Computation of the nonnegative canonical tensor decomposition with two accelerated proximal gradient algorithms

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Multidimensional signal analysis has become an important part of many signal processing problems. This type of analysis allows to take advantage of different diversities of a signal in order to extract useful information. This paper focuses on the design and development of multidimensional data decomposition algorithms called Canonical Polyadic (CP) tensor decomposition, a powerful tool in a variety of real-world applications due to its uniqueness and ease of interpretation of its factor matrices. More precisely, it is desired to compute simultaneously the factor matrices involved in the CP decomposition of a real nonnegative tensor, under nonnegative constraints. For this purpose, two proximal algorithms are proposed, the Monotone Accelerated Proximal Gradient (M-APG) and the Non-monotone Accelerated Proximal Gradient (Nm-APG) algorithms. These algorithms are implemented via a regularization function with a simple control strategy capable of efficiently taking advantage of previous iterations. Simulation results demonstrate better performance of the two proposed algorithms in terms of accuracy when compared to other nonnegative CP algorithms in the literature.