  Clustering, like covariate selection for classification, is an important step
to compress and interpret the data. However, clustering of covariates is often
performed independently of the classification step, which can lead to
undesirable clustering results that harm interpretability and compression rate.
Therefore, we propose a method that can cluster covariates while taking into
account class label information of samples. We formulate the problem as a
convex optimization problem which uses both, a-priori similarity information
between covariates, and information from class-labeled samples. Like ordinary
convex clustering [Chi and Lange, 2015], the proposed method offers a unique
global minima making it insensitive to initialization. In order to solve the
convex problem, we propose a specialized alternating direction method of
multipliers (ADMM), which scales up to several thousands of variables.
Furthermore, in order to circumvent computationally expensive cross-validation,
we propose a model selection criterion based on approximating the marginal
likelihood. Experiments on synthetic and real data confirm the usefulness of
the proposed clustering method and the selection criterion.
