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Protein-protein interaction (PPI) network analysis presents an essential role in understanding the functional relationship among proteins in a living biological system. Despite the success of current approaches for understanding the PPI network, the large fraction of missing and spurious PPIs and a low coverage of complete PPI network are the sources of major concern. In this paper, based on the diffusion process, we propose a new concept of global geometric affinity and an accompanying computational scheme to filter the uncertain PPIs, namely, reduce the spurious PPIs and recover the missing PPIs in the network. The main concept defines a diffusion process in which all proteins simultaneously participate to define a similarity metric (global geometric affinity (GGA)) to robustly reflect the internal connectivity among proteins. The robustness of the GGA is attributed to propagating the local connectivity to a global representation of similarity among proteins in a diffusion process. The propagation process is extremely fast as only simple matrix products are required in this computation process and thus our method is geared toward applications in high-throughput PPI networks. Furthermore, we proposed two new approaches that determine the optimal geometric scale of the PPI network and the optimal threshold for assigning the PPI from the GGA matrix. Our approach is tested with three protein-protein interaction networks and performs well with significant random noises of deletions and insertions in true PPIs. Our approach has the potential to benefit biological experiments, to better characterize network data sets, and to drive new discoveries. [ABSTRACT FROM AUTHOR]