L1-Quantization and clustering in Banach spaces

LetX be a random variable with distribution μ taking values in a Banach spaceH. First, we establish the existence of an optimal quantization of μ with respect to the L ₁-distance. Second, we propose several estimators of the optimal quantizer in the potentially infinite-dimensional space H, with associated algorithms. Finally, we discuss practical results obtained from real-life data sets.