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Exact recovery of tensor decomposition (TD) methods is a desirable propertyin both unsupervised learning and scientific data analysis. The numericaldefects of TD methods, however, limit their practical applications onreal-world data. As an alternative, convex tensor decomposition (CTD) wasproposed to alleviate these problems, but its exact-recovery property is notproperly addressed so far. To this end, we focus on latent convex tensordecomposition (LCTD), a practically widely-used CTD model, and rigorously provea sufficient condition for its exact-recovery property. Furthermore, we showthat such property can be also achieved by a more general model than LCTD. Inthe new model, we generalize the classic tensor (un-)folding into reshufflingoperation, a more flexible mapping to relocate the entries of the matrix into atensor. Armed with the reshuffling operations and exact-recovery property, weexplore a totally novel application for (generalized) LCTD, i.e., imagesteganography. Experimental results on synthetic data validate our theory, andresults on image steganography show that our method outperforms thestate-of-the-art methods.

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