Codes and Expansions (CodEx) Seminar

Jameson Cahill (University of North Carolina at Wilmington)
Max filtering

We consider the problem of effectively separating the orbits of the action of a group \(G\) on a vector space \(V\). After briefly discussing the history of this problem, we introduce a family of \(G\)-invariant functions which we call max filters. In the case where \(V=R^d\) and \(G\) is a finite subgroup of \(O(d)\), we show that a sufficiently large max filter bank can separate the orbits and can even be bilipschitz in an appropriate metric. We will discuss the complexity of evaluating max filters in several instances, and we establish that max filters are well suited for various classification tasks, both in theory and in practice. Throughout the talk, we will discuss several important open problems.