DeepAI AI Chat
Log In Sign Up

Fast Approximate CoSimRanks via Random Projections

by   Renchi Yang, et al.
Nanyang Technological University

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<<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 k-dimensional subspace in O(n^2k) time. Theoretically, RP-CoSimruns 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.


page 1

page 2

page 3

page 4


Random Projections and Dimension Reduction

This paper, broadly speaking, covers the use of randomness in two main a...

SsAG: Summarization and sparsification of Attributed Graphs

We present SSAG, an efficient and scalable method for computing a lossy ...

Constant Time Graph Neural Networks

Recent advancements in graph neural networks (GNN) have led to state-of-...

Fast Incremental von Neumann Graph Entropy Computation: Theory, Algorithm, and Applications

The von Neumann graph entropy (VNGE) facilitates the measure of informat...

Fast Graph Filters for Decentralized Subspace Projection

A number of inference problems with sensor networks involve projecting a...