Modular-transform based clustering

TL;DR: A K-way clustering algorithm – spectral modular transformation, based on the fact that the graph Laplacian has an equivalent representation, which has a diagonal modular structure, which outperforms spectral clustering using other initializations is proposed and studied.

Abstract: Spectral clustering uses eigenvectors of the Laplacian of the similarity matrix It is convenient to solve binary clustering problems When applied to multi-way clustering, either the binary spectral clustering is recursively applied or an embedding to spectral space is done and some other methods, such as K-means clustering, are used to cluster the points Here we propose and study a K-way clustering algorithm – spectral modular transformation, based on the fact that the graph Laplacian has an equivalent representation, which has a diagonal modular structure The method first transforms the original similarity matrix into a new one, which is nearly disconnected and reveals a cluster structure clearly, then we apply linearized cluster assignment algorithm to split the clusters In this way, we can find some samples for each cluster recursively using the divide and conquer method To get the overall clustering results, we apply the cluster assignment obtained in the previous step as the initialization of m