Holographic and other Point Set Distances for Machine Learning

Lukas Balles, Thomas Fischbacher

Abstract: We introduce an analytic distance function for moderately sized point sets of known cardinality that is shown to have very desirable properties, both as a loss function as well as a regularizer for machine learning applications. We compare our novel construction to other point set distance functions and show proof of concept experiments for training neural networks end-to-end on point set prediction tasks such as object detection.

Keywords: point set, set, permutation-invariant, loss function

TL;DR: Permutation-invariant loss function for point set prediction.