Link prediction via linear optimization

Abstract

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...

Protein Interface Complementarity and Gene Duplication Improve Link Prediction of Protein-Protein Interaction Network

“…These common characteristics have inspired scholars to study PPI networks in the way of studying social networks. These methodologies are mainly divided into three categories: neighborhood-based or paths-based approaches (Cannistraci et al, 2013;Huang et al, 2017;Muscoloni et al, 2018;Kovács et al, 2019;Pech et al, 2019), hierarchical clustering approaches (Clauset et al, 2008;Symeonidis et al, 2013), and random walkbased approaches (Lichtenwalter et al, 2010;Backstrom and Leskovec, 2011).…”

“…However, the principle that people tend to build relationships with people who are close to them in social networks cannot explain the interaction of two proteins. Therefore, some scholars (Muscoloni et al, 2018;Kovács et al, 2019;Pech et al, 2019) attempt to explain the link mechanism of PPI networks with 3-hop paths rather than 2-hop paths.…”

“…where z 1 , z 2 are the intermediate nodes in the 3-hop path L3; a iz 1 , a z 1 z 2 , and a z 2 j are the link strength of iz 1 , z 1 z 2 , and z 2 j, respectively. Through a simple assumption that the possibility of a link between two nodes can be unfolded by the linear summation of the contributions of neighbors, Pech et al (2019) proposed an optimization problem for similarity matrix S (i.e., Equation 2).…”

“…In summary, Kovács et al (2019) illustrates the basis of their methods: Principle of L3 from the perspective of protein structure and evolution. Pech et al (2019) assumes that the link likelihood of node i and j equals the linear combination of the similarity between i's neighbors and j. And then they use linear optimization to obtain the optimal similarity matrix and the link likelihood matrix.…”

“…We will give some examples to illustrate this in section 2.4. Another disadvantage of LO is that there is no good way to determine the value of the free parameter α, it is just declared that α is a very small number in Pech et al (2019). We set α = 0.00001 in this paper.…”