TY - GEN
T1 - Community Detection from Low-Rank Excitations of a Graph Filter
AU - Wai, Hoi To
AU - Segarra, Santiago
AU - Ozdaglar, Asuman E.
AU - Scaglione, Anna
AU - Jadbabaie, Ali
N1 - Funding Information:
Work supported by NSF CCF-BSF 1714672 and the MIT IDSS seed fund.
Publisher Copyright:
© 2018 IEEE.
PY - 2018/9/10
Y1 - 2018/9/10
N2 - This paper considers the problem of inferring the topology of a graph from noisy outputs of an unknown graph filter excited by low-rank signals. Limited by this low-rank structure, we focus on solving the community detection problem, whose aim is to partition the node set of the unknown graph into subsets with high edge densities. We propose to detect the communities by applying spectral clustering on the low-rank output covariance matrix. To analyze the performance, we show that the low-rank covariance yields a sketch of the eigenvectors of the unknown graph. Importantly, we provide theoretical bounds on the error introduced by this sketching procedure based on spectral features of the graph filter involved. Finally, our theoretical findings are validated via numerical experiments.
AB - This paper considers the problem of inferring the topology of a graph from noisy outputs of an unknown graph filter excited by low-rank signals. Limited by this low-rank structure, we focus on solving the community detection problem, whose aim is to partition the node set of the unknown graph into subsets with high edge densities. We propose to detect the communities by applying spectral clustering on the low-rank output covariance matrix. To analyze the performance, we show that the low-rank covariance yields a sketch of the eigenvectors of the unknown graph. Importantly, we provide theoretical bounds on the error introduced by this sketching procedure based on spectral features of the graph filter involved. Finally, our theoretical findings are validated via numerical experiments.
KW - Community detection
KW - Graph filter
KW - Graph signal processing
KW - Low rank excitation
KW - Topology identification
UR - http://www.scopus.com/inward/record.url?scp=85054216578&partnerID=8YFLogxK
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U2 - 10.1109/ICASSP.2018.8462239
DO - 10.1109/ICASSP.2018.8462239
M3 - Conference contribution
AN - SCOPUS:85054216578
SN - 9781538646588
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 4044
EP - 4048
BT - 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018
Y2 - 15 April 2018 through 20 April 2018
ER -