School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China.
School of Automation, Guangdong University of Technology, Guangzhou 510006, China.
Neural Netw. 2022 Sep;153:314-324. doi: 10.1016/j.neunet.2022.05.023. Epub 2022 Jun 6.
This paper considers the completion problem of a partially observed high-order streaming data, which is cast as an online low-rank tensor completion problem. Though the online low-rank tensor completion problem has drawn lots of attention in recent years, most of them are designed based on the traditional decomposition method, such as CP and Tucker. Inspired by the advantages of Tensor Ring decomposition over the traditional decompositions in expressing high-order data and its superiority in missing values estimation, this paper proposes two online subspace learning and imputation methods based on Tensor Ring decomposition. Specifically, we first propose an online Tensor Ring subspace learning and imputation model by formulating an exponentially weighted least squares with Frobenium norm regularization of TR-cores. Then, two commonly used optimization algorithms, i.e. alternating recursive least squares and stochastic-gradient algorithms, are developed to solve the proposed model. Numerical experiments show that the proposed methods are more effective to exploit the time-varying subspace in comparison with the conventional Tensor Ring completion methods. Besides, the proposed methods are demonstrated to be superior to obtain better results than state-of-the-art online methods in streaming data completion under varying missing ratios and noise.
本文考虑部分观测的高阶流数据的完成问题，将其建模为在线低秩张量完成问题。尽管在线低秩张量完成问题近年来引起了广泛关注，但大多数都是基于传统的分解方法，如 CP 和 Tucker 设计的。受张量环分解在表示高阶数据方面的优势及其在缺失值估计方面的优越性的启发，本文提出了两种基于张量环分解的在线子空间学习和插补方法。具体来说，我们首先通过对 TR 核的 Frobenium 范数正则化的指数加权最小二乘法，提出了一种在线张量环子空间学习和插补模型。然后，开发了两种常用的优化算法，即交替递归最小二乘法和随机梯度算法，来求解所提出的模型。数值实验表明，与传统的张量环完成方法相比，所提出的方法在利用时变子空间方面更为有效。此外，在不同缺失率和噪声下的流数据完成中，所提出的方法在获得更好的结果方面优于最新的在线方法。
