Machine learning on rigid classes of Euclidean clouds of unordered points

Yury Elkin, Vitaliy Kurlin

TL;DR: The paper develops machine learning based on complete and continuous invariants driven by chemistry applications.

Abstract: Most real objects allow infinitely many different representations. Robust machine learning aims to use only invariant features independent of object representations to guarantee that any output (class label or predicted property) is preserved if the same object is represented differently. For Euclidean clouds of unordered points under rigid motion, we introduce complete invariants (with no false negatives, no false positives) and a Lipschitz continuous distance that satisfies all metric axioms and is computable in polynomial time of the number of points. The new realizability property implies that the space of all rigid clouds is efficiently parametrized by vectorial invariants like geographic coordinates. The proposed invariants distinguished all rigid classes of atomic clouds in the world's largest collections of molecules with 3D coordinates and predicted chemical elements by pure geometry with over 98% accuracy.

Primary Area: Applications->Chemistry, Physics, and Earth Sciences

Keywords: application-driven machine learning, point cloud, rigid motion, complete invariant, continuous metric, molecule

Application-Driven Machine Learning: This submission is on Application-Driven Machine Learning.

Submission Number: 13229