HADES: Fast Singularity Detection with Local Measure Comparison
This addresses the need for efficient singularity detection in various domains like road networks and image data, though it appears incremental as it builds on existing concepts with improvements in speed and scalability.
The paper tackles the problem of detecting singularities in data by introducing Hades, an unsupervised algorithm that uses a kernel goodness-of-fit test, resulting in a method that is much faster and more scalable than existing topology-based alternatives, with proven correctness under certain conditions.
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 scaleable 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.