Detection-Aware Sparse Network Recovery for Climate-Relevant Ecosystem Monitoring

Climate adaptation and ecosystem management increasingly rely on repeated biodiversity surveys, yet rare interactions and species calls are easily missed. Such surveys are naturally represented as bipartite count networks, motivating the need for reliable monitoring and recovery of both cross-group interactions (e.g., species--site or plant--pollinator links) and within-group similarity patterns (e.g., sites with related communities or species with related interaction profiles) without interpreting non-detections as ecological absences. Such networks are often sparse and inherently imperfect in their detection. Existing models mainly focus on interaction recovery, while the induced similarity graphs are much less studied. Moreover, sparsity is often uncontrolled, and scale is unbalanced, leading to oversparse or poorly rescaled estimates that degrade structural recovery. To address these issues, we propose a framework for structured sparse nonnegative low-rank factorization with detection probability estimation. We impose a nonconvex $\ell_{1/2}$ regularization on the latent similarity and connectivity structures to promote sparsity in within-group similarity and cross-group connectivity, with better relative scale. The resulting optimization problem is nonconvex and nonsmooth. To solve it, we develop an ADMM-based algorithm with adaptive penalization and scale-aware initialization and establish its asymptotic feasibility and KKT stationarity of cluster points under mild regularity conditions. Experiments on synthetic and real-world ecological datasets demonstrate improved recovery of latent factors and similarity/connectivity structure relative to existing baselines.