TY - GEN
T1 - Fast eigen-functions tracking on dynamic graphs
AU - Chen, Chen
AU - Tong, Hanghang
N1 - Funding Information:
Acknowledgement: This material is supported by the National Science Foundation under Grant No. IIS1017415, by the Army Research Laboratory under Cooperative Agreement Number W911NF-09-2-0053, by Defense Advanced Research Projects Agency (DARPA) under Contract Number W911NF-1 l-C-0200 and W911NF-12-C-0028, by National Institutes of Health under the grant number R01LM011986, Region II University Transportation Center under the project number 49997-33 25.
Publisher Copyright:
Copyright © SIAM.
PY - 2015
Y1 - 2015
N2 - Many important graph parameters can be expressed as eigen-functions of its adjacency matrix. Examples include epidemic threshold, graph robustness, etc. It is often of key importance to accurately monitor these parameters. For example, knowing that Ebola virus has already been brought to the US continent, to avoid the virus from spreading away, it is important to know which emerging connections among related people would cause great reduction on the epidemic threshold of the network. However, most, if not all, of the existing algorithms computing these measures assume that the input graph is static, despite the fact that almost all real graphs are evolving over time. In this paper, we propose two online algorithms to track the eigen-functions of a dynamic graph with linear complexity wrt the number of nodes and number of changed edges in the graph. The key idea is to leverage matrix perturbation theory to efficiently update the top eigen-pairs of the underlying graph without recomputing them from scratch at each time stamp. Experiment results demonstrate that our methods can reach up to 20 x speedup with precision more than 80% for fairly long period of time.
AB - Many important graph parameters can be expressed as eigen-functions of its adjacency matrix. Examples include epidemic threshold, graph robustness, etc. It is often of key importance to accurately monitor these parameters. For example, knowing that Ebola virus has already been brought to the US continent, to avoid the virus from spreading away, it is important to know which emerging connections among related people would cause great reduction on the epidemic threshold of the network. However, most, if not all, of the existing algorithms computing these measures assume that the input graph is static, despite the fact that almost all real graphs are evolving over time. In this paper, we propose two online algorithms to track the eigen-functions of a dynamic graph with linear complexity wrt the number of nodes and number of changed edges in the graph. The key idea is to leverage matrix perturbation theory to efficiently update the top eigen-pairs of the underlying graph without recomputing them from scratch at each time stamp. Experiment results demonstrate that our methods can reach up to 20 x speedup with precision more than 80% for fairly long period of time.
KW - Attribution analysis
KW - Connectivity
KW - Dynamic graph
KW - Graph spectrum
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U2 - 10.1137/1.9781611974010.63
DO - 10.1137/1.9781611974010.63
M3 - Conference contribution
AN - SCOPUS:84961901889
T3 - SIAM International Conference on Data Mining 2015, SDM 2015
SP - 559
EP - 567
BT - SIAM International Conference on Data Mining 2015, SDM 2015
A2 - Venkatasubramanian, Suresh
A2 - Ye, Jieping
PB - Society for Industrial and Applied Mathematics Publications
T2 - SIAM International Conference on Data Mining 2015, SDM 2015
Y2 - 30 April 2015 through 2 May 2015
ER -