The minimax distortion redundancy in empirical quantizer design

Author

Bartlett, Peter L. ; Linder, Tamas ; Lugosi, Gabor

Author_Institution

Dept. of Electr. & Comput. Eng., Australian Nat. Univ., Canberra, ACT, Australia

Volume

44

Issue

5

fYear

1998

fDate

9/1/1998 12:00:00 AM

Firstpage

1802

Lastpage

1813

Abstract

We obtain minimax lower and upper bounds for the expected distortion redundancy of empirically designed vector quantizers. We show that the mean-squared distortion of a vector quantizer designed from n independent and identically distributed (i.i.d.) data points using any design algorithm is at least Ω(n^-1/2) away from the optimal distortion for some distribution on a bounded subset of ℛ ^d. Together with existing upper bounds this result shows that the minimax distortion redundancy for empirical quantizer design, as a function of the size of the training data, is asymptotically on the order of n^-1/2. We also derive a new upper bound for the performance of the empirically optimal quantizer

Keywords

minimax techniques; rate distortion theory; redundancy; vector quantisation; data compression; design algorithm; empirical quantizer design; i.i.d. data; independent identically distributed data; lower bounds; mean-squared distortion; minimax distortion redundancy; optimal distortion; performance; training data size; upper bounds; vector quantizer; Algorithm design and analysis; Convergence; Data compression; Minimax techniques; Minimization methods; Redundancy; Statistics; Training data; Upper bound; Vector quantization;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.705560

Filename

705560