Coauthor prediction for junior researchers

Research collaboration can bring in different perspectives and generate more productive results. However, finding an appropriate collaborator can be difficult due to the lacking of sufficient information. Link prediction is a related technique for collaborator discovery; but its focus has been mostly on the core authors who have relatively more publications. We argue that junior researchers actually need more help in finding collaborators. Thus, in this paper, we focus on coauthor prediction for junior researchers. Most of the previous works on coauthor prediction considered global network feature and local network feature separately, or tried to combine local network feature and content feature. But we found a significant improvement by simply combing local network feature and global network feature. We further developed a regularization based approach to incorporate multiple features simultaneously. Experimental results demonstrated that this approach outperformed the simple linear combination of multiple features. We further showed that content features, which were proved to be useful in link prediction, can be easily integrated into our regularization approach. © 2013 Springer-Verlag

Scalable Katz ranking computation in large static and dynamic graphs

Network analysis defines a number of centrality measures to identify the most central nodes in a network. Fast computation of those measures is a major challenge in algorithmic network analysis. Aside from closeness and betweenness, Katz centrality is one of the established centrality measures. In this paper, we consider the problem of computing rankings for Katz centrality. In particular, we propose upper and lower bounds on the Katz score of a given node. While previous approaches relied on numerical approximation or heuristics to compute Katz centrality rankings, we construct an algorithm that iteratively improves those upper and lower bounds until a correct Katz ranking is obtained. We extend our algorithm to dynamic graphs while maintaining its correctness guarantees. Experiments demonstrate that our static graph algorithm outperforms both numerical approaches and heuristics with speedups between 1.5× and 3.5×, depending on the desired quality guarantees. Our dynamic graph algorithm improves upon the static algorithm for update batches of less than 10000 edges. We provide efficient parallel CPU and GPU implementations of our algorithms that enable near real-time Katz centrality computation for graphs with hundreds of millions of nodes in fractions of seconds

Block Gauss and anti-Gauss quadrature with application to networks

Approximations of matrix-valued functions of the form WT f(A)W, where A ∈Rm×m is symmetric, W ∈ Rm×k, with m large and k ≪ m, has orthonormal columns, and f is a function, can be computed by applying a few steps of the symmetric block Lanczos method to A with initial block-vector W ∈ Rm×k. Golub and Meurant have shown that the approximants obtained in this manner may be considered block Gauss quadrature rules associated with a matrix-valued measure. This paper generalizes anti-Gauss quadrature rules, introduced by Laurie for real-valued measures, to matrix-valued measures, and shows that under suitable conditions pairs of block Gauss and block anti-Gauss rules provide upper and lower bounds for the entries of the desired matrix-valued function. Extensions to matrix-valued functions of the form WT f(A)V , where A ∈ Rm×m may be nonsymmetric, and the matrices V, W ∈ Rm×k satisfy VT W = Ik also are discussed. Approximations of the latter functions are computed by applying a few steps of the nonsymmetric block Lanczos method to A with initial block-vectors V and W. We describe applications to the evaluation of functions of a symmetric or nonsymmetric adjacency matrix for a network. Numerical examples illustrate that a combination of block Gauss and anti-Gauss quadrature rules typically provides upper and lower bounds for such problems. We introduce some new quantities that describe properties of nodes in directed or undirected networks, and demonstrate how these and other quantities can be computed inexpensively with the quadrature rules of the present paper

Graph diffusions and matrix functions: fast algorithms and localization results

Network analysis provides tools for addressing fundamental applications in graphs such as webpage ranking, protein-function prediction, and product categorization and recommendation. As real-world networks grow to have millions of nodes and billions of edges, the scalability of network analysis algorithms becomes increasingly important. Whereas many standard graph algorithms rely on matrix-vector operations that require exploring the entire graph, this thesis is concerned with graph algorithms that are local (that explore only the graph region near the nodes of interest) as well as the localized behavior of global algorithms. We prove that two well-studied matrix functions for graph analysis, PageRank and the matrix exponential, stay localized on networks that have a skewed degree sequence related to the power-law degree distribution common to many real-world networks. Our results give the first theoretical explanation of a localization phenomenon that has long been observed in real-world networks. We prove our novel method for the matrix exponential converges in sublinear work on graphs with the specified degree sequence, and we adapt our method to produce the first deterministic algorithm for computing the related heat kernel diffusion in constant-time. Finally, we generalize this framework to compute any graph diffusion in constant time