  We study a multi-factor block model for variable clustering and connect it to
the regularized subspace clustering by formulating a distributionally robust
version of the nodewise regression. To solve the latter problem, we derive a
convex relaxation, provide guidance on selecting the size of the robust region,
and hence the regularization weighting parameter, based on the data, and
propose an ADMM algorithm for implementation. We validate our method in an
extensive simulation study. Finally, we propose and apply a variant of our
method to stock return data, obtain interpretable clusters that facilitate
portfolio selection and compare its out-of-sample performance with other
clustering methods in an empirical study.
