Lagrangian empirical design of variable-rate vector quantizers: consistency and convergence rates

Abstract--The Lagrangian formulation of variable-rate vector quantization is known to yield useful necessary conditions for quantizer optimality and generalized Lloyd algorithms for quantizer design. In this correspondence, the Lagrangian formulation is demonstrated to provide a convenient framework for analyzing the empirical design of variable-rate vector quantizers. In particular, the consistency of empirical design based on minimizing the Lagrangian performance over a stationary and ergodic training sequence is shown for sources with finite second moment. The finite sample performance is also studied for independent training data and sources with bounded support.

• Type: Journal
• Year: 2002
• Where: TIT
• Authors: Tamás Linder
• Keywords: Empirical Design, Lagrangian Formulation, TIT 2002, Variable-rate Vector