Geometric Analysis of Speech Representation Spaces: Topological Disentanglement and Confound Detection

Speech-based clinical tools are increasingly deployed in multilingual settings, yet whether pathological speech markers remain geometrically separable from accent variation remains unclear. Systems may misclassify healthy non-native speakers or miss pathology in multilingual patients. We propose a four-metric clustering framework to evaluate geometric disentanglement of emotional, linguistic, and pathological speech features across six corpora and eight dataset combinations. A consistent hierarchy emerges: emotional features form the tightest clusters (Silhouette 0.250), followed by pathological (0.141) and linguistic (0.077). Confound analysis shows pathological-linguistic overlap remains below 0.21, which is above the permutation null but bounded for clinical deployment. Trustworthiness analysis confirms embedding fidelity and robustness of the geometric conclusions. Our framework provides actionable guidelines for equitable and reliable speech health systems across diverse populations.