NONNEGATIVE 3-WAY TENSOR FACTORIZATION TAKING INTO ACCOUNT POSSIBLE MISSING DATA

This paper deals with the problem of incomplete data i.e. data with missing, unknown or unreliable values, in the polyadic decomposition of a nonnegative three-way tensor. The main advantage of the nonnegativity constraint is that the approx-imation problem becomes well posed. To tackle simultane-ously these two problems, we suggest the use of a weighted least square cost function whose weights are gradually modi-fied through the iterations. Moreover, the nonnegative nature of the loading matrices is taken into account directly in the problem parameterization. Then, the three gradient compo-nents can be explicitly derived allowing to efficiently imple-ment the CP decomposition using standard optimization algo-rithms. In our case, we focus on the conjugate gradient and the BFGS algorithms. Finally, the good behaviour of the pro-posed approaches and their robustness versus possible model errors is illustrated through computer simulations in the con-text of data analysis