RETRACTED: Low Multilinear Rank Tensor Completion with Missing Data (Retracted Article)

We present a novel method for tensor completion with missing data. The problem of missing data comes up in many areas of science and engineering including data mining, machine learning, biomedical signal, and computer vision. These data are always very large and have multi-modes. Therefore, we need a well method to find the missing data of multi-way arrays (i.e., tensors). In this paper we propose an algorithm to solve the problem by tensor multilinear rank minimization. The contribution of our paper is that we convert tensor rank minimization to minimize the mode-n rank of a tensor along each mode and then formulate as low rank matrix completion for mode-n matricization of a tensor. The resulting nuclear norm related minimization problem can be efficiently solved by many recent developed methods. Our numerical results on randomly generated data demonstrate that our algorithm is quick and provides much better recoverability than a few state-of-art tensor completion algorithms. Numerical experiments on image inpainting problems demonstrate the effectiveness of our method in real world. (C) 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Organizers of 2011 International Conference on Energy and Environmental Science.