  This paper is to consider a general low-rank signal plus noise model in high
dimensional settings. Specifically, we consider the noise with a general
covariance structure and the signal to be at the same magnitude as the noise.
Our study focuses on exploring various asymptotic properties related to the
spiked eigenvalues and eigenvectors. As applications, we propose a new
criterion to estimate the number of clusters, and investigate the properties of
spectral clustering.
