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.

翻译：本文旨在研究高维设置下的一般低秩信号加噪声模型。具体而言，我们考虑具有一般协方差结构的噪声，且信号强度与噪声同级。研究重点在于探索与尖峰特征值和特征向量相关的各种渐近性质。作为应用，我们提出了一种估计聚类数量的新准则，并研究了谱聚类的性质。