Multilevel Diffusion Based Spectral Graph Clustering

Spectral clustering and kernel k-means are ubiq-uitous methods for dividing non-linearly separable data into distinct groups. Spectral methods, while effective in partitioning non-convex spaces, are computationally intensive as they involve eigenvector computations. Conversely, kernel k-means maps data to higher dimensions and circumvents the need for this costly computation, with a weighted variant of it being mathemati-cally equivalent to spectral clustering. This work extends this equivalence to diffusion based spectral methods and introduces the Multilevel Diffusion Clustering (MDC) algorithm. MDC leverages diffusion principles to minimize the normalized cut, adds flexibility through a diffusion parameter, and retrieves high-quality partitions in a multilevel fashion without computing eigenpairs. Our numerical examples and comparative results with modern multilevel graph clustering packages reveal that the proposed method can improve the clustering of graphs both in terms of balanced cut criteria and classification accuracy.