A formal explanation space for the simultaneous clustering of neurologic diseases based on their signs and symptoms.

OBJECTIVE: Clustering is widely used to identify meaningful subgroups in biomedical data, but interpretation remains challenging, especially in the absence of ground-truth labels. Moreover, clustering often produces multiple plausible solutions without a single correct answer. Using dementia phenotypes as a case study, we introduce a Formal Explanation Space (FES) to improve interpretability and facilitate comparison across competing cluster solutions. METHODS: We used spectral coclustering and spectral biclustering to cluster a dataset of dementia patients based on clinical phenotypes (signs and symptoms). To enhance interpretability, we constructed an FES to explain algorithm behavior, assess cluster quality, identify influential features, and characterize cluster composition. Although simultaneous clustering is unsupervised, interpretation was aided by diagnostic labels, which we used for external validation of cluster composition. RESULTS: Spectral coclustering and spectral biclustering each identified five biologically plausible dementia subgroups, though subgroup composition differed by method. The FES provided a structured framework for comparing these divergent outputs. CONCLUSIONS: Clustering complex biomedical data often produces multiple biologically plausible solutions. Retaining and comparing such solutions within a formal explanation space enhances interpretability and supports the discovery of complementary insights across methods.