A randomized algorithm for spectral clustering

Spectral Clustering has reached a wide level of diffusion among unsupervised learning applications. Despite its practical success we believe that for a correct usage one has to face a difficult problem: given a target number of classes K the optimal K-dimensional subspace is not necessarily spanned by the first K eigenvectors of the graph Normalized Laplacian. The contribution of this paper is twofold. First, we show a bound for choosing a correct number of eigenvectors. Second, we propose a randomized spectral algorithm able to find a clustering solution. We show the efficacy of the algorithm with experiments on real world graphs. Our proposal is a scheme that naturally extends the current usage of Spectral