NDLI: Quantization via Empirical Divergence Maximization

Content Provider	IEEE Xplore Digital Library
Author	Lexa, M.A.
Copyright Year	1991
Abstract	Empirical divergence maximization (EDM) refers to a recently proposed strategy for estimating f-divergences and likelihood ratio functions. This paper extends the idea to empirical vector quantization where one seeks to empirically derive quantization rules that maximize the Kullback-Leibler divergence between two statistical hypotheses. We analyze the estimator's error convergence rate leveraging Tsybakov's margin condition and show that rates as fast as n^-1 are possible, where n equals the number of training samples. We also show that the Flynn and Gray algorithm can be used to efficiently compute EDM estimates and show that they can be efficiently and accurately represented by recursive dyadic partitions. The EDM formulation have several advantages. First, the formulation gives access to the tools and results of empirical process theory that quantify the estimator's error convergence rate. Second, the formulation provides a previously unknown derivation for the Flynn and Gray algorithm. Third, the flexibility it affords allows one to avoid a small-cell assumption common in other approaches. Finally, we illustrate the potential use of the method through an example.
Sponsorship	IEEE Signal Processing Society
Starting Page	6408
Ending Page	6420
Page Count	13
File Size	3799384
File Format	PDF
ISSN	1053587X
Volume Number	60
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-12-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Signal processing algorithms Convergence Partitioning algorithms Risk management Vector quantization Probability distribution vector quantization Empirical divergence maximization error convergence rates Kullback-Leibler divergence recursive dyadic partitions
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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