Abstract Disease heterogeneity is a significant obstacle to understanding pathological processes and delivering precision diagnostics and treatment. Clustering methods have gained popularity for stratifying patients into subpopulations (i.e., subtypes) of brain diseases using imaging data. However, unsupervised clustering approaches are often confounded by anatomical and functional variations not related to a disease or pathology of interest. Semi-supervised clustering techniques have been proposed to overcome this and, therefore, capture disease-specific patterns more effectively. An additional limitation of both unsupervised and semi-supervised conventional machine learning methods is that they typically model, learn and infer from data using a basis of feature sets pre-defined at a fixed anatomical or functional scale (e.g., atlas-based regions of interest). Herein we propose a novel method, “Multi-scAle heteroGeneity analysIs and Clustering” (MAGIC), to depict the multi-scale presentation of disease heterogeneity, which builds on a previously proposed semi-supervised clustering method, HYDRA. It derives multi-scale and clinically interpretable feature representations and exploits a double-cyclic optimization procedure to effectively drive identification of inter-scale-consistent disease subtypes. More importantly, to understand the conditions under which the clustering model can estimate true heterogeneity related to diseases, we conducted extensive and systematic semi-simulated experiments to evaluate the proposed method on a sizeable healthy control sample from the UK Biobank (N=4403). We then applied MAGIC to imaging data from Alzheimer’s disease (ADNI, N =1728) and schizophrenia (PHENOM, N =1166) patients to demonstrate its potential and challenges in dissecting the neuroanatomical heterogeneity of common brain diseases. Taken together, we aim to provide guidance regarding when such analyses can succeed or should be taken with caution. The code of the proposed method is publicly available at https://github.com/anbai106/MAGIC . Highlights We propose a novel multi-scale semi-supervised clustering method, termed MAGIC, to disentangle the heterogeneity of brain diseases. We perform extensive semi-simulated experiments on large control samples (UK Biobank, N =4403) to precisely quantify performance under various conditions, including varying degrees of brain atrophy, different levels of heterogeneity, overlapping disease subtypes, class imbalance, and varying sample sizes. We apply MAGIC to MCI and Alzheimer’s disease (ADNI, N =1728) and schizophrenia (PHENOM, N =1166) patients to dissect their neuroanatomical heterogeneity, providing guidance regarding the use of the semi-simulated experiments to validate the subtypes found in actual clinical applications. Graphical abstract

Multi-scale semi-supervised clustering of brain images: deriving disease subtypes