Matrix Polynomial Predictive Model: A New Approach to Accelerating the PARAFAC Decomposition

Ming Shi, Dan Li, Jian Qiu Zhang
2019 IEEE Access  
Alternating least squares (ALS) and its variations are the most commonly used algorithms for the PARAFAC decomposition of a tensor. However, it is still troubled for one how to accelerate the ALS algorithm with the reduced computational complexity. In this paper, a new acceleration method for the ALS with a matrix polynomial predictive model (MPPM) is proposed. In the MPPM, a matrix-valued function is first approximated by a matrix polynomial. It is shown that the future value of the function
more » ... n be predicted by an FIR filter with the coefficients determined offline. By viewing each factor matrix of a tensor as a matrix-valued function, a new ALS algorithm, the ALS-MPPM algorithm, is then given. Analyses show that our ALS-MPPM algorithm is of low computational complexity and a close relation with the existing ALS algorithms. Moreover, to further accelerate the convergence of the proposed algorithm, a new technique called the multi-model (MM) prediction is also introduced. While the analytical results are verified by the numerical simulations, it is also shown that our ALS-MPPM outperforms the existing ALS-based algorithms in terms of the rate of convergence. INDEX TERMS Alternating least squares, matrix polynomial predictive model, PARAFAC decomposition, tensor.
doi:10.1109/access.2019.2927440 fatcat:3gesfcmjlvajve6xnfksbhpiya