Nonnegative 3-way tensor factorization via conjugate gradient with globally optimal stepsize

This paper deals with the minimal polyadic decomposition (also known as canonical decomposition or Parafac) of a 3-way array, assuming each entry is positive. In this case, the low-rank approximation problem becomes well-posed. The suggested approach consists of taking into account the nonnegative nature of the loading matrices directly in the problem parameterization. Then, the three gradient components are derived allowing to efficiently implement the decomposition using classical optimization algorithms. In our case, we focus on the conjugate gradient algorithm, well matched to large problems. The good behaviour of the proposed approach is illustrated through computer simulations in the context of data analysis and compared to other existing approaches.