New Methods for Spectral Clustering

Analyzing the affinity matrix spectrum is an increasingly popular data clustering method. We propose three new algorithmic components which are appropriate for improving performance of spectral clustering. First, observing the eigenvectors suggests to use a K-lines algorithm instead of the commonly applied K-means. Second, the clustering works best if the affinity matrix has a clear block structure, which can be achieved by computing a conductivity matrix. Third, many clustering problems are inhomogeneous or asymmetric in the sense that some clusters are concentrated while others are dispersed. In this case, a context-dependent calculation of the affinity matrix helps. This method also turns out to allow a robust automatic determination of the kernel radius σ.