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A Two-Stage Geometric Method for Pruning Unreliable Links in Protein-Protein Networks Protein-protein interactions (PPIs) play essential roles for determining the outcomes of most of the cellular functions of the cell. Although the experimentally detected high-throughput PPI data promise new opportunities for the study of many biological mechanisms including cellular metabolism and protein functions, experimentally detected PPIs have high levels of false positive rate. Therefore, it is of high practical value to develop novel computational tools for pruning low-confidence PPIs. In this paper, we propose a new geometric approach called Leave-One-Out Logistic Metric Embedding (LOO-LME) for assessing the reliability of interactions. Unlike previous approaches which mainly seek to preserve the noisy topological information of the PPI networks in the embedding space, LOO-LME first transforms the learning task into an equivalent discriminant form, then directly deals with the uncertainty in PPI networks using a leave-one-out-style approach. The experimental results show that LOO-LME substantially outperforms previous methods on PPI assessment problems. LOO-LME could thus facilitate further graph-based studies of PPIs and may help infer their hidden underlying biological knowledge.