It is established that spectral clustering of the sample covariance matrix achieves exact recovery of the underlying communities under a stochastic blockmodel even when the adjacency matrix is unobserved.
Abstract
Spectral clustering for community detection is analysed in multivariate time series models whose dependence structure is determined by an unobserved stochastic blockmodel. We establish that spectral clustering of the sample covariance matrix achieves exact recovery of the underlying communities. The recovery rates depend explicitly on the network size, sample length, block separation, and degree of data dependence. This demonstrates that exact community recovery under a stochastic blockmodel is possible even when the adjacency matrix is unobserved. Our theory provides extensions of both classical and fine-grained matrix perturbation theory to the setting of dependent data, which may be of independent interest.
DBSPEC is a density-based spectral clustering algorithm that requires only approximate localization of the informative eigenvalue and is robust to poor eigenvalue separation, overcoming restrictions to homogeneous toroidal models in prior works.
Konstantin Avrachenkov, L. Sibemberg, A. Van Werde· 0 citations
A fuzzy network jump model for clustering time-varying observations indexed by the nodes of a weighted graph that accurately recovers the true membership probabilities and outperforms competing clustering methods is introduced.
It is shown that approximate $K$-means applied to the multi-kernel spectral embedding achieves exact recovery with high probability, which is more informative than conventional global eigenspace perturbation estimates.
Ze-Qin Lin, Guang-Ming Pan, Zhi-Xiang Zhang et al.· 0 citations
A novel method of inference for network-dependent high-dimensional random vectors is developed, allowing the approximation theory to capture the interaction between the decay of dependence and the growth of network neighborhoods.
This study explores an alternative condition-free analysis for the clustering quality of DCSC from a pure spectral view, without any random graph models, and proposes ASCENT (Adaptive Spectral Clustering with Node-wise correcTion), a simple yet effective extension of DCSC.
The Hierarchical Distance Matrix is introduced, a specific class of population-level distance matrices that encodes latent hierarchical organization through recursively nested distance separation, accommodating unbalanced tree depths, in a fully data-driven top-down procedure: network hierarchical clustering based on t...
Li Chen, Nathaniel Josephs, E. Kolaczyk et al.· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
