The performance of topological classifiers on sonar data

Abstract

For various reasons, synthetic aperture sonar (SAS) target classification in various clutter contexts is usually done using a data-driven, machine learning approach. Unfortunately, the resulting feature set can be rather inscrutable—what features is it really using? Topological methods are particularly well-aligned with the goal of gaining insight into physical processes, since they highlight symmetries which are driven by these physical processes. For instance, collating multiple image looks of a round object uncovers rotational symmetries in an appropriate feature space derived from the images. The use of topological invariants allows one to infer that the object is round by reasoning about its feature space. The fact that sonar target signatures are (mostly) translation invariant in range can also be deduced from topological invariants. I will describe a principled, foundational analysis of target echo structure through the lens of topological signal processing, and then analyze the performance of this approach as compared to more traditional classification methods.