Link prediction is an elemental challenge in network science, which has already found applications in guiding laboratorial experiments, digging out drug targets, recommending online friends, probing network evolution mechanisms, and so on. With a simple assumption that the likelihood of the existence of a link between two nodes can be unfolded by a linear summation of neighboring nodes' contributions, we obtain the analytical solution of the optimal likelihood matrix, which shows remarkably better performance in predicting missing links than the state-of-the-art algorithms for not only simple networks, but also weighted and directed networks. To our surprise, even some degenerated local similarity indices from the solution outperform well-known local indices, which largely refines our knowledge, for example, the number of 3-hop paths between two nodes more accurately predicts missing links than the number of 2-hop paths (i.e., the number of common neighbors), while in previous methods, longer paths are always considered to be less important than shorter paths.Thanks to the breakthrough in uncovering the structural complexity (e.g., small-world 1 and scale-free 2 properties) in real networks, the recent twenty years have witnessed an explosion in the studies of networks, which is turning the so-called network science from niche branches of science in mathematics (i.e., graph theory) and social science (i.e., social network analysis) to an interdisciplinary focus that attracts increasing attentions from physicists, mathematicians, social scientists, computer scientists, biologists, and so on. Recently, the research focus of network science has been shifting from macroscopic statistical regularities 3 to different roles played by microscopic elements, such as nodes 4 and links 5 , in network structure and functions. Therein, link prediction is an elemental challenge that aims at estimating the likelihood that a nonobserved link exists, on the basis of observed links in a network 6 .Link prediction is of particular significance. Theoretically speaking, link prediction can be used as a probe to quantify to which extent the network formation and evolution can be explained by a mechanism model, since a better model should be in principle transferred to a more accurate algorithm 7, 8 . Beyond theoretical interests, link prediction has already found many applications.For example, our knowledge of biological interactions is highly limited, with approximately 99.7% of the molecular interactions in human beings still unknown 9 . Instead of blindly checking all possible interactions, to predict based on known interactions and focus on those links most likely to exist can sharply reduce the experimental costs if the predictions are accurate enough 10 . Analogously, the known interactions between drugs and target proteins are very limited, while it is believed that any single drug can interact with multiple targets 11 . By this time, link prediction algorithms have already played a critical role in finding out new uses of old d...

Inspired by practical importance of social networks, economic networks, biological networks and so on, studies on large and complex networks have attracted a surge of attentions in the recent years. Link prediction is a fundamental issue to understand the mechanisms by which new links are added to the networks. We introduce the method of robust principal component analysis (robust PCA) into link prediction, and estimate the missing entries of the adjacency matrix. On one hand, our algorithm is based on the sparsity and low rank property of the matrix, on the other hand, it also performs very well when the network is dense. This is because a relatively dense real network is also sparse in comparison to the complete graph. According to extensive experiments on real networks from disparate fields, when the target network is connected and sufficiently dense, whatever it is weighted or unweighted, our method is demonstrated to be very effective and with prediction accuracy being considerably improved comparing with many state-of-the-art algorithms.

Drug-target interaction (DTI) prediction plays a very important role in drug development and drug discovery. Biochemical experiments or in vitro methods are very expensive, laborious and time-consuming. Therefore, in silico approaches including docking simulation and machine learning have been proposed to solve this problem. In particular, machine learning approaches have attracted increasing attentions recently. However, in addition to the known drug-target interactions, most of the machine learning methods require extra characteristic information such as chemical structures, genome sequences, binding types and so on. Whenever such information is not available, they may perform poor. Very recently, the similarity-based link prediction methods were extended to bipartite networks, which can be applied to solve the DTI prediction problem by using topological information only. In this work, we propose a method based on low-rank matrix projection to solve the DTI prediction problem. On one hand, when there is no extra characteristic information of drugs or

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MicroRNAs (miRNAs) have been playing a crucial role in many important biological processes. Currently, the validated associations between miRNAs and diseases are insufficient comparing to all underlying associations. To identify these hidden associations based on biological experiment is expensive, laborious and time consuming. Therefore, computationally inferring the potential associations from biological data for further biological experiment has attracted increasing interests from different communities ranging from biological to computational science. In this work, we propose an effective and flexible method to predict the associations between miRNAs and diseases, namely linear optimization (LOMDA). The proposed method is capable of predicting the associations in three manners e.g., extra information such as miRNA functional similarity, gene functional similarity and known miRNA-disease associations are available;only some associations are known; and new miRNAs or diseases that do not have any known associations at all. The average AUC obtained from LOMDA over 15 diseases in a 5-fold-cross validation is 0.997, while the AUC of 5-fold cross validation on all diseases is 0.957. Moreover, the average AUC on leave-one-out cross validation is 0.866. We compare LOMDA with the state-of-the-art meth- *