  It becomes an interesting problem to identify subgroup structures in data
analysis as populations are probably heterogeneous in practice. In this paper,
we consider M-estimators together with both concave and pairwise fusion
penalties, which can deal with high-dimensional data containing some outliers.
The penalties are applied both on covariates and treatment effects, where the
estimation is expected to achieve both variable selection and data clustering
simultaneously. An algorithm is proposed to process relatively large datasets
based on parallel computing. We establish the convergence analysis of the
proposed algorithm, the oracle property of the penalized M-estimators, and the
selection consistency of the proposed criterion. Our numerical study
demonstrates that the proposed method is promising to efficiently identify
subgroups hidden in high-dimensional data.
