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Fast and Provable Nonconvex Tensor RPCA
Haiquan Qiu · Yao Wang · Shaojie Tang · Deyu Meng · QUANMING YAO
In this paper, we study nonconvex tensor robust principal component analysis (RPCA) based on the $t$-SVD. We first propose an alternating projection method, i.e., APT, which converges linearly to the ground-truth under the incoherence conditions of tensors. However, as the projection to the low-rank tensor space in APT can be slow, we further propose to speedup such a process by utilizing the property of low-rank tangent space. The resulting algorithm, i.e., EAPT, is not only more efficient than APT but also keeps the linear convergence. Compared with existing tensor RPCA works, the proposed method, especially EAPT, is not only more effective due to the recovery guarantee and adaption in the transformed (frequency) domain but also more efficient due to faster convergence rate and lower iteration complexity. These benefits are also empirically verified both on synthetic data, and real applications, e.g., hyperspectral image denoising and video background subtraction.

Author Information

Haiquan Qiu (Xi'an Jiaotong University)
Yao Wang
Shaojie Tang (University of Texas at Dallas)
Deyu Meng
QUANMING YAO (4Paradigm)

Dr. Quanming Yao is currently a leading researcher in 4Paradigm and managing the company's research group. He obtained his Ph.D. degree at the Department of Computer Science and Engineering at Hong Kong University of Science and Technology (HKUST) in 2018 and received his bachelor degree at HuaZhong University of Science and Technology (HUST) in 2013. He is Qiming Star (HUST, 2012), Tse Cheuk Ng Tai Research Excellence Prize (CSE, HKUST, 2014-2015), Google Fellowship (machine learning, 2016) and Ph.D. Research Excellence Award (School of Engineering, HKUST, 2018-2019). He has 23 top-tier journal and conference papers, including ICML, NeurIPS, JMLR, TPAMI, KDD, ICDE, CVPR, IJCAI, and AAAI; he was an outstanding reviewer of Neurocomputing in 2017; served as program committee of many prestigious conferences, including ICML, NeurIPS, CVPR, AAAI, and IJCAI; one of the committees of AutoML competition in NeurIPS-2018, IJCNN-2019 and IJCAI-2019.

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