江苏省应用数学（中国矿业大学）中心系列学术报告
报告题目：On the asymptotic properties of spike eigenvalues and eigenvectors of signal-plus-noise matrices with their applications
报告人：刘一鸣助理教授
报告时间：2023/12/19 （周二）15:30-16:30
报告地点：数学学院A310
报告摘要：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.
报告人简介：暨南大经济学院助理教授，博士毕业于新加坡南洋理工大学。目前主要研究方向：机器学习、经验似然、随机矩阵及其相关应用等。主持国自然科学基金，广东省自然科学面上基金，博士后面上，暨南大学宁静致远启明星等项目。至今已在IEEE Transactions on Information Theory, Bernoulli, Statistica Sinica, Statistics and Computing，Scandinavian Journal of Statistics等杂志发表论文10余篇。