Clustering Underwater Sound Speed Profiles via Elastic Shape Metric and Elastic Partial Matching

Elastic Riemannian metrics have been used success-fully for statistical treatments of both fully observed functional data with fixed boundaries as well as partially observed functional data with a sliding right boundary. Here, we make use of elastic distance metrics, through both dense and partial elastic registration, to cluster sound speed profile (SSP) datasets. We compare the clustering performance with non-elastic methods through the use of certain clustering quality measures. Furthermore, we validate clustering results by measuring how well the SSP clusters separate the profiles’ respective acoustic transmission properties. That is, for each SSP, we generate a Transmission Loss (TL) diagram, assign SSP cluster labels to respective TL diagrams, and analyze the resulting clustering quality. We show that SSP clustering via the elastic metric yields a more sensible grouping of TL diagrams created from shallow water sound sources compared to non-elastic SSP clustering. Finally, we use elastic partial matching to cluster incomplete SSPs with shallow max depths and show that within-class variation is reduced compared to non-elastic methods.