From random walks to distances on unweighted graphs
Name
from-random-walks-to-distances-on-unweighted-graphs.pdf
Size
1.69 MB
Format
Adobe PDF
Checksum (MD5)
e76d869afc013f436679377abbcc7999
Author(s)
Hashimoto, Tatsunori Benjamin
Jaakkola, Tommi S
Sun, Yi
Date Issued
December 2015
Journal
Advances in Neural Information Processing Systems 28 (NIPS 2015)
Publisher
Neural Information Processing Systems Foundation, Inc.
Citation
Hashimoto, Tatsunori, Yi Sun, and Tommi Jaakkola. "From random walks to distances on unweighted graphs." Advances in Neural Information Processing Systems 28 (NIPS 2015), 7-12 December, 2015, Montreal, Canada, edited by C. Cortes and N.D. Lawrence and D.D. Lee, Neural Information Processing Systems Foundation, 2017. © 2015 Neural Information Processing Systems Foundation, Inc.
Version
Final published version
Abstract
Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the significance of this problem, statistical characterization of the proposed metrics has been limited.We introduce and develop a class of techniques for analyzing random walks on graphs using stochastic calculus. Using these techniques we generalize results on the degeneracy of hitting times and analyze a metric based on the Laplace transformed hitting time (LTHT). The metric serves as a natural, provably well-behaved alternative to the expected hitting time. We establish a general correspondence between hitting times of the Brownian motion and analogous hitting times on the graph. We show that the LTHT is consistent with respect to the underlying metric of a geometric graph, preserves clustering tendency, and remains robust against random addition of non-geometric edges. Tests on simulated and real-world data show that the LTHT matches theoretical predictions and outperforms alternatives.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://papers.nips.cc/paper/6009-from-random-walks-to-distances-on-unweighted-graphs
