L 1 -Quantization and Clustering in Banach Spaces

T Lalöe (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

—Let X be a random variable with distribution μ taking values in a Banach space H. 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.

Mots clés: quantization; clustering; L 1 -distance; Banach space 2000 Mathematics Subject Classification: 62H30

Domaines: Mathématiques [math]

T Lalöe. L 1 -Quantization and Clustering in Banach Spaces. Mathematical Methods of Statistics, 2010, ⟨10.3103/S1066530710020031⟩. ⟨hal-01292694⟩