革新知能統合研究センター

Speaker:
Andong Wang, Guangdong University of Technology

Title:
Tensor recovery with low-rankness in the spectral domain

Abstract:
Data modelling is one of the fundamental problems in high-dimensional data analysis. Although the emerging tensor (i.e., multi-way array) data are typically high-dimensional, they frequently have intrinsic low-dimensional structures which can be successfully modeled by tensor low-rankness. However, various types of real tensor data (like natural images/videos) also possess strong spatial-temporal smoothness which is a basic signal property that traditional low-rank tensor models often fail to capture. Exampled by the tensor Singular Value Decomposition (t-SVD), recent frontier studies in computer vision and signal processing have pointed out that when transformed to certain spectral domain (e.g., the Fourier domain), smooth tensor data tend to show stronger low-rankness. By exploiting low-rankness in the spectral domain, we have proposed several models for tensor recovery in the presence of missing values, noises, and/or outliers caused by sensor failures, malicious attacks, information loss, etc. Most of the models introduced in this talk are based on t-SVD and we focus on both statistical efficiency and scalable algorithms. Our preliminary practices suggest that spectral low-rank tensor models are more suitable for real smooth multi-way data since they could model both low-rankness and smoothness simultaneously, whereas traditional tensor decompositions (like CP and Tucker) can only exploit low-rankness in the original domain.