Quantization and the Method of k-Means

IEEE Transactions on Information Theory

Volumn 28, Issue 2, 1982, Pages 199-205

  Pollard, David ^a  

^a YALE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

QUANTIZATION;

DATA CONVERSION, ANALOG TO DIGITAL;

EID: 0020101636     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/TIT.1982.1056481     Document Type: Article

References (13)

1. R. L. Dobrushin, “Prescribing a system of random variables by conditional distributions,” Theory of Probability and its Applications, vol. 15, 458–486, 1970.
2. R. M. Dudley, “Distances of probability measures and random variables,” Annals of Mathematical Statistics, vol. 39, 1563–1572, 1968.
3. J. Elker, D. Pollard, and W. Stute, “Glivenko–Cantelli theorems for classes of convex sets,” Advances in Applied Probability, vol. 11, 820–833, 1979.
4. P. Gaenssler and W. Stute, “Empirical processes: A survey of results for independent and identically distributed random variables,” Annals of Probability, vol. 7, 193–243, 1979.
5. R. M. Gray, D. L. Neuhoff, and P. C. Shields, “A generalization of Omstein's distance with applications to information theory,” Annals of Probability, vol. 3, 315–328, 1975.
6. J. A. Hartigan, “Asymptotic distributions for clustering criteria,” Annals of Statistics, vol. 6, 117–131, 1978.
7. Y. Linde, A. Buzo, and R. M. Gray, “An algorithm for vector quantizer design,” IEEE Transactions on Communications, vol. 18, 84–95, 1980.
8. S. P. Lloyd, “Least squares quantization in PCM,” IEEE Trans. Inform. Theory, vol. IT-28, no. 2, pp. 129–137, 1982, this issue, (Originally a 1957 Bell Labs memorandum).
9. P. Papantoni-Kazakos and R. M. Gray, “Robustness of estimators on stationary observations,” Annals of Probability, vol. 7, 989–1002, 1979.
10. D. Pollard, “Strong consistency of k-means clustering,” Annals of Statistics, vol. 9, 135–140, 1981.
11. D. Pollard, “Limit theorems for empirical processes,” Zeitschrift fur Wahrscheinlichkeitstheorie und Verw. Geb., vol. 57, 181–195, 1981.
12. D. Pollard, “A central limit theorem for k-means clustering,” Annals of Probability, to be published.
13. V. S. Varadarajan, “On the convergence of probability distributions,” Sankhya, vol. 19, 23–26, 1958.