The identification of homogeneous subgroups of patients with psychiatric disorders can play an important role in achieving personalized medicine and is essential to provide insights for understanding neuropsychological mechanisms of various mental disorders. The functional connectivity profiles obtained from functional magnetic resonance imaging (fMRI) data have been shown to be unique to each individual, similar to fingerprints; however, their use in characterizing psychiatric disorders in a clinically useful way is still being studied. In this work, we propose a framework that makes use of functional activity maps for subgroup identification using the Gershgorin disc theorem. The proposed pipeline is designed to analyze a large-scale multi-subject fMRI dataset with a fully data-driven method, a new constrained independent component analysis algorithm based on entropy bound minimization (c-EBM), followed by an eigenspectrum analysis approach. A set of resting-state network (RSN) templates is generated from an independent dataset and used as constraints for c-EBM. The constraints present a foundation for subgroup identification by establishing a connection across the subjects and aligning subject-wise separate ICA analyses. The proposed pipeline was applied to a dataset comprising 464 psychiatric patients and discovered meaningful subgroups. Subjects within the identified subgroups share similar activation patterns in certain brain areas. The identified subgroups show significant group differences in multiple meaningful brain areas including dorsolateral prefrontal cortex and anterior cingulate cortex. Three sets of cognitive test scores were used to verify the identified subgroups, and most of them showed significant differences across subgroups, which provides further confirmation of the identified subgroups. In summary, this work represents an important step forward in using neuroimaging data to characterize mental disorders.