Dynamic Similarity Graph Construction with Kernel Density Estimation

Steinar Laenen, Peter Macgregor, He Sun

Keywords: kernel density estimation, similarity graphs, spectral clustering

TL;DR: This paper introduces dynamic data structures for kernel density estimation and sparse similarity graph constructions, with an application to clustering.

Abstract:

In the kernel density estimation (KDE) problem, we are given a set $X$ of data points in $\mathbb{R}^d$, a kernel function $k: \mathbb{R}^d \times \mathbb{R}^d \rightarrow \mathbb{R}$, and a query point $\mathbf{q} \in \mathbb{R}^d$, and the objective is to quickly output an estimate of $\sum_{\mathbf{x} \in X} k(\mathbf{q}, \mathbf{x})$.
In this paper, we consider $\textsf{KDE}$ in the dynamic setting, and introduce a data structure that efficiently maintains the estimates for a set of query points as data points are added to $X$ over time.
Based on this, we design a dynamic data structure that maintains a sparse approximation of the fully connected similarity graph on
$X$, and develop a fast dynamic spectral clustering algorithm.
We further evaluate the effectiveness of our algorithms on both synthetic and real-world datasets.

Primary Area: learning on graphs and other geometries & topologies

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 7800