Computing the nonnegative 3-way tensor factorization using Tikhonov regularization, ICASSP

This paper deals with the minimum polyadic decomposition of a nonnegative three-way array. The main advantage of the nonnegativity constraint is that the approximation problem becomes well posed. To tackle this problem, we suggest the use of a cost function including penalty terms built with ma-trix exponentials. Gradient components are then derived, al-lowing to efficiently implement the decomposition using clas-sical optimization algorithms. In our case ALS and conjugate gradient algorithms are studied and compared with another existing algorithm, thanks to computer simulations performed in the context of data analysis. Index Terms — Data analysis, data mining, non lin-ear conjugate gradient, nonnegative 3-way array, Canonical Polyadic decomposition, Tikhonov regularization. 1