Reviews: Legendre Decomposition for Tensors

Main ideas of the submission The manuscript presents an approximation of nonnegative multi-way tensorial data (or high-order probability mass functions) based on structured energy function form that minimizes the Kullback-Leibler divergence. Comparing against other multilinear decomposition methods of nonnegative tensors, the proposal approach operates on multiplicative parameters under convex objective function and converges to a globally optimal solution. It also shows interesting connections with graphical models such as the high-order Boltzmann machines. Two optimization algorithms are developed, based upon gradient and natural gradient, respectively. The experiment shows that under the same number of parameters, the proposed approach yields smaller RMSEs than the other two baseline non-negative tensor decomposition methods.