Title: Fully Dynamic Coreset Spectral Clustering
Primary area: learning on graphs and other geometries & topologies
Keywords: Clustering, coresets, spectral clustering, dynamic data structures

Abstract: We present a fully dynamic data structure that supports edge and node updates and cluster membership queries for spectral clustering with strong theoretical guarantees. Furthermore, our data structure outperforms the state of the art significantly on real world datasets. At the heart of our data structure is the novel notion of *Just-in-Time Sampling Trees*. 

The worst-case edge update time of our data structure is $O(\log n)$ and the worst-case query time is $O(d_{\max}^2\log^3(n) + \text{vol}(Y))$ where $d_{\max}$ is the maximum degree of the current graph and $\text{vol}(Y)$ is the sum of the unweighted degrees of all nodes in $Y$. Assuming $d_{\max}$ is polylogarithmic, as is the case with many sparse real-world graphs, our method achieves the best known trade-off between query time and update time.

TL;DR: We present the first fully dynamic coreset data structure for spectral clustering