Dynamic Spectral Clustering with Provable Approximation Guarantee

Steinar Laenen; He Sun

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arXiv · 2406.03152

Dynamic Spectral Clustering with Provable Approximation Guarantee

Steinar Laenen·He Sun

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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.

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Steinar Laenen, He Sun. 2024-06-05. Dynamic Spectral Clustering with Provable Approximation Guarantee. https://arxiv.org/abs/2406.03152

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