Taming computational complexity: efficient and parallel SimRank optimizations on undirected graphs

SimRank has been considered as one of the promising link-based ranking algorithms to evaluate similarities of web documents in many modern search engines. In this paper, we investigate the optimization problem of SimRank similarity computation on undirected web graphs. We first present a novel algorithm to estimate the SimRank between vertices in O(n3+ Kn2) time, where n is the number of vertices, and K is the number of iterations. In comparison, the most efficient implementation of SimRank algorithm in [1] takes O(K n3 ) time in the worst case. To efficiently handle large-scale computations, we also propose a parallel implementation of the SimRank algorithm on multiple processors. The experimental evaluations on both synthetic and real-life data sets demonstrate the better computational time and parallel efficiency of our proposed techniques

More is simpler : effectively and efficiently assessing node-pair similarities based on hyperlinks

Similarity assessment is one of the core tasks in hyperlink analysis. Recently, with the proliferation of applications, e.g., web search and collaborative filtering, SimRank has been a well-studied measure of similarity between two nodes in a graph. It recursively follows the philosophy that "two nodes are similar if they are referenced (have incoming edges) from similar nodes", which can be viewed as an aggregation of similarities based on incoming paths. Despite its popularity, SimRank has an undesirable property, i.e., "zero-similarity": It only accommodates paths with equal length from a common "center" node. Thus, a large portion of other paths are fully ignored. This paper attempts to remedy this issue. (1) We propose and rigorously justify SimRank*, a revised version of SimRank, which resolves such counter-intuitive "zero-similarity" issues while inheriting merits of the basic SimRank philosophy. (2) We show that the series form of SimRank* can be reduced to a fairly succinct and elegant closed form, which looks even simpler than SimRank, yet enriches semantics without suffering from increased computational cost. This leads to a fixed-point iterative paradigm of SimRank* in O(Knm) time on a graph of n nodes and m edges for K iterations, which is comparable to SimRank. (3) To further optimize SimRank* computation, we leverage a novel clustering strategy via edge concentration. Due to its NP-hardness, we devise an efficient and effective heuristic to speed up SimRank* computation to O(Knm) time, where m is generally much smaller than m. (4) Using real and synthetic data, we empirically verify the rich semantics of SimRank*, and demonstrate its high computation efficiency

Towards efficient SimRank computation on large networks

SimRank has been a powerful model for assessing the similarity of pairs of vertices in a graph. It is based on the concept that two vertices are similar if they are referenced by similar vertices. Due to its self-referentiality, fast SimRank computation on large graphs poses significant challenges. The state-of-the-art work [17] exploits partial sums memorization for computing SimRank in O(Kmn) time on a graph with n vertices and m edges, where K is the number of iterations. Partial sums memorizing can reduce repeated calculations by caching part of similarity summations for later reuse. However, we observe that computations among different partial sums may have duplicate redundancy. Besides, for a desired accuracy ϵ, the existing SimRank model requires K = [logC ϵ] iterations [17], where C is a damping factor. Nevertheless, such a geometric rate of convergence is slow in practice if a high accuracy is desirable. In this paper, we address these gaps. (1) We propose an adaptive clustering strategy to eliminate partial sums redundancy (i.e., duplicate computations occurring in partial sums), and devise an efficient algorithm for speeding up the computation of SimRank to 0(Kdn2) time, where d is typically much smaller than the average in-degree of a graph. (2) We also present a new notion of SimRank that is based on a differential equation and can be represented as an exponential sum of transition matrices, as opposed to the geometric sum of the conventional counterpart. This leads to a further speedup in the convergence rate of SimRank iterations. (3) Using real and synthetic data, we empirically verify that our approach of partial sums sharing outperforms the best known algorithm by up to one order of magnitude, and that our revised notion of SimRank further achieves a 5X speedup on large graphs while also fairly preserving the relative order of original SimRank scores

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

Exact Single-Source SimRank Computation on Large Graphs

SimRank is a popular measurement for evaluating the node-to-node similarities based on the graph topology. In recent years, single-source and top-$k$ SimRank queries have received increasing attention due to their applications in web mining, social network analysis, and spam detection. However, a fundamental obstacle in studying SimRank has been the lack of ground truths. The only exact algorithm, Power Method, is computationally infeasible on graphs with more than $10^6$ nodes. Consequently, no existing work has evaluated the actual trade-offs between query time and accuracy on large real-world graphs. In this paper, we present ExactSim, the first algorithm that computes the exact single-source and top-$k$ SimRank results on large graphs. With high probability, this algorithm produces ground truths with a rigorous theoretical guarantee. We conduct extensive experiments on real-world datasets to demonstrate the efficiency of ExactSim. The results show that ExactSim provides the ground truth for any single-source SimRank query with a precision up to 7 decimal places within a reasonable query time.Comment: ACM SIGMOD 202

Representation Independent Analytics Over Structured Data

Database analytics algorithms leverage quantifiable structural properties of the data to predict interesting concepts and relationships. The same information, however, can be represented using many different structures and the structural properties observed over particular representations do not necessarily hold for alternative structures. Thus, there is no guarantee that current database analytics algorithms will still provide the correct insights, no matter what structures are chosen to organize the database. Because these algorithms tend to be highly effective over some choices of structure, such as that of the databases used to validate them, but not so effective with others, database analytics has largely remained the province of experts who can find the desired forms for these algorithms. We argue that in order to make database analytics usable, we should use or develop algorithms that are effective over a wide range of choices of structural organizations. We introduce the notion of representation independence, study its fundamental properties for a wide range of data analytics algorithms, and empirically analyze the amount of representation independence of some popular database analytics algorithms. Our results indicate that most algorithms are not generally representation independent and find the characteristics of more representation independent heuristics under certain representational shifts