Tensor decomposition of multi-frequency echosounder time series

In this paper we use tensor decomposition to analyze multi-frequency ocean sonar time series recorded by a moored echosounder on a cabled ocean observatory. Echosounders are high-frequency sonar systems widely used to observe biological aggregations in the ocean. Conventional echo analysis procedures rely heavily on human experts to manually analyze and extract synoptic information from the observations, a procedure that is difficult to scale up for large volumes of data. Frequency-dependent echo features, which varies strongly depending on the size and material properties of the scatterer, is one of the main features human experts use in this process to identify biological aggregations of interest. Tensor decomposition generalizes standard latent decomposition techniques to multi-way analysis and thus is a natural fit for extracting patterns from multi-frequency echo data. We show that, by explicitly accounting for frequency information in the formulation, tensor decomposition discovers patterns that capture the dominant spatio-temporal structures in the echoes with frequency dependencies that are potentially biologically meaningful. The fully separable component contributions in the Kruskal form of tensor decomposition make the biological sources of these structures more interpretable, as all elements within the same component share an identical frequency signature. This research lays the foundation for further development of methodologies capable of handling large multi-modal echosounder data sets that stretch in time, space, and frequency.