Boundedness and Consistency of Greedy Growing for Tree-Structured Vector Quantizes
Andrew B. Nobel, Richard A. Olshen · 2005
The problem of designing a TSVQ from random data has received considerable recent attention. A key step in many methods of design is the application of a greedy growing algorithm to the empirical distribution of the data. In applications of interest to us these empirical distributions are of vectorial pixel intensities. Here we analyze the behavior of the greedy growing algorithm when it is applied to the true underlying distribution of the observations, and we show that quantizers produced from large data sets will be close to quantizers produced from the true distribution.