Automatic Determination of the Number of Clusters Using Spectral Algorithms

We introduce a novel spectral clustering algorithm that al lows us to automatically determine the number of clusters in a dataset. The algorithm is based on a theoretical analysis of the spectral properties of block diagonal affinity matrices; in contrast to established methods, we do not normalise the rows of the matrix of eigenvectors, and argue that the non-normalised data contains key information that allows the automatic determination of the number of clusters present. We present several examples of datasets successfully clustered by our algorithm, both artificial and real, obtaining good results even without employing refined feature extraction techniques. The software used in our experiments is available for download from http://www.dcs.shef.ac.uk/~guido/.