Continuity and consistency of greedy growing for tree-structured vector quantizers

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. A widely used approach to the design problem is the greedy growing algorithm, which produces a labeled binary tree one node at a time by optimizing a simple splitting criterion at each stage. While the greedy growing algorithm is well understood from an experimental standpoint, there has been little theory to support its use, or to examine its behavior on large training sets. This talk presents the results of a rigorous analysis of the greedy growing algorithm