Riemannian Geometric Characterization of Underwater Biological Signals via Fisher-Optimized SPD Manifolds

Abstract

Automated fish welfare monitoring in intensive aquaculture is hindered by environmental noise, individual variability, and data scarcity. These challenges have not been fully resolved by existing deep learning approaches. Traditional computer-vision methods are constrained by underwater turbidity, whereas Passive Acoustic Monitoring (PAM) offers a promising non-invasive alternative for assessing aquatic environments. This study proposes Fisher-SPD, a lightweight, geometry-aware framework for classifying the acoustic behaviour of cage-farmed Larimichthys crocea. A Fisher-score mechanism adaptively selects discriminative frequency bands, effectively filtering complex broadband noise commonly found in commercial sea cages. Acoustic segments are modelled as Symmetric Positive Definite (SPD) covariance matrices and mapped onto a linear tangent space via the Log-Euclidean Metric, preserving intrinsic statistical structure even under data-scarce conditions. Furthermore, a Physics-Consistency Masking mechanism applies source-level physical priors as hard inference-time constraints to robustly suppress false positives originating from background interference. Under a strict Leave-One-Subject-Out Cross-Validation (LOSO-CV) protocol, the framework achieved a mean zero-shot accuracy of 89.22% ± 2.59%, significantly outperforming ResNet-18 and other deep learning baselines, while maintaining a low inference latency of only 3.60 ms on edge devices. Through few-shot domain calibration, the system achieved 92.86% accuracy in a dual-fish overlapping-source environment. Ultimately, this framework provides a robust, data-efficient solution for real-time stress detection and welfare monitoring in modern intensive aquaculture.