Optimal multiple description and multiresolution scalar quantizer design

The author presents new algorithms for fixed-rate multiple description and multiresolution scalar quantizer design. The algorithms both run in time polynomial in the size of the source alphabet and guarantee globally optimal solutions. To the author's knowledge, these are the first globally optimal design algorithms for multiple description and multiresolution quantizers

Network vector quantization

We present an algorithm for designing locally optimal vector quantizers for general networks. We discuss the algorithm's implementation and compare the performance of the resulting "network vector quantizers" to traditional vector quantizers (VQs) and to rate-distortion (R-D) bounds where available. While some special cases of network codes (e.g., multiresolution (MR) and multiple description (MD) codes) have been studied in the literature, we here present a unifying approach that both includes these existing solutions as special cases and provides solutions to previously unsolved examples

Optimal modeling for complex system design

The article begins with a brief introduction to the theory describing optimal data compression systems and their performance. A brief outline is then given of a representative algorithm that employs these lessons for optimal data compression system design. The implications of rate-distortion theory for practical data compression system design is then described, followed by a description of the tensions between theoretical optimality and system practicality and a discussion of common tools used in current algorithms to resolve these tensions. Next, the generalization of rate-distortion principles to the design of optimal collections of models is presented. The discussion focuses initially on data compression systems, but later widens to describe how rate-distortion theory principles generalize to model design for a wide variety of modeling applications. The article ends with a discussion of the performance benefits to be achieved using the multiple-model design algorithms

Batch and median neural gas

Neural Gas (NG) constitutes a very robust clustering algorithm given euclidian data which does not suffer from the problem of local minima like simple vector quantization, or topological restrictions like the self-organizing map. Based on the cost function of NG, we introduce a batch variant of NG which shows much faster convergence and which can be interpreted as an optimization of the cost function by the Newton method. This formulation has the additional benefit that, based on the notion of the generalized median in analogy to Median SOM, a variant for non-vectorial proximity data can be introduced. We prove convergence of batch and median versions of NG, SOM, and k-means in a unified formulation, and we investigate the behavior of the algorithms in several experiments.Comment: In Special Issue after WSOM 05 Conference, 5-8 september, 2005, Pari