Spectral Kernel Methods for Clustering

In this paper we introduce new algorithms for unsupervised learning basedon the use of a kernel matrix. All the information required bysuch algorithms is contained in the eigenvectors of the matrix or of closely related matrices. We use two different but related costfunctions, the Alignment and the'cut cost'. The first one is discussed in a companion paper [3], the second one is based on graph theoretic concepts. Both functions measure the level of clustering of a labeled dataset, or the correlation between data clusters andlabels.