  Feature selection in clustering is a hard task which involves simultaneously
the discovery of relevant clusters as well as relevant variables with respect
to these clusters. While feature selection algorithms are often model-based
through optimised model selection or strong assumptions on the data
distribution, we introduce a discriminative clustering model trying to maximise
a geometry-aware generalisation of the mutual information called GEMINI with a
simple l1 penalty: the Sparse GEMINI. This algorithm avoids the burden of
combinatorial feature subset exploration and is easily scalable to
high-dimensional data and large amounts of samples while only designing a
discriminative clustering model. We demonstrate the performances of Sparse
GEMINI on synthetic datasets and large-scale datasets. Our results show that
Sparse GEMINI is a competitive algorithm and has the ability to select relevant
subsets of variables with respect to the clustering without using relevance
criteria or prior hypotheses.
