NOVEL HIERARCHICAL ALS ALGORITHM FOR NONNEGATIVE TENSOR FACTORIZATION

Non-negative Tensor Factorization and Blind Separation

Presented by: Anh-Huy Phan, Author(s): Anh-Huy Phan, Andrzej Cichocki, Brain Science Institue, Japan; Kiyotoshi Matsuoka, Kyushu University of Technology, Japan; Jianting Cao, Brain Science Institue, Japan

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 benchmarks, and for real-world EEG dataset.

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