TY - JOUR

T1 - Remember where you came from

T2 - 43rd International Conference on Very Large Data Bases, VLDB 2017

AU - Wu, Yubao

AU - Bian, Yuchen

AU - Zhang, Xiang

N1 - Funding Information:
This work was partially supported by the National Science Foundation grants IIS-1162374, CAREER, and the NIH grant R01GM115833.
Publisher Copyright:
© 2016. VLDB Endowment.

PY - 2016

Y1 - 2016

N2 - Measuring the proximity between different nodes is a fundamental problem in graph analysis. Random walk based proximity measures have been shown to be effective and widely used. Most existing random walk measures are based on the first-order Markov model, i.e., they assume that the next step of the random surfer only depends on the current node. However, this assumption neither holds in many real- life applications nor captures the clustering structure in the graph. To address the limitation of the existing first-order measures, in this paper, we study the second-order random walk measures, which take the previously visited node into consideration. While the existing first-order measures are built on node-to-node transition probabilities, in the second-order random walk, we need to consider the edge-to-edge transition probabilities. Using incidence matrices, we develop simple and elegant matrix representations for the second-order proximity measures. A desirable property of the developed measures is that they degenerate to their original first-order forms when the effect of the previous step is zero. We further develop Monte Carlo methods to efficiently compute the second-order measures and provide theoretical performance guarantees. Experimental results show that in a variety of applications, the second-order measures can dramatically improve the performance compared to their first-order counterparts.

AB - Measuring the proximity between different nodes is a fundamental problem in graph analysis. Random walk based proximity measures have been shown to be effective and widely used. Most existing random walk measures are based on the first-order Markov model, i.e., they assume that the next step of the random surfer only depends on the current node. However, this assumption neither holds in many real- life applications nor captures the clustering structure in the graph. To address the limitation of the existing first-order measures, in this paper, we study the second-order random walk measures, which take the previously visited node into consideration. While the existing first-order measures are built on node-to-node transition probabilities, in the second-order random walk, we need to consider the edge-to-edge transition probabilities. Using incidence matrices, we develop simple and elegant matrix representations for the second-order proximity measures. A desirable property of the developed measures is that they degenerate to their original first-order forms when the effect of the previous step is zero. We further develop Monte Carlo methods to efficiently compute the second-order measures and provide theoretical performance guarantees. Experimental results show that in a variety of applications, the second-order measures can dramatically improve the performance compared to their first-order counterparts.

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U2 - 10.14778/3015270.3015272

DO - 10.14778/3015270.3015272

M3 - Conference article

AN - SCOPUS:85020385238

SN - 2150-8097

VL - 10

SP - 13

EP - 24

JO - Proceedings of the VLDB Endowment

JF - Proceedings of the VLDB Endowment

IS - 1

Y2 - 28 August 2017 through 1 September 2017

ER -