Monotone and non-monotone accelerated proximal gradient for nonnegative canonical polyadic tensor decomposition

Tensors may be seen as multi-dimensional arrays that generalize vectors and matrices to more than two dimensions. Among tensor decompositions, we are especially interested in the Canonical Polyadic tensor decomposition, which is important in various real-world applications, for its uniqueness and ease of interpretation of its factor matrices. In this research, we consider the estimation of factor matrices of the Nonnegative Canonical Polyadic (NCP) decomposition in a simultaneous way. 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 through a regularization function that incorporates previous iterations while using a monitoring capable of efficiently conducting this incorporation. Simulation results demonstrate better performance of the two proposed algorithms in terms of accuracy for the normal situation as well as for the bottleneck case when compared to other NCP algorithms in the literature.