Abstract: Spectral clustering is one of the most popular methods for data clustering, and its performance is determined by the quality of the eigenvectors of the related graph Laplacian matrix. For a K clustering problem, Ng-Jordan-Weiss(NJW) spectral clustering method adopts the eigenvectors corresponding to the K largest eigenvalues of the Laplacian matrix derived from a dataset as a novel representation of the original data. However, these K eigenvectors can not always reflect the information of the original data for some classification problems. This paper proposes an eigenvector selection method for spectral clustering. First this method calculates the mean of the 3K largest eigenvalues from Laplacian matrix, and then select K eigenvectors whose eigenvalues are the nearest the mean eigenvalue. Experiments show that it can get better cluster results on UCI datasets and obtain more satisfying performance than classical spectral clustering algorithms.

Key words: spectral clustering, Laplacian matrix, eigenvalue, mean, eigenvector selection