学术报告

Singular Value Decomposition of Dual Matrices and its Application to Traveling Wave Identification in the Brain

丁维洋（复旦大学）

报告时间：2023年6月30日 星期五  16：00-17：00

报告地点：沙河主楼E404

腾讯会议：802-256-565

报告摘要: Matrix factorization in dual number algebra, a hypercomplex system, has been applied to kinematics, mechanisms, and other fields recently. We develop an approach to identify spatiotemporal patterns in the brain such as traveling waves using the singular value decomposition of dual matrices. Theoretically, we propose the compact dual singular value decomposition (CDSVD) of dual complex matrices with explicit expressions as well as a necessary and sufficient condition for its existence. Furthermore, based on the CDSVD, we report on the optimal solution to the best rank-k approximation under a newly defined quasi-metric in dual complex number system. The CDSVD is also related to the dual Moore-Penrose generalized inverse. Numerically, comparisons with other available algorithms are conducted, which indicate the less computational cost of our proposed CDSVD. Next, we employ experiments on simulated time-series data and a road monitoring video to demonstrate the beneficial effect of infinitesimal parts of dual matrices in spatiotemporal pattern identification. Finally, we apply this approach to the large-scale brain fMRI data and then identify three kinds of traveling waves, and further validate the consistency between our analytical results and the current knowledge of cerebral cortex function.

报告人简介：丁维洋博士现在就职于复旦大学类脑智能科学与技术研究院，担任青年研究员。于2011年和2016年在复旦大学太阳成集团tyc7111cc获得数学与应用数学专业的学士学位和计算数学专业的博士学位，其后在香港理工大学应用数学系作博士后研究，2017至2020年在香港浸会大学数学系担任研究助理教授。其后于2020年11月加入复旦大学类脑智能科学与技术研究院。丁博士近期的主要研究兴趣包括张量计算和优化及其在脑与类脑科学中的应用。丁博士出版了1本学术专著，发表了18篇期刊和会议论文，其中有2篇是ESI高被引论文，1篇获得中国计算数学学会优秀青年论文二等奖。

邀请人：崔春风