Concurrent Supervised-Unsupervised Representative Subspace Clustering (CSU-RSC)

The biological heterogeneity of psychotic disorders (PDs) has motivated the identification of psychosis imaging neurosubtypes (PINs), which aims to stratify the PD population into subgroups with similar neurobiological underpinnings. Yet the influence of sex, although well documented in the literature, has not been well counted in the existing subtyping paradigm. Here, we introduce concurrent supervised-unsupervised representative subspace clustering (CSU-RSC), a general functional neurosubtyping framework that jointly estimates cluster-specific subspaces and a partition while softly incorporating a supervised label, aiming to identify sex-dominant subgroups based on differences in the spatial organization of brain networks. This soft supervising design differentiates CSU-RSC from unsupervised approaches that completely ignore a label as well as from supervised approaches that exclusively analyze each label group separately. On simulated data, CSU-RSC recovered the ground truth of subgroups more accurately than its unsupervised counterpart. Applied to resting-state fMRI from 1,239 individuals with psychosis, CSU-RSC identified two sex-dominant PINs that replicated across discovery and validation sets, and showed significant differences in clinical characteristics, including cognitive impairment and symptom severity, with the most cognitively impaired subtype being female-dominant. Projecting controls onto the patient-derived subspaces showed that the female-dominant pattern did not persist in controls, suggesting psychosis-specific sex heterogeneity. Overall, by incorporating sex as an explicit source of information, CSU-RSC highlights the value of sex for resolving biological heterogeneity and provides a basis for more reproducible and biologically informative patient stratification.