内容简介：Matrix approximation is a crucial technique in numerous research areas across science and engineering, such as machine learning, scientific computing, and signal processing. These fields often deal with high-dimensional datasets formatted as matrices, which necessitates the use of matrix approximation as a fundamental step in data processing. In this talk, we address the problem of approximating a data matrix by selecting a subset of its columns and/or rows either from the matrix itself or from other source matrices. We apply the method of interlacing polynomials, introduced by Marcus, Spielman, and Srivastava, to develop new deterministic algorithms and establish a theoretical limit on the minimum approximation error. Our algorithm is deterministic and operates in polynomial time. Additionally, our new bounds are asymptotically sharp in several challenging scenarios where current methods provide unnecessarily large error bounds.

报告人：蔡剑锋

报告人简介：香港科技大学数学系教授，拥有丰富的学术背景和卓越的研究成果。他于2000年获得复旦大学计算数学学士学位，2007年获得香港中文大学数学博士学位。博士毕业后，蔡剑锋曾在多所世界知名大学工作，包括新加坡国立大学（2007-2009）、美国洛杉矶加州大学（UCLA）（2009-2011）、美国爱荷华大学（University of Iowa）（2011-2015）和香港科技大学（2015-今）。2019年，他在香港科技大学数学系晋升为教授。蔡剑锋的研究兴趣主要集中在成像技术和数据科学中的算法和数学理论基础。他在这些领域取得了一系列开创性的科研成果，发表了多篇高引用论文，并在2017年和2018年被评为全球高被引学者。蔡剑锋目前担任《Frontiers in Applied Mathematics and Statistics》杂志优化方向的主编和《Journal of Mathematical Imaging and Vision》的编委。

题目二：Phase Retrieval and Blind Deconvolution Theory under Random Mask Assumption

内容简介：Instead of traditional Gaussian random measurements, we focus on the phase retrieval problem under masked Fourier measurements. It is one of the phase retrieval settings which is realizable in real applications. We discuss some truncated Wirtinger flow algorithm and improve the sampling complexity. Furthermore, we also analyze the blind deconvolution problem with modulated inputs. It is a challenging problem as both the blur kernel and the input signal are not known. When the signal is sparse and the blur kernel is short-supported, we present an algorithm with the sampling complexity smaller than nuclear norm minimization and least square method.

报告人：夏羽

报告人简介：杭州师范大学数学学院副教授，毕业于浙江大学数学系（导师: 李松教授），主要从事信号图像处理中的数学理论和算法研究。现阶段在应用数学及数学与信息交叉领域发表一系列学术论文, 包括 Applied and Computational Harmonic Analysis, Inverse Problems, IEEE Transactions on Information Theory, IEEE Transactions on Signal Processing等。主持国家自然科学基金项目两项。

题目三：Randomized Iterative Methods: Acceleration and Applications

内容简介：Randomized iterative methods, such as the randomized Kaczmarz method and its variants, have gained growing attention due to their simplicity and efficiency in solving large-scale linear systems.  In this talk, we will explore the most recent advancements in the field of randomized iterative methods. This includes the exploration of the randomized Douglas-Rachford method, the adaptive parameter selection strategy for heavy ball momentum, and the application of randomized iterative methods to generalized absolute value equations.

报告人：谢家新

报告人简介：北京航空航天大学副教授，博士生导师，2017年获湖南大学计算数学博士学位，随后进入中国科学院数学与系统科学研究院从事博士后研究，2019年入职北京航空航天大学数学科学学院。研究兴趣为数据科学中的数学问题，特别是随机迭代法和矩阵子集选择等问题。已在SIMAX, SIOPT, IJM, JCM, COAP等期刊发表论文多篇。现为中国运筹学会算法软件及应用分会理事，中国运筹学会数学规划分会青年理事。

时  间：2024年12月1日（周日）下午16：00开始

地  点：暨南大学番禺校区图书馆617会议室

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信息科学技术学院

2024年11月28日