Robust and sparse clustering for high-dimensional data

We introduce a robust and sparse clustering procedure for high-dimensional data. The robustness aspect is addressed by a weighting function incorporated in the k-means procedure, consequently leading to an automatic weight assignment for each observation. The sparsity aspect is given by a lasso-type penalty on weighted between-cluster sum of squares. We additionally propose a framework for determining the optimal number of both clusters and variables that contribute to a cluster separation.