Dynamic Spectral Clustering with Provable Approximation Guarantee

TL;DR

This paper introduces a dynamic spectral clustering algorithm for evolving graphs, providing provable approximation guarantees, efficient update and query times, and validated by experiments on synthetic and real data.

Contribution

It develops a novel dynamic spectral clustering method with theoretical guarantees and practical efficiency for evolving graph structures.

Findings

Algorithm achieves $O(1)$ amortised update time.

Clusters are well approximated under mild conditions.

Experimental results confirm practicality on real datasets.

Abstract

This paper studies clustering algorithms for dynamically evolving graphs $\{G_t\}$, 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 $G_T$ of $n_T$ 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 $o(n_T)$. Experimental studies on both synthetic and real-world datasets further confirm the practicality of our designed algorithm.