江蘇省應用數學（中國礦業大學）中心系列學術報告
報告題目：On the asymptotic properties of spike eigenvalues and eigenvectors of signal-plus-noise matrices with their applications
報告人：劉一鳴助理教授
報告時間：2023/12/19 （周二）15:30-16:30
報告地點：伟德bvA310
報告摘要：This paper is to investigate the asymptotic properties of the spike eigenvalues and the corresponding eigenvalues under a general low-rank signal plus noise model in high dimensions. Under mild conditions concerning the leading eigenvalue of the underlying covariance matrix and the noises, we find the limits of both spike eigenvalues and eigenvectors of the sample covariance matrix. Based on the discovered results, some related applications are also considered. Specifically, for a general mixture model, a new criterion to estimate the number of clusters is proposed; the properties of spectral clustering are also investigated. In addition, some classification and dimension reduction problems are also considered.
報告人簡介：暨南大經濟學院助理教授，博士畢業于新加坡南洋理工大學。目前主要研究方向：機器學習、經驗似然、随機矩陣及其相關應用等。主持國自然科學基金，廣東省自然科學面上基金，博士後面上，暨南大學甯靜緻遠啟明星等項目。至今已在IEEE Transactions on Information Theory, Bernoulli, Statistica Sinica, Statistics and Computing，Scandinavian Journal of Statistics等雜志發表論文10餘篇。