Issue No. 11 - Nov. (2017 vol. 29)
ISSN: 1041-4347
pp: 2522-2536
Rong Zhu , School of Computer Science and Technology, Harbin Institute of Technology, Harbin, Heilongjiang, China
Zhaonian Zou , School of Computer Science and Technology, Harbin Institute of Technology, Harbin, Heilongjiang, China
Jianzhong Li , School of Computer Science and Technology, Harbin Institute of Technology, Harbin, Heilongjiang, China
ABSTRACT
SimRank is a similarity measure between vertices in a graph. Recently, many algorithms have been proposed to efficiently evaluate SimRank similarities. However, the existing algorithms either overlook uncertainty in graph structures or depends on an unreasonable assumption. In this paper, we study SimRank on uncertain graphs. Following the random-walk-based formulation of SimRank on deterministic graphs and the possible world model of uncertain graphs, we first define random walks on uncertain graphs and show that our definition of random walks satisfies Markov’s property. We formulate our SimRank measure based on random walks on uncertain graphs. We discover a critical difference between random walks on uncertain graphs and random walks on deterministic graphs, which makes all existing SimRank computation algorithms on deterministic graphs inapplicable to uncertain graphs. For SimRank computation, we consider computing both single-pair SimRank and single-source top-$K$ SimRank. We propose three algorithms, namely the sampling algorithm with high efficiency, the two-phase algorithm with comparable efficiency and higher accuracy, and a speeding-up algorithm with much higher efficiency. Meanwhile, we present an optimized algorithm for efficient computing the single-source top- $K$ SimRank. The experimental results verify the effectiveness of our SimRank measure and the efficiency of the proposed SimRank computation algorithms.
INDEX TERMS
Proteins, Uncertainty, Approximation algorithms, Measurement uncertainty, Linear matrix inequalities, Markov processes, Erbium
CITATION

R. Zhu, Z. Zou and J. Li, "SimRank on Uncertain Graphs," in IEEE Transactions on Knowledge & Data Engineering, vol. 29, no. 11, pp. 2522-2536, 2017.
doi:10.1109/TKDE.2017.2725275