Tensor Decompositions and Low-rank Tensor Recovery
Tensor methods provide effective tools for representing, processing, analyzing, and recovering high-dimensional multiway data arising from imaging, sensing, communications, scientific computing, and machine learning applications. This talk reviews tensor decompositions and low-rank tensor recovery problems, together with applications and recent research directions. For tensor decompositions, we focus on their algebraic forms and characteristic properties. For low-rank tensor recovery, we introduce a generalized model that covers representative problems such as tensor completion and tensor robust principal component analysis. The corresponding methodologies are reviewed from three perspectives: low-rankness characterization, noise modeling, and structural priors for tensor data. We also summarize representative applications such as natural image and video restoration, hyperspectral image restoration, spatiotemporal traffic data imputation, and signal reconstruction.
Contatti:
paola.antonietti@polimi.it
gabriele.ciaramella@polimi.it
Michael K. Ng received the BSc and MPhil degrees from the University of Hong Kong, in 1990 and 1992,respectively, and the PhD degree from the Chinese University of Hong Kong, in 1995. He was a research fellow with Computer Sciences Laboratory, Australian National University, from 1995 to 1997, and assistant/associate professor with the University of Hong Kong, from 1997 to 2005. He was a professor/chair professor with the Department of Mathematics, Hong Kong Baptist University, from 2006 to 2019. He was the chair professor with the Research Division of Mathematical and Statistical Science, The University of Hong Kong, from 2019 to 2023. He is currently the chair professor of mathematics and chair professor in data science with Hong Kong Baptist University. His research interests include applied and computational mathematics, machine learning, and artificial intelligence. He was selected for the 2017 Class of Fellows of the Society for Industrial and Applied Mathematics, and the 2025 Class of Fellows of the American Mathematical Society. He was the recipient of Feng Kang Prize for his significant contributions in scientific computing.