Lagrangian empirical design of variable-rate vector quantizers: consistency and convergence rates
Tamás Linder · IEEE Transactions on Information Theory · 2002
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. 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.