Smooth PARAFAC Decomposition for Tensor Completion
Smooth PARAFAC Decomposition for Tensor Completion
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DOI：
10.1109/tsp.2016.2586759
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发表时间：
2015-05
影响因子：
5.4
通讯作者：
Tatsuya Yokota;Qibin Zhao;A. Cichocki
中科院分区：
文献类型：
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作者：
Tatsuya Yokota;Qibin Zhao;A. Cichocki
近年来，基于低秩的张量完备化作为矩阵完备化的高阶推广，受到了广泛的关注。然而，低秩假设是不足以恢复的视觉数据，如彩色和3D图像，当丢失的数据的比例是非常高的。在本文中，我们认为“平滑”的约束，以及低秩近似，并提出了一个有效的算法，用于执行张量完成，这是特别强大的视觉数据。所提出的方法承认显着的优势，由于光滑PARAFAC分解不完整的张量和有效的选择模型，以尽量减少张量秩的集成。因此，我们提出的方法被称为“光滑PARAFAC张量完成（SPC）”。为了施加平滑性约束，我们采用了两种策略，总变差（SPC-TV）和二次变差（SPC-QV），并调用相应的算法进行模型学习。对合成和真实世界的视觉数据进行了广泛的实验评估，与许多最先进的张量完成方法相比，我们的方法在预测性能和效率方面都有了显着的改进。
In recent years, low-rank based tensor completion, which is a higher order extension of matrix completion, has received considerable attention. However, the low-rank assumption is not sufficient for the recovery of visual data, such as color and 3D images, when the ratio of missing data is extremely high. In this paper, we consider “smoothness” constraints as well as low-rank approximations and propose an efficient algorithm for performing tensor completion that is particularly powerful regarding visual data. The proposed method admits significant advantages, owing to the integration of smooth PARAFAC decomposition for incomplete tensors and the efficient selection of models in order to minimize the tensor rank. Thus, our proposed method is termed as “smooth PARAFAC tensor completion (SPC).” In order to impose the smoothness constraints, we employ two strategies, total variation (SPC-TV) and quadratic variation (SPC-QV), and invoke the corresponding algorithms for model learning. Extensive experimental evaluations on both synthetic and real-world visual data illustrate the significant improvements of our method, in terms of both prediction performance and efficiency, compared with many state-of-the-art tensor completion methods.