Beyond Unfolding: Exact Recovery of Latent Convex Tensor Decomposition under Reshuffling
This work addresses a theoretical gap in convex tensor decomposition for unsupervised learning and data analysis, with practical impact in image steganography.
The paper tackles the problem of exact recovery in latent convex tensor decomposition (LCTD) by proving a sufficient condition for this property and generalizing it with reshuffling operations, leading to a novel application in image steganography where it outperforms state-of-the-art methods.
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.