Dynamic Spectral Clustering with Provable Approximation Guarantee

This paper studies clustering algorithms for dynamically evolving graphs ₜ\, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually change. The paper proves that, under some mild condition on the cluster-structure, the clusters of the final graph GT of nT vertices at time T can be well approximated by a dynamic variant of the spectral clustering algorithm. The algorithm runs in amortised update time $O(1)$ and query time o(nT). Experimental studies on both synthetic and real-world datasets further confirm the practicality of our designed algorithm.