Gauging Correct Relative Rankings For Similarity Search

© 2015 ACM.One of the important tasks in link analysis is to quantify the similarity between two objects based on hyperlink structure. SimRank is an attractive similarity measure of this type. Existing work mainly focuses on absolute SimRank scores, and often harnesses an iterative paradigm to compute them. While these iterative scores converge to exact ones with the increasing number of iterations, it is still notoriously difficult to determine how well the relative orders of these iterative scores can be preserved for a given iteration. In this paper, we propose efficient ranking criteria that can secure correct relative orders of node-pairs with respect to SimRank scores when they are computed in an iterative fashion. Moreover, we show the superiority of our criteria in harvesting top-K SimRank scores and bucket orders from a full ranking list. Finally, viable empirical studies verify the usefulness of our techniques for SimRank top-K ranking and bucket ordering

CLUDE: An Efficient Algorithm for LU Decomposition Over a Sequence of Evolving Graphs

Session: Matrix Factorization, Clustering and Probabilistic DataIn many applications, entities and their relationships are represented by graphs. Examples include the WWW (web pages and hyperlinks) and bibliographic networks (authors and co-authorship). A graph can be conveniently modeled by a matrix from which various quantitative measures are derived. Some example measures include PageRank and SALSA (which measure nodes’ importance), and Personalized PageRank and Random Walk with Restart (which measure proximities between nodes). To compute these measures, linear systems of the form Ax = b, where A is a matrix that captures a graph’s structure, need to be solved. To facilitate solving the linear system, the matrix A is often decomposed into two triangular matrices (L and U). In a dynamic world, the graph that models it changes with time and thus is the matrix A that represents the graph. We consider a sequence of evolving graphs and its associated sequence of evolving matrices. We study how LU-decomposition should be done over the sequence so that (1) the decomposition is efficient and (2) the resulting LU matrices best preserve the sparsity of the matrices A’s (i.e., the number of extra non-zero entries introduced in L and U are minimized.) We propose a cluster-based algorithm CLUDE for solving the problem. Through an experimental study, we show that CLUDE is about an order of magnitude faster than the traditional incremental update algorithm. The number of extra non-zero entries introduced by CLUDE is also about an order of magnitude fewer than that of the traditional algorithm. CLUDE is thus an efficient algorithm for LU decomposition that produces high-quality LU matrices over an evolving matrix sequence.published_or_final_versio

Evolving Networks and Social Network Analysis Methods and Techniques

Evolving networks by definition are networks that change as a function of time. They are a natural extension of network science since almost all real-world networks evolve over time, either by adding or by removing nodes or links over time: elementary actor-level network measures like network centrality change as a function of time, popularity and influence of individuals grow or fade depending on processes, and events occur in networks during time intervals. Other problems such as network-level statistics computation, link prediction, community detection, and visualization gain additional research importance when applied to dynamic online social networks (OSNs). Due to their temporal dimension, rapid growth of users, velocity of changes in networks, and amount of data that these OSNs generate, effective and efficient methods and techniques for small static networks are now required to scale and deal with the temporal dimension in case of streaming settings. This chapter reviews the state of the art in selected aspects of evolving social networks presenting open research challenges related to OSNs. The challenges suggest that significant further research is required in evolving social networks, i.e., existent methods, techniques, and algorithms must be rethought and designed toward incremental and dynamic versions that allow the efficient analysis of evolving networks