufmann, 1991, pp. 61-74.
10. F. Itakura and S. Saito, “Analysis synthesis telephony based on the maximum likelihood method,” in Proc. 6th Int. Congress Acoustics, Tokyo, Japan. New York: Elsevier, 1968, pp. c17—c20.
11. J. Lin and J. Vitter, “F-approximations with minimum constraint violation,” in Prot. 24th Annual ACM Symp. Theory of Computing, Victoria, Canada, May 1992, pp. 771-782.
12. Y. Linde, A. Buzo, and R. M. Gray, “An algorithm for vector quantizer design,” IEEE Trans. Commun., vol. COM-28, pp. 84-95, Jan. 1980.
13. A. N. Netravali and B. G. Haskell, Digital Pictures Representation. and Compression. New York: Plenum, 1988.
14. D. Pollard, “A central limit theorem for k-means clustering,” Annals Probability, vol. 10, no. 4, pp. 919-926, 1982.
15. R. Ulichney, Digital Halftoning. Cambridge, MA: MIT Press, 1987.
16. V. Vapnik, Estimation of Dependencies Based on Empirical Data. New York: Springer-Verlag, 1982.
17. V. Vapnik and A. Chervonenkis, “On the uniform convergence of relative frequencies of events to their probabilities,” Theory of Probability and its Applications, vol. 16, no. 2, pp. 264-280, 1971.
18. S. Weiss and C. Kulikowski, Computer Systems that Learn. San Mateo, CA: Morgan Kaufmann, 1991.
19. P. Zehna, Probability Distributions and Statistics. Boston: Allyn and Bacon, 1970, pp. 286-289.
20. T. Linder, G. Lugosi, and K. Zeger, Rates of convergence in the source coding theorem, in empirical quantizer design, and in universal lossy source coding,” IEEE Trans. Inform. Theory; to be published.