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. A vector quantization strategy is discussed that 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 different complexity functions is investigated in the limit of asymptotic quantization levels. How different complexity measures influence the efficiency of vector quantizers is studied for the task of image compression, i.e., we quantize the wavelet coefficients of gray-level images and measure the reconstruction error. Our approach establishes a unifying framework for different quantization methods like K-means clustering and its fuzzy version, entropy constrained vector quantization or topological feature maps and competitive neural networks.