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Similarity is a fundamental measure in network analyses and machine learning algorithms, with wide applications ranging from personalized recommendation to socio-economic dynamics. We argue that an effective similarity measurement should guarantee the stability even under some information loss. With six bipartite networks, we investigate the stabilities of fifteen similarity measurements by comparing the similarity matrixes of two data samples which are randomly divided from original data sets. Results show that, the fifteen measurements can be well classified into three clusters according to their stabilities, and measurements in the same cluster have similar mathematical definitions. In addition, we develop a top-$n$-stability method for personalized recommendation, and find that the unstable similarities would recommend false information to users, and the performance of recommendation would be largely improved by using stable similarity measurements. This work provides a novel dimension to analyze and evaluate similarity measurements, which can further find applications in link prediction, personalized recommendation, clustering algorithms, community detection and so on.
Despite the abundance of bipartite networked systems, their organizing principles are less studied, compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the pro
We use the information present in a bipartite network to detect cores of communities of each set of the bipartite system. Cores of communities are found by investigating statistically validated projected networks obtained using information present in
Many real-world complex systems are well represented as multilayer networks; predicting interactions in those systems is one of the most pressing problems in predictive network science. To address this challenge, we introduce two stochastic block mod
Bipartite networks are currently regarded as providing a major insight into the organization of many real-world systems, unveiling the mechanisms driving the interactions occurring between distinct groups of nodes. One of the most important issues en
In human society, a lot of social phenomena can be concluded into a mathematical problem called the bipartite matching, one of the most well known model is the marriage problem proposed by Gale and Shapley. In this article, we try to find out some in