  In real-world application scenarios, the identification of groups poses a
significant challenge due to possibly occurring outliers and existing noise
variables. Therefore, there is a need for a clustering method which is capable
of revealing the group structure in data containing both outliers and noise
variables without any pre-knowledge. In this paper, we propose a
$k$-means-based algorithm incorporating a weighting function which leads to an
automatic weight assignment for each observation. In order to cope with noise
variables, a lasso-type penalty is used in an objective function adjusted by
observation weights. We finally introduce a framework for selecting both the
number of clusters and variables based on a modified gap statistic. The
conducted experiments on simulated and real-world data demonstrate the
advantage of the method to identify groups, outliers, and informative variables
simultaneously.
