Variable selection for k means quantization

Clément Levrard (1, 2, 3)

1 UP11 - Université Paris-Sud - Paris 11
2 UPMC - Université Pierre et Marie Curie - Paris 6
3 SELECT - Model selection in statistical learning

Recent results in quantization theory provide theoretical bounds on the distortion of squared-norm based quantizers. These bounds are valid whenever the source distribution has a bounded support, regardless of the dimension of the underlying Hilbertian space. However, it remains of interest to select relevant variable for quantization. This task is usually performed using coordinate energy-ratio thresholding , or maximizing a constrained empirical Between Cluster Sum of Squares criterion. This paper offers a Lasso type procedure to select the relevant variables for $k$-means clustering. Moreover, some non-asymptotic convergence results on the distortion are derived for this procedure, along with consistency results toward sparse codebooks.

Mots clés: k means; quantization; Lasso; variable selection

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Clément Levrard. Variable selection for k means quantization. 2014. ⟨hal-01005545v1⟩