Convergence acceleration of alternating least squares with a matrix polynomial predictive model for PARAFAC decomposition of a tensor. Shi, M., Zhang, J., Hu, B., Wang, B., & Lu, Q. In *2017 25th European Signal Processing Conference (EUSIPCO)*, pages 1115-1119, Aug, 2017.

Paper doi abstract bibtex

Paper doi abstract bibtex

In this paper, a matrix polynomial whose coefficients are matrices is first defined. Its predictive model, called as the Matrix Polynomial Predictive Model (MPPM), is then derived. When the loading matrices of a decomposed tensor in the Alternating Least Squares (ALS) are replaced by the predicted ones of the MPPM, a new ALS algorithm with the MPPM (ALS-MPPM) is proposed. Analyses show that the convergent rate of the proposed ALS-MPPM is closely related to the degree of the matrix polynomial. Namely, when an accelerative convergence rate is expected, the polynomial with a high degree is preferred. Although a high degree means a high possibility of prediction failure, a simple solution can be used to handle such failure. Moreover, the relationship between our ALS-MPPM and the existing ALS-based algorithms is also analyzed. The results of numerical simulations show that the proposed ALS-MPPM outperforms the reported ALS-based algorithms in the literature while the analytical results are verified.

@InProceedings{8081381, author = {M. Shi and J. Zhang and B. Hu and B. Wang and Q. Lu}, booktitle = {2017 25th European Signal Processing Conference (EUSIPCO)}, title = {Convergence acceleration of alternating least squares with a matrix polynomial predictive model for PARAFAC decomposition of a tensor}, year = {2017}, pages = {1115-1119}, abstract = {In this paper, a matrix polynomial whose coefficients are matrices is first defined. Its predictive model, called as the Matrix Polynomial Predictive Model (MPPM), is then derived. When the loading matrices of a decomposed tensor in the Alternating Least Squares (ALS) are replaced by the predicted ones of the MPPM, a new ALS algorithm with the MPPM (ALS-MPPM) is proposed. Analyses show that the convergent rate of the proposed ALS-MPPM is closely related to the degree of the matrix polynomial. Namely, when an accelerative convergence rate is expected, the polynomial with a high degree is preferred. Although a high degree means a high possibility of prediction failure, a simple solution can be used to handle such failure. Moreover, the relationship between our ALS-MPPM and the existing ALS-based algorithms is also analyzed. The results of numerical simulations show that the proposed ALS-MPPM outperforms the reported ALS-based algorithms in the literature while the analytical results are verified.}, keywords = {convergence of numerical methods;least squares approximations;matrix algebra;polynomials;tensors;convergence acceleration;alternating least squares;matrix polynomial predictive model;ALS-MPPM;accelerative convergence rate;prediction failure;PARAFAC tensor decomposition;numerical simulations;Convergence;Matrix decomposition;Tensile stress;Predictive models;Signal processing algorithms;Prediction algorithms;Acceleration}, doi = {10.23919/EUSIPCO.2017.8081381}, issn = {2076-1465}, month = {Aug}, url = {https://www.eurasip.org/proceedings/eusipco/eusipco2017/papers/1570342730.pdf}, }

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