报告题目： An Average Curvature Proximal Gradient Method for Symmetric Nonnegative

                 Matrix Factoriz ation

报 告 人： 朱红 副教授

单  位： 江苏大学理学院数学与应用数学系

时  间： 2022年3月15日9:00

地  点： 九章学堂302

摘  要： Symmetric nonnegative matrix factorization (SymNMF) is a powerful tool for data dimensionality reduction and has found many applications in pattern recognition, data mining, etc.  The objection function of SymNMF is a fourth-order nonconvex function, which has non-Lipschitz gradient over the feasible set. In this paper, we propose a bounded form of SymNMF, which has a one-to-one correspondence stationary points with SymNMF. The resulting problem is defined on a compact convex set and the objective function has Lipschitz gradient over the feasible set. Moreover, it is a nonconvex smooth composite optimization problem. We then propose an average curvature proximal gradient method (ACPGM) with backtracking procedure to SymNMF. Experiments on synthetic data and real data demonstrate that the proposed method provides  state-of-the-art performance compared with existing methods.

简  介： 朱红，江苏大学副教授，硕士生导师。2016年毕业于香港浸会大学，获得哲学博士。2012年毕业于河南大学，获理学硕士。2018年12月到2019年12月受国家留学基金委的资助在加拿大西蒙弗雷泽大学访问。主要从事非线性最优化理论及非负矩阵分解等相关领域的研究。主持国家自然科学基金1项，江苏省青年基金1项。

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