Unsupervised Feature Ranking via Spectral Analysis

Spectral clustering algorithm has been demonstrated to be an effective unsupervised learning method. The spectral graph theory indicates that the eigenvalues and eigenvectors of the graph Laplacian are closely related with the clustering results. In this paper we prove that the distribution of the eigenvalues describes the distinctness of clusters and the eigenvectors implicitly present the target values of the samples when normalized graph Laplacian is adopted. Based on this observation we propose a feature significance ranking algorithm, and the experiments on synthetic and real-world data sets have shown the efficacy of our approach.