Some Issues on the Parameter Selection in the Spectral Methods for Clustering

Spectral methods for clustering have emerged as effective approaches for finding non-convex clusters in the data; moreover, such methods do not require assumptions on the data because they are based on a matrix of pairwise similarities between the observations depending on some kernel function. The main underlying idea is to cluster the data in a suitable feature space depending on a spectral-based mapping rather than in the original space of the units. Two main issues concern the choice of the kernel function and the estimation of the number of groups. In this paper, we analyze some different proposals presented in literature and provide an explorative approach for the selection of both the number of groups and the proximity measure between the observations.