Seeking an appropriate alternative least squares algorithm for nonnegative tensor factorizations

Alternative least squares (ALS) algorithm is considered as a work-horse algorithm for general tensor factorizations. A common form of this algorithm for nonnegative tensor factorizations (NTF) is always combined with a nonlinear projection (rectifier) to enforce nonnegative entries during the estimation. Such simple modification often provides acceptable results for general data. However, this does not establish an appropriate ALS algorithm for NTF. This kind of ALS algorithm often converges slowly, or cannot converge to the desired solution, especially for collinear data. To this end, in this paper, we reinvestigate the nonnegative quadratic programming, propose a recursive method for solving this problem. Then, we formulate a novel ALS algorithm for NTF. The validity and high performance of the proposed algorithm has been confirmed for difficult benchmarks, and also in an application of object classification, and analysis of EEG signals.