  This paper investigates the intrinsic group structures within the framework
of large-dimensional approximate factor models, which portrays homogeneous
effects of the common factors on the individuals that fall into the same group.
To this end, we propose a fusion Penalized Principal Component Analysis (PPCA)
method and derive a closed-form solution for the $\ell_2$-norm optimization
problem. We also show the asymptotic properties of our proposed PPCA estimates.
With the PPCA estimates as an initialization, we identify the unknown group
structure by a combination of the agglomerative hierarchical clustering
algorithm and an information criterion. Then the factor loadings and factor
scores are re-estimated conditional on the identified latent groups. Under some
regularity conditions, we establish the consistency of the membership
estimators as well as that of the group number estimator derived from the
information criterion. Theoretically, we show that the post-clustering
estimators for the factor loadings and factor scores with group pursuit achieve
efficiency gains compared to the estimators by conventional PCA method.
Thorough numerical studies validate the established theory and a real financial
example illustrates the practical usefulness of the proposed method.
