Spectral Bridges: Scalable Spectral Clustering Based on Vector Quantization

Abstract

In this paper, Spectral Bridges, a novel clustering algorithm, is introduced. This algorithm builds upon the traditional k-means and spectral clustering frameworks by subdividing data into small Voronoï regions, which are subsequently merged according to a connectivity measure. Drawing inspiration from Support Vector Machine’s margin concept, a non-parametric clustering approach is proposed, building an affinity margin between each pair of Voronoï regions. This approach delineates intricate, non-convex cluster structures and is robust to hyperparameter choice. The numerical experiments underscore Spectral Bridges as a fast, robust, and versatile tool for clustering tasks spanning diverse domains. Its efficacy extends to large-scale scenarios encompassing both real-world and synthetic datasets. The Spectral Bridge algorithm is implemented both in Python (https://pypi.org/project/spectral-bridges) and R (https://github.com/cambroise/spectral-bridges-Rpackage).