Journal of the ACM (JACM)
Graph Visualization and Navigation in Information Visualization: A Survey
IEEE Transactions on Visualization and Computer Graphics
Between Min Cut and Graph Bisection
MFCS '93 Proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Fastest Mixing Markov Chain on a Graph
SIAM Review
A tutorial on spectral clustering
Statistics and Computing
A decentralized algorithm for spectral analysis
Journal of Computer and System Sciences
Towards a theoretical foundation for Laplacian-based manifold methods
Journal of Computer and System Sciences
An efficient algorithm for the parallel solution of high-dimensional differential equations
Journal of Computational and Applied Mathematics
Uniform convergence of adaptive graph-based regularization
COLT'06 Proceedings of the 19th annual conference on Learning Theory
From graphs to manifolds – weak and strong pointwise consistency of graph laplacians
COLT'05 Proceedings of the 18th annual conference on Learning Theory
IEEE Communications Magazine
A distributed minimum variance estimator for sensor networks
IEEE Journal on Selected Areas in Communications
Distributed Kalman filtering based on consensus strategies
IEEE Journal on Selected Areas in Communications
Graph Laplacian Tomography From Unknown Random Projections
IEEE Transactions on Image Processing
Decentralized estimation of Laplacian eigenvalues in multi-agent systems
Automatica (Journal of IFAC)
Hi-index | 22.15 |
We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/eigenvector computations. We prove that, by propagating waves through the graph, a local fast Fourier transform yields the local component of every eigenvector of the Laplacian matrix, thus providing clustering information. For large graphs, the proposed algorithm is orders of magnitude faster than random walk based approaches. We prove the equivalence of the proposed algorithm to spectral clustering and derive convergence rates. We demonstrate the benefit of using this decentralized clustering algorithm for community detection in social graphs, accelerating distributed estimation in sensor networks and efficient computation of distributed multi-agent search strategies.