By Topic

Termination and continuity of greedy growing for tree-structured vector quantizers

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Nobel, A.B. ; Dept. of Stat., North Carolina Univ., Chapel Hill, NC, USA ; Olshen, R.A.

Tree-structured vector quantizers (TSVQ) provide a computationally efficient, variable-rate method of compressing vector-valued data. In applications, the problem of designing a TSVQ from empirical training data is critical. Greedy growing algorithms are a common and effective approach to the design problem. They are recursive procedures that produce a TSVQ one node at a time by optimizing a simple splitting criterion at each step. While unsupervised greedy growing algorithms are well-understood from an experimental point of view, there has been little theory to support their use, or to examine their behavior on large training sets. The authors present a rigorous analysis of a greedy growing algorithm proposed by Riskin (1990), Riskin and Gray (1991), and Balakrishnan (1991). The first part of the paper is a description of the algorithm and an examination of its asymptotic behavior as it applies to a fixed, absolutely continuous distribution. The second part of the paper establishes the structural consistency of the algorithm with respect to a convergent sequence of distributions. As an application, the authors obtain results concerning the large-sample empirical behavior of the algorithm when it is applied to stationary ergodic training vectors

Published in:

Information Theory, IEEE Transactions on  (Volume:42 ,  Issue: 1 )