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.

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

UR - http://www.scopus.com/inward/record.url?scp=84961901889&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961901889&partnerID=8YFLogxK

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 -