Link Prediction Under Imperfect Detection: Collaborative Filtering for Ecological Networks
<italic>Matrix completion</italic> based <italic>collaborative filtering</italic> is considered scalable and effective for online service link prediction (e.g., movie recommendation) but does not meet the challenges of link prediction in ecological networks. A unique challenge of ecological networks is that the observed data are subject to systematic <italic>imperfect detection</italic>, due to the difficulty of accurate field sampling. In this work, we propose a new framework customized for ecological bipartite network link prediction. Our approach starts with incorporating the Poisson <inline-formula><tex-math notation="LaTeX">$N$</tex-math><alternatives><mml:math><mml:mi>N</mml:mi></mml:math><inline-graphic xlink:href="fu-ieq1-2962031.gif"/></alternatives></inline-formula>-mixture model, a widely used framework in statistical ecology for modeling imperfect detection of a single species in field sampling. Despite its extensive use for single species analysis, this model has never been considered for link prediction between different species, perhaps because of the complex nature of both link prediction and <inline-formula><tex-math notation="LaTeX">$N$</tex-math><alternatives><mml:math><mml:mi>N</mml:mi></mml:math><inline-graphic xlink:href="fu-ieq2-2962031.gif"/></alternatives></inline-formula>-mixture model inference. By judiciously combining the Poisson <inline-formula><tex-math notation="LaTeX">$N$</tex-math><alternatives><mml:math><mml:mi>N</mml:mi></mml:math><inline-graphic xlink:href="fu-ieq3-2962031.gif"/></alternatives></inline-formula>-mixture model with a probabilistic nonnegative matrix factorization (NMF) model in latent space, we propose an intuitive statistical model for the problem of interest. We also offer a scalable and convergence-guaranteed optimization algorithm to handle the associated maximum likelihood identification problem. Experimental results on synthetic data and two real-world ecological networks data are employed to validate our proposed approach.