Vector quantization with complexity costs

Vector quantization is a data compression method where a set of data points is encoded by a reduced set of reference vectors, the codebook. We discuss a vector quantiza-tion strategy which jointly optimizes distortion errors and the codebook complexity, thereby, determining the size of the codebook. A maximum entropy estimation of the cost function yields an optimal number of reference vectors, their positions and their assignment probabilities. The dependence of the codebook density on the data density for diierent complexity functions is investigated in the limit of asymptotic quantization levels. How diierent complexity measures innuence the eeciency of vector quantizers is studied for the task of image compression, i.e., we quantize the wavelet coeecients of gray level images and measure the reconstruction error. Our approach establishes a unifying framework for diierent quantization methods like K-means clustering and its fuzzy version, entropy constrained vector quantization or topological feature maps and competitive neural networks. y Supported by a graduate fellowship of the Technische Universitt at M unchen.