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Paper details
Number 4 - December 2018
Volume 28 - 2018
Clustering based on eigenvectors of the adjacency matrix
Małgorzata Lucińska, Sławomir T. Wierzchoń
Abstract
The paper presents a novel spectral algorithm EVSA (eigenvector structure analysis), which uses eigenvalues and eigenvectors of the adjacency matrix in order to discover clusters. Based on matrix perturbation theory and properties of graph spectra we show that the adjacency matrix can be more suitable for partitioning than other Laplacian matrices. The main problem concerning the use of the adjacency matrix is the selection of the appropriate eigenvectors. We thus propose an
approach based on analysis of the adjacency matrix spectrum and eigenvector pairwise correlations. Formulated rules and
heuristics allow choosing the right eigenvectors representing clusters, i.e., automatically establishing the number of groups.
The algorithm requires only one parameter—the number of nearest neighbors. Unlike many other spectral methods, our
solution does not need an additional clustering algorithm for final partitioning. We evaluate the proposed approach using
real-world datasets of different sizes. Its performance is competitive to other both standard and new solutions, which require
the number of clusters to be given as an input parameter.
Keywords
spectral clustering, adjacency matrix eigenvalues/eigenvectors, graph perturbation theory, eigengap heuristics