Spectral clustering with eigenvector selection based on ensemble ranking

Ng-Jordan-Weiss (NJW) method is one of the most widely used spectral clustering algorithms. For a clustering problem with K clusters, this method clusters data using the largest K eigenvectors of the normalized affinity matrix derived from the data set. However, the top K eigenvectors are not always the most important eigenvectors for clustering. In this paper, we propose an eigenvector selection method based on an ensemble of multiple eigenvector rankings (ESEER) for spectral clustering. In ESEER method, first multiple rankings of eigenvectors are obtained by using the entropy metric, which is used to measure the importance of each eigenvector, next the multiple eigenvector rankings are aggregated into a single consensus one, then the first K eigenvectors in the consensus ranking list are adopted as the selected eigenvectors. We have performed experiments on artificial data sets, standard data sets of UCI repository and handwritten digits from MNIST database. The experimental results show that ESEER method is more effective than NJW method in some cases.