Group-Invariant Max Filtering

Abstract: Given a group action on a vector space, and we study the problem of effectively separating the orbits under this action. After briefly discussing the history of this problem, we introduce a family of invariant functions that we call max filters. When the group is a finite subgroup of the orthogonal group, a sufficiently large max filter bank can separate the orbits, and even be bilipschitz in the quotient metric. We conclude by applying max filters to various machine learning tasks.

Bio: Dustin Mixon is an associate professor in the Department of Mathematics at The Ohio State University. In 2012, he received his PhD in Applied and Computational Mathematics from Princeton University under the supervision of Robert Calderbank. From there, he was an assistant professor at the Air Force Institute of Technology before joining the faculty at Ohio State in 2017. His research interests include applied harmonic analysis and mathematical data science.