Adding global shape to conventional features
Conventional machine-learning models often rely on statistical features while overlooking the global shape of complex datasets. PHAML—Persistent Homology-Augmented Machine Learning—explores how topological descriptors can complement those inputs.
The pipeline builds Vietoris–Rips filtrations, computes persistent homology, and converts persistence landscapes and barcodes into quantitative feature vectors. Those vectors are combined with conventional inputs for supervised models such as support-vector machines and logistic regression.
Evaluation
PHAML compares baseline models using conventional features with models augmented by topological information. The experiments investigate changes in classification behaviour and robustness under noise, with particular attention to the stability of topological invariants under perturbation.