Functional data analysis to describe and classify southern resident killer whale calls

The Southern Resident Killer Whale (SRKW) is an endangered population of whales found in the northeast Pacific. They have a vocal dialect unique from other killer whales, having a repertoire of distinct stereotyped calls. A framework for distinguishing SRKW call types using the frequency traces of the amplitude ridges from their spectrograms (termed frequency ridges) is proposed. The first step is the extraction of these ridges of SRKW calls using an Sequential Monte Carlo approach. Next, they are converted into functional data using B-spline functions. They are analyzed with a functional principal component (FPC) analysis to characterise the intrinsic variability of frequency ridges within a call type. The FPCs are able to capture the general patterns in the frequency ridges of the different SRKW call types. The FPCs are also used as the basis for call classification. Using a cross-validation procedure to assess the robustness of the classification, this framework proves to be successful for classification with some call types having an F1-score $\ge 80\%$, but other calls less well discriminated. On balance, this approach showed reasonable performance given the small sample size available, and provides a useful contribution towards the development of a universal tool for call classification.