Novel hierarchical ALS algorithm for nonnegative tensor factorization

The multiplicative algorithms are well-known for nonnegative matrix and tensor factorizations. The ALS algorithm for canonical decomposition (CP) has been proved as a "work horse" algorithm for general multiway data. Unfortunately, for CP with nonnegativity constraints, this algorithm with a rectifier (projection) may not converge to the desired solution without additional regularization parameters in matrix inverses. The hierarchical ALS algorithm improves the performance of the ALS algorithm, outperforms the multiplicative algorithm. However, NTF algorithms can face problem with collinear or bias data. In this paper, we propose a novel algorithm which overwhelmingly outperforms all the multiplicative, and (H)ALS algorithms. By solving the nonnegative quadratic programming problems, a general algorithm of the HALS has been derived and experimentally confirmed its validity and high performance for normal and difficult bench marks, and for real-world EEG dataset.