Fast Approximate CoSimRanks via Random Projections

Given a graph G with n nodes, and two nodes u,v in G, the CoSim-Rank value s(u,v) quantifies the similarity between u and v based on graph topology. Compared to SimRank, CoSimRank has been shown to be more accurate and effective in many real-world applications including synonym expansion, lexicon extraction, and entity relatedness in knowledge graphs. The computation of all-pair CoSimRank values in G is highly expensive and challenging. Existing methods all focus on devising approximate algorithms for the computation of all-pair CoSimRanks. To attain the desired absolute error delta, the state-of-the-art approximate algorithm for computing all-pair CoSimRank values requires O(n^3log2(ln(1/delta))) time. In this paper, we propose RP-CoSim, a randomized algorithm for computing all-pair CoSimRank values. The basic idea of RP-CoSim is to reduce the n*n matrix multiplications into a k-dimensional(k<

Keywords:

• Approximation error
• Computation
• Matrix multiplication
• Discrete mathematics
• SimRank
• Randomized algorithm
• Random projection
• Topological graph theory
• Mathematics
• Subspace topology

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