In tensor completion, one of the challenges is the calculation of the tensor rank. Recently, a tensor nuclear norm, which is a weighted sum of matrix nuclear norms of all unfoldings, has been proposed to solve this difficulty. However, in the matrix nuclear norm based approach, all the singular values are minimized simultaneously. Hence the rank may not be well approximated. This paper presents a tensor completion algorithm based on the concept of matrix truncated nuclear norm, which is superior to the traditional matrix nuclear norm. Since most existing tensor completion algorithms do not consider of the tensor, we add an additional term in the objective function so that we can utilize the spatial regular feature in the tensor data. Simulation results show that our proposed algorithm outperforms some the state-of-the-art tensor/matrix completion algorithms.
CITATION STYLE
Han, Z. F., Feng, R., Huang, L. T., Xiao, Y., Leung, C. S., & So, H. C. (2014). Tensor completion based on structural information. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8835, pp. 479–486). Springer Verlag. https://doi.org/10.1007/978-3-319-12640-1_58
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