HADES: Fast Singularity Detection with Local Measure Comparison
Uzu Lim, Harald Oberhauser, Vidit Nanda · SIAM Journal on Mathematics of Data Science · 2025
Abstract. We introduce HADES , an unsupervised algorithm to detect singularities in data. This algorithm employs a kernel goodness-of-fit test, and as a consequence it is much faster and far more scalable than the existing topology-based alternatives. Using tools from differential geometry and optimal transport theory, we prove that HADES correctly detects singularities with high probability when the data sample lives on a transverse intersection of equidimensional manifolds. In computational experiments, HADES recovers singularities in synthetically generated data, branching points in road network data, intersection rings in molecular conformation space, and anomalies in image data.