Intrinsic Stationarity for Vector Quantization: Foundation of Dual Quantization

Intrinsic Stationarity for Vector Quantization: Foundation of Dual Quantization

We develop a new approach to vector quantization, which guarantees an intrinsic stationarity property that also holds, in contrast to regular quantization, for non-optimal quantization grids. This goal is achieved by replacing the usual nearest neighbor projection operator for Voronoi quantization by a random splitting operator, which maps the random source to the vertices of a triangle of d-si...

Stationarity of Matrix Relevance Learning Vector Quantization

We investigate the convergence properties of heuristic matrix relevance updates in Learning Vector Quantization. Under mild assumptions on the training process, stationarity conditions can be worked out which characterize the outcome of training in terms of the relevance matrix. It is shown that the original training schemes single out one specific direction in feature space which depends on th...

Vector Quantization for Image Compression-Concept Quantization

Extension of two-stage vector quantization-lattice vector quantization

This paper is the extension of two-stage vector quantization–(spherical) lattice vector quantization (VQ–(S)LVQ) recently introduced by Pan and Fischer [1]. First, according to high resolution quantization theory, generalized vector quantization–lattice vector quantization (G-VQ–LVQ) is formulated in order to release the constraint of the spherical boundary for the second-stage lattice vector q...

Estimation of Intrinsic Dimensionality Using High-Rate Vector Quantization

We introduce a technique for dimensionality estimation based on the notion of quantization dimension, which connects the asymptotic optimal quantization error for a probability distribution on a manifold to its intrinsic dimension. The definition of quantization dimension yields a family of estimation algorithms, whose limiting case is equivalent to a recent method based on packing numbers. Usi...