  We propose the Lasso Weighted $k$-means ($LW$-$k$-means) algorithm as a
simple yet efficient sparse clustering procedure for high-dimensional data
where the number of features ($p$) can be much larger compared to the number of
observations ($n$). In the $LW$-$k$-means algorithm, we introduce a lasso-based
penalty term, directly on the feature weights to incorporate feature selection
in the framework of sparse clustering. $LW$-$k$-means does not make any
distributional assumption of the given dataset and thus, induces a
non-parametric method for feature selection. We also analytically investigate
the convergence of the underlying optimization procedure in $LW$-$k$-means and
establish the strong consistency of our algorithm. $LW$-$k$-means is tested on
several real-life and synthetic datasets and through detailed experimental
analysis, we find that the performance of the method is highly competitive
against some state-of-the-art procedures for clustering and feature selection,
not only in terms of clustering accuracy but also with respect to computational
time.
