Regularity-based spectral clustering and mapping the Fiedler-carpet

Abstract We discuss spectral clustering from a variety of perspectives that include extending techniques to rectangular arrays, considering the problem discrepancy minimization, and applying methods directed graphs. Near-optimal clusters can be obtained by singular value decomposition together with weighted k k -means algorithm. In case this means enhancing method correspondence analysis clustering, while in edge-weighted graphs, normalized Laplacian-based clustering. latter case, it is proved gap between ( − 1 ) \left(k-1) st th smallest positive eigenvalues Laplacian matrix gives rise sudden decrease inner cluster variances when number vertex representatives 2 {2}^{k-1} , but only first k-1 eigenvectors are used representation. The ensemble these constitute so-called Fiedler-carpet.