Constrained Graph Clustering with Signed Laplacians
Keywords: constrained graph clustering, spectral graph theory
TL;DR: We develop a spectral algorithm for the constrained graph clustering problem
Abstract: Given two weighted graphs $G = (V, E, w_G)$ and $H = (V, F, w_H)$ defined on the same vertex set, the constrained clustering problem asks to find a set $S\subset V$ that minimises the cut ratio between $w_G(S, V\setminus S)$ and $w_H(S, V\setminus S)$. We develop a Cheeger-type inequality that relates the solution of the constrained clustering problem to the spectral properties of $G$ and $H$. To reduce computational complexity, we use the signed Laplacian on $H$, simplifying the calculations while maintaining accurate results. By solving a generalized eigenvalue problem, our algorithm provides improvements in performance, particularly in scenarios where traditional spectral clustering methods face difficulties. We demonstrate its practical effectiveness through experiments on both synthetic and real-world datasets.
Supplementary Material: zip
Primary Area: learning on graphs and other geometries & topologies
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Submission Number: 10843
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