Spectral Density Peaks Clustering

Cluster analysis is still an open problem despite the wide range of techniques available in the literature. Each family of clustering algorithms has distinct strengths and limitations: graph-theoretical approaches benefit from a solid linear algebra foundation, but struggle with structures of varying size and density; density-based methods can detect arbitrarily-shaped clusters, yet they often rely on sensitive and method-dependent heuristics. We introduce a spectral formulation of Density Peaks clustering, based on a transition matrix that encodes the probability of a point being the nearest higher-density neighbor of another. This matrix naturally integrates with Perron Cluster Analysis to coarse-grain Markov chains with complex spectra, addressing the limitations of both the aforementioned paradigms. The proposed method, Spectral Density Peaks, is evaluated on synthetic and real-world datasets against state-of-the-art competitors.