The Morse Transform for Discrete Shape Analysis
A new topological transform, the Morse Transform, has been developed to numerically describe the geometry of objects for statistical inference and classification tasks. This method leverages Morse theory to catalog critical points across multiple height-functions, retaining finer shape information than existing transforms. The Morse feature vector has been benchmarked as a descriptor for ligand-based virtual screening, achieving the highest mean AUROC compared to other topological and standard shape-based descriptors. AI