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arXiv · 1805.08465

Beyond Unfolding: Exact Recovery of Latent Convex Tensor Decomposition under Reshuffling

Chao Li·Mohammad Emtiyaz Khan·Zhun Sun·Gang Niu·Bo Han·Shengli Xie·Qibin Zhao
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Abstract

Exact recovery of tensor decomposition (TD) methods is a desirable property in both unsupervised learning and scientific data analysis. The numerical defects of TD methods, however, limit their practical applications on real-world data. As an alternative, convex tensor decomposition (CTD) was proposed to alleviate these problems, but its exact-recovery property is not properly addressed so far. To this end, we focus on latent convex tensor decomposition (LCTD), a practically widely-used CTD model, and rigorously prove a sufficient condition for its exact-recovery property. Furthermore, we show that such property can be also achieved by a more general model than LCTD. In the new model, we generalize the classic tensor (un-)folding into reshuffling operation, a more flexible mapping to relocate the entries of the matrix into a tensor. Armed with the reshuffling operations and exact-recovery property, we explore a totally novel application for (generalized) LCTD, i.e., image steganography. Experimental results on synthetic data validate our theory, and results on image steganography show that our method outperforms the state-of-the-art methods.

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Chao Li, Mohammad Emtiyaz Khan, Zhun Sun, Gang Niu, Bo Han, Shengli Xie, Qibin Zhao. 2018-05-22. Beyond Unfolding: Exact Recovery of Latent Convex Tensor Decomposition under Reshuffling. https://arxiv.org/abs/1805.08465

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