Infer user interests via link structure regularization

Learning user interests from online social networks helps to better understand user behaviors and provides useful guidance to design user-centric applications. Apart from analyzing users' online content, it is also important to consider users' social connections in the social Web. Graph regularization methods have been widely used in various text mining tasks, which can leverage the graph structure information extracted from data. Previously, graph regularization methods operate under the cluster assumption that nearby nodes are more similar and nodes on the same structure (typically referred to as a cluster or a manifold) are likely to be similar. We argue that learning user interests from complex, sparse, and dynamic social networks should be based on the link structure assumption under which node similarities are evaluated based on the local link structures instead of explicit links between two nodes. We propose a regularization framework based on the relation bipartite graph, which can be constructed from any type of relations. Using Twitter as our case study, we evaluate our proposed framework from social networks built from retweet relations. Both quantitative and qualitative experiments show that our proposed method outperforms a few competitive baselines in learning user interests over a set of predefined topics. It also gives superior results compared to the baselines on retweet prediction and topical authority identification

Explicit and Exact Solutions to a Kolmogorov-Petrovskii-Piskunov Equation

Some explicit traveling wave solutions to a Kolmogorov-Petrovskii-Piskunov equation are presented through two ans\"atze. By a Cole-Hopf transformation, this Kolmogorov-Petrovskii-Piskunov equation is also written as a bilinear equation and further two solutions to describe nonlinear interaction of traveling waves are generated. B\"acklund transformations of the linear form and some special cases are considered.Comment: 14pages, Latex, to appear in Intern. J. Nonlinear Mechanics, the original latex file is not complet