：Graph Refinement via Simultaneously Low-rank and Sparse Approximation
报告人：张振跃教授（浙江大学）
报告时间：2022年11月17日（周四）15：00-17：00
腾讯会议：205-264-855
报告摘要：Graph plays an important role in many fields of machine learning such as clustering. Many graph-based machine learning approaches assume that the graphs have hidden group structures. However, the group structures are unclear or noisy in applications generally. Graph refinement aims to clarify the underlying group structures. In this work, a novel approach, named as SLSA, is proposed for graph refinement, which imposes a strong cluster structure through strict sparse and low-rank assumptions simultaneously. This approach minimizes a non-convex function. Fortunately, the optimization problem can be efficiently solved via an alternating iteration method, and the iterative method converges globally under a weak condition.
A fast iterative algorithm is also given for large-scale sparse graphs, which costs O(n) in each iteration. Compared with other two related methods for graph refinement, SLSA performs better on both synthetic and real-world data sets.
Applications of the refinement method SLSA on several machine learning algorithms are discussed in detail. Numerical experiments show that the improvements of these algorithms are significant under the SLSA modifications, and better than that based on the refinements of other approaches.
报告人简介：张振跃，浙江大学数学学院二级教授，博士生导师。2013年获浙江大学心平教学杰出贡献奖，2014年获国务院政府津贴。主要从事数值代数、科学计算、机器学习和大数据分析等研究领域的模型与算法的理论分析与计算。先后在在国际著名学术刊物SIAM Review、SIAM J. Scientific Computing、SIAM J. Matrix Analysis and Application、SIAM J Numerical Analysis、The Journal of American Statistical Association, IEEE Transactions on Pattern Analysis and Machine Intelligence、Journal of Machine Learning Research, Patten Recognition, 以及NIPS、CVPR等会议上发表近百篇研究论文，在相关研究中取得了许多受国际关注的基础性、系统性、理论性的研究成果。早期研究工作被多位国际数值代数专家的专著引用。张振跃教授是第一位在SIAM Review上发表研究论文的国内大陆学者，其关于非线性降维算法的工作，多年来一直列SIAM J. Scientific Computing 10年高引用率第4、5位。在国际机器学习领域中被广泛应用的Scikit-Learn 中收录的8个关于流形学习的经典算法中，有两个属于张振跃教授及其合作者。近年来在多源数据学习、图矩阵优化、子空间学习、全正分解等研究领域取得了具有开创性的一些研究成果，先后担任30余家国际学术刊物的评审人。张振跃教授现任《计算数学》和《高校计算数学》编委。
邀请人：黄金枝