L1-Quantization and clustering in Banach spaces
Thomas Laloë · Mathematical Methods of Statistics · 2010
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.