  Based on a Gaussian mixture type model , we derive an eigen selection
procedure that improves the usual spectral clustering in high-dimensional
settings. Concretely, we derive the asymptotic expansion of the spiked
eigenvalues under eigenvalue multiplicity and eigenvalue ratio concentration
results, giving rise to the first theory-backed eigen selection procedure in
spectral clustering. The resulting eigen-selected spectral clustering (ESSC)
algorithm enjoys better stability and compares favorably against canonical
alternatives. We demonstrate the advantages of ESSC using extensive simulation
and multiple real data studies.
