Unsupervised Radiomic Phenotyping of Glioblastoma via Task-Optimized Latent Representations

Computational models of brain-related phenomena often depend on latent representations whose geometry determines what structure can be inferred from complex data. In glioblastoma, tumours with similar molecular profiles frequently exhibit divergent imaging characteristics and clinical trajectories, suggesting intrinsic phenotypic structure not captured by standard labels. This work formalizes unsupervised radiomic clustering as a latent-state inference problem, examining how representation geometry influences the detectability of meaningful subgroups. Using multi-parametric MRI data from the UPENN-GBM cohort (n = 599), 432 radiomic features were extracted across enhancing tumour, necrotic core, and peritumoral edema regions. Linear Principal Component Analysis (PCA) and non-linear Uniform Manifold Approximation and Projection (UMAP) were systematically compared using topology-preservation metrics and clustering stability analyses. While PCA preserved global variance and pairwise distances, it retained the high-dimensional concentration of measure that limited density-based clustering. In contrast, UMAP introduced controlled topological distortion that increased structural contrast and facilitated manifold unfolding, producing a task-optimized latent space for HDBSCAN clustering. The resulting phenotypes were structurally stable and exhibited significant radiomic differentiation, with approximately 90% of features differing between clusters (p < 0.01). Kaplan–Meier analysis demonstrated these imaging-defined states were independently prognostic for overall survival (p < 0.05), remaining statistically independent of age, sex, IDH1 mutation status, and MGMT promoter methylation. This framework provides a principled foundation for representation-aware modeling and explainable AI in neuro-oncology.