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Researchers are regularly interested in interpreting the multipartite structure of data entities according to their functional relationships. Data is often heterogeneous with intricately hidden inner structure. With limited prior knowledge, researchers are likely to confront the problem of transforming this data into knowledge. We develop a new framework, called heat-passing, which exploits intrinsic similarity relationships within noisy and incomplete raw data, and constructs a meaningful map of the data. The proposed framework is able to rank, cluster, and visualize the data all at once. The novelty of this framework is derived from an analogy between the process of data interpretation and that of heat transfer, in which all data points contribute simultaneously and globally to reveal intrinsic similarities between regions of data, meaningful coordinates for embedding the data, and exemplar data points that lie at optimal positions for heat transfer. We demonstrate the effectiveness of the heat-passing framework for robustly partitioning the complex networks, analyzing the globin family of proteins and determining conformational states of macromolecules in the presence of high levels of noise. The results indicate that the methodology is able to reveal functionally consistent relationships in a robust fashion with no reference to prior knowledge. The heat-passing framework is very general and has the potential for applications to a broad range of research fields, for example, biological networks, social networks and semantic analysis of documents. [ABSTRACT FROM AUTHOR]

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]