Echosounders are high-frequency sonar systems widely used to observe mid-trophic level animals in the ocean. The recent deluge of echosounder data from diverse ocean observing platforms has created unprecedented opportunities to study marine ecosystems at broad scales. However, there is a critical lack of methods capable of automatic and adaptive extraction of ecologically relevant Spatio-temporal structures from echosounder observation, thwarting effective use of these rich data in marine ecological research.

Here we present a data-driven methodology based on matrix decomposition that builds a compact representation of long-term echosounder time series using intrinsic features in the data. We use Principal Component Pursuit (PCP) to remove noisy outliers and employ temporally smooth Nonnegative Matrix Factorization (tsNMF) to discover high-level Spatio-temporal structures, such as scattering layers and diel migration patterns, from the data. We demonstrate the utility of this methodology by analyzing a multi-frequency time series from an echosounder moored at the shelf break of the northeast Pacific Ocean.

Our methodology successfully removes noise interference and automatically discovers a small number of distinct daily echogram patterns, whose time-varying linear combination (activation) reconstructs the dominant structures in the original time series. Each pattern represents a distribution of echo energy across time (hour of the day) and space (depth) that co-varies throughout the observation. Compact representation of echosounder time series tion period, with multi-frequency features suggestive of scatterer identity. The pattern activations further o er quantitative summarization of temporal processes
embedded in the data, in a format that is suitable for visualization and systematic analysis with other ocean variables such as currents.

We show that matrix decomposition methods are powerful techniques that could transform complex echo observation into low-dimensional components that are more tractable and interpretable than the original data. Unlike existing echo analysis methods that rely on xed, handcrafted rules, the data-driven and thus adaptable nature of our methodology are well-suited for analyzing data collected from unfamiliar ecosystems or ecosystems undergoing rapid changes in the changing climate. Future developments and applications based on this work will catalyze advancements in marine ecology by providing robust time-series analytics for large-scale, acoustics-based biological observation in the ocean.