TY - GEN
T1 - Weighted Spectral Embedding of Graphs
AU - Bonald, Thomas
AU - Hollocou, Alexandre
AU - Lelarge, Marc
N1 - Publisher Copyright:
© 2018 IEEE.
PY - 2018/7/2
Y1 - 2018/7/2
N2 - We present a novel spectral embedding of graphs that incorporates weights assigned to the nodes, quantifying their relative importance. This spectral embedding is based on the first eigenvectors of some properly normalized version of the Laplacian. We prove that these eigenvectors correspond to the configurations of lowest energy of an equivalent physical system, either mechanical or electrical, in which the weight of each node can be interpreted as its mass or its capacitance, respectively. Experiments on a real dataset illustrate the impact of weighting on the embedding.
AB - We present a novel spectral embedding of graphs that incorporates weights assigned to the nodes, quantifying their relative importance. This spectral embedding is based on the first eigenvectors of some properly normalized version of the Laplacian. We prove that these eigenvectors correspond to the configurations of lowest energy of an equivalent physical system, either mechanical or electrical, in which the weight of each node can be interpreted as its mass or its capacitance, respectively. Experiments on a real dataset illustrate the impact of weighting on the embedding.
UR - https://www.scopus.com/pages/publications/85062845590
U2 - 10.1109/ALLERTON.2018.8636037
DO - 10.1109/ALLERTON.2018.8636037
M3 - Conference contribution
AN - SCOPUS:85062845590
T3 - 2018 56th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2018
SP - 494
EP - 501
BT - 2018 56th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 56th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2018
Y2 - 2 October 2018 through 5 October 2018
ER -