Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Candès, E.J., Recht, B.: Exact matrix completion via convex optimization. Commun. ACM 55(6), 111–119 (2012)
Zhang, Z., Ganesh, A., Liang, X., Ma, Y.: Tilt: Transform invariant low-rank textures. International Journal of Computer Vision 99(1), 1–24 (2012)
Candès, E.J., Tao, T.: The power of convex relaxation: Near-optimal matrix completion. IEEE Trans. Inf. Theor. 56(5), 2053–2080 (2010)
Liang, X., Ren, X., Zhang, Z., Ma, Y.: Repairing sparse low-rank texture. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part V. LNCS, vol. 7576, pp. 482–495. Springer, Heidelberg (2012)
Hu, Y., Zhang, D., Ye, J., Li, X., He, X.: Fast and accurate matrix completion via truncated nuclear norm regularization. IEEE Trans. Pattern Anal. 35(9), 2117–2130 (2013)
Xu, Y., Hao, R., Yin, W., Su, Z.: Parallel matrix factorization for low-rank tensor completion (submitted)
Liu, J., Musialski, P., Wonka, P., Ye, J.: Tensor completion for estimating missing values in visual data. IEEE Trans. Pattern Anal. 35(1), 208–220 (2013)
Donoho, D.L., Elad, M.: Maximal sparsity representation via l 1 minimization. Proc. Nat. Aca. Sci. 100, 1297–2202 (2003)
Lin, Z., Liu, R., Su, Z.: Linearized alternating direction method with adaptive penalty for low-rank representation. In: Proc. NIPS 2011, pp. 612–620 (2012)
Cai, J.F., Candès, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20(4), 1956–1982 (2010)
Donoho, C.L., Johnstone, I.M.: Adapting to unknown smoothness via wavelet shrinkage. J. Am. Stat. Assoc. 90(432), 1200–1224 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Han, ZF., Feng, R., Huang, LT., Xiao, Y., Leung, CS., So, H.C. (2014). Tensor Completion Based on Structural Information. In: Loo, C.K., Yap, K.S., Wong, K.W., Teoh, A., Huang, K. (eds) Neural Information Processing. ICONIP 2014. Lecture Notes in Computer Science, vol 8835. Springer, Cham. https://doi.org/10.1007/978-3-319-12640-1_58
Download citation
DOI: https://doi.org/10.1007/978-3-319-12640-1_58
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12639-5
Online ISBN: 978-3-319-12640-1
eBook Packages: Computer ScienceComputer Science (R0)