Higher-dimension Tensor Completion via Low-rank Tensor Ring Decomposition
Higher-dimension Tensor Completion via Low-rank Tensor Ring Decomposition
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DOI：
10.23919/apsipa.2018.8659708
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
Longhao Yuan;Jianting Cao;Qiang Wu;Qibin Zhao
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文献类型：
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作者：
Longhao Yuan;Jianting Cao;Qiang Wu;Qibin Zhao
数据不完整的问题在信号处理和机器学习中是很常见的。张量补全算法的目标是从部分观测到的数据中恢复不完整的数据。本文利用最近提出的张量环分解的高可压缩性和灵活性的优点，提出了一种新的张量补全方法--张量环加权优化方法(TRWOPT)。利用梯度下降算法找出不完全张量的潜在因子，并利用潜在因子对张量的缺失条目进行预测。我们在合成数据和真实数据上进行了各种张量补全实验。仿真结果表明，TR-WOPT在各种高维张量下都表现出良好的性能。此外，图像补全结果表明，我们提出的算法在很多情况下都优于最先进的算法。特别是当测试图像的缺失率很高时(例如，超过0.9)，我们的TR-WOPT算法的性能明显好于比较的算法。
The problem of incomplete data is common in signal processing and machine learning. Tensor completion algorithms aim to recover the incomplete data from its partially observed entries. In this paper, taking advantages of high compressibility and flexibility of recently proposed tensor ring (TR) decomposition, we propose a new tensor completion approach named tensor ring weighted optimization (TR-WOPT). It finds the latent factors of the incomplete tensor by gradient descent algorithm, then the latent factors are employed to predict the missing entries of the tensor. We conduct various tensor completion experiments on synthetic data and real-world data. The simulation results show that TR-WOPT performs well in various high-dimension tensors. Furthermore, image completion results show that our proposed algorithm outperforms the state-of-the-art algorithms in many situations. Especially when the missing rate of the test images is high (e.g., over 0.9), the performance of our TR-WOPT is significantly better than the compared algorithms.