TY - GEN
T1 - Clustering the Nodes of Sparse Edge-weighted Graphs via Non-backtracking Spectra
AU - Reittu, Hannu
AU - Bolla, Marianna
AU - Abdelkhalek, Fatma
PY - 2025
Y1 - 2025
N2 - Theoretically supported techniques are given for clustering the nodes of edge-weighted graphs via non-backtracking spectra when the number of nodes is large and the skeleton graph is sparse. If the graph comes from a sparse stochastic block model, the structural real eigenvalues, out of the bulk of the spectrum, of the non-backtracking matrix are aligned with those of the expected adjacency matrix if it is of low rank. However, only the unweighted or weighted non-backtracking matrix is at our disposal. We show how the corresponding eigenvectors of the non-backtracking matrix and lower order companion matrices can be used to find assortative clusters of the nodes even in the case, when the expected adjacency matrix does not have a reduced rank, but it has a low-rank approximation. The paper gives the theoretical background and tools for sparse spectral clustering in very general frameworks. Application to sparse quantum chemistry networks is also presented.
AB - Theoretically supported techniques are given for clustering the nodes of edge-weighted graphs via non-backtracking spectra when the number of nodes is large and the skeleton graph is sparse. If the graph comes from a sparse stochastic block model, the structural real eigenvalues, out of the bulk of the spectrum, of the non-backtracking matrix are aligned with those of the expected adjacency matrix if it is of low rank. However, only the unweighted or weighted non-backtracking matrix is at our disposal. We show how the corresponding eigenvectors of the non-backtracking matrix and lower order companion matrices can be used to find assortative clusters of the nodes even in the case, when the expected adjacency matrix does not have a reduced rank, but it has a low-rank approximation. The paper gives the theoretical background and tools for sparse spectral clustering in very general frameworks. Application to sparse quantum chemistry networks is also presented.
KW - Weighted non-backtracking matrix
KW - Stochastic block models
KW - K-means clustering
UR - http://www.scopus.com/inward/record.url?scp=105000949966&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-85363-0_6
DO - 10.1007/978-3-031-85363-0_6
M3 - Conference article in proceedings
SN - 978-3-031-85362-3
VL - 2
T3 - Lecture Notes in Networks and Systems
SP - 81
EP - 99
BT - Advances in Information and Communication - Proceedings of the 2025 Future of Information and Communication Conference, FICC 2025
A2 - Arai, Kohei
PB - Springer
T2 - 8th Future of Information and Communication Conference 2025 (FICC 2025)
Y2 - 28 April 2025 through 29 April 2025
ER -