Variable selection for k means quantization
Clément Levrard · arXiv (Cornell University) · 2014
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.