Fast Approximate CoSimRanks via Random Projections
Abstract
Given a graph G with n nodes, and two nodes u,v in G, the CoSimRank 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 realworld applications including synonym expansion, lexicon extraction, and entity relatedness in knowledge graphs. The computation of allpair CoSimRank values in G is highly expensive and challenging. Existing methods all focus on devising approximate algorithms for the computation of allpair CoSimRanks. To attain the desired absolute error delta, the stateoftheart approximate algorithm for computing allpair CoSimRank values requires O(n^3log2(ln(1/delta))) time. In this paper, we propose RPCoSim, a randomized algorithm for computing allpair CoSimRank values. The basic idea of RPCoSim is to reduce the n*n matrix multiplications into a kdimensional(k<<n) subspace via a random projection such that the pairwise inner product is preserved within a certain error, and then iteratively approximate CoSimRank values in the kdimensional subspace in O(n^2k) time. Theoretically, RPCoSimruns in O(n^2*ln(n)*ln(1/delta)/delta^2) time, and meanwhile ensures an absolute error of at most delta in the CoSimRank value of every two nodes in G with a high probability.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 DOI:
 10.48550/arXiv.2010.11880
 arXiv:
 arXiv:2010.11880
 Bibcode:
 2020arXiv201011880Y
 Keywords:

 Computer Science  Social and Information Networks;
 Computer Science  Data Structures and Algorithms
 EPrint:
 Severe issues in the paper