Tensor Component Analysis and Its Applications
- Yipeng Liu, University of Electronic Science and Technology of China (UESTC)
Many classical machine learning methods rely on representation and computation in the form of vectors and matrices, where multi-dimensional data is unfolded into matrix for processing. However, the multi-linear structure would be lost in such vectorization or matricization, which leads to sub-optimal performance in data processing. In fact, a natural representation for multi-dimensional data is tensor. The techniques based on tensor can avoid damaging the multi-linear data structures.
This tutorial will first provide a basic coverage of tensor notations, preliminary operations, and main tensor decompositions and their properties. Based on them, a series of tensor component analysis methods are presented, as the multi-linear extensions of classical sparse component analysis, principle component analysis, missing component analysis, non-negative component analysis, linear regression, subspace cluster, etc. The experimental results for some applications are given, such as image reconstruction, denoising, illumination normalization, background extraction, classification, etc. Finally, some advanced tensor networks are discussed for possible applications in tensor component analysis.
received the B.Sc. degree in biomedical engineering and the Ph.D. degree in information and communication engineering from University of Electronic Science and Technology of China (UESTC), Chengdu, in 2006 and 2011, respectively. From 2010 to 2011, he was a visiting PhD student in Tsinghua University, Beijing, China. In 2011, he was a research engineer at Huawei Technologies, Chengdu, China. From 2011 to 2014, he was a postdoctoral research fellow at University of Leuven, Leuven, Belgium. Since 2014, he has been an associate professor with University of Electronic Science and Technology of China (UESTC), Chengdu, China.
His research interests include tensor learning methods and its image processing applications. He has authored or co-authored over 50 publications on these areas. The recently published 7 IEEE journal papers and 1 review paper well cover the main tensor component analysis methods, such as omni-directional total variation for sparse component analysis, smooth low rank tensor tree based missing component analysis, low rank core matrix based tensor principle component analysis, tensor-on-tensor regression, etc. One of the co-authored papers received the ISMRM MERIT AWARD of Magna cum laude at ISMRM 2015. He also holds 9 patents. He has been a principal investigator (PI) or Co-PI for a number of R&D projects (funded by government and industry) on tensor learning theory and its applications.
He serves as managing guest editor of the Special Isssue on Tensor Image Processing of the journal Signal Processing: Image Communiucation. As an expert on tensor learning, he has served 4 international conferences as a technical/program committee member. He is an IEEE senior member, affiliated member of the Image, Video, and Multi-dimensional Signal Processing Technical Committee of IEEE Signal Processing Society. He is also the member the Multimedia Technology Technical Committee of Chinese Computer Federation. He is the scientific advisor of Beiton AI. He has been teaching the course optimization theory and applications for graduates since 2015, and got the first prize of the 8th University Teaching Achievement Award in 2016.