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 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},
}
Downloads: 0
{"_id":"R9AC3Xq6sk3uW7gE8","bibbaseid":"shi-zhang-hu-wang-lu-convergenceaccelerationofalternatingleastsquareswithamatrixpolynomialpredictivemodelforparafacdecompositionofatensor-2017","authorIDs":[],"author_short":["Shi, M.","Zhang, J.","Hu, B.","Wang, B.","Lu, Q."],"bibdata":{"bibtype":"inproceedings","type":"inproceedings","author":[{"firstnames":["M."],"propositions":[],"lastnames":["Shi"],"suffixes":[]},{"firstnames":["J."],"propositions":[],"lastnames":["Zhang"],"suffixes":[]},{"firstnames":["B."],"propositions":[],"lastnames":["Hu"],"suffixes":[]},{"firstnames":["B."],"propositions":[],"lastnames":["Wang"],"suffixes":[]},{"firstnames":["Q."],"propositions":[],"lastnames":["Lu"],"suffixes":[]}],"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","bibtex":"@InProceedings{8081381,\n author = {M. Shi and J. Zhang and B. Hu and B. Wang and Q. Lu},\n booktitle = {2017 25th European Signal Processing Conference (EUSIPCO)},\n title = {Convergence acceleration of alternating least squares with a matrix polynomial predictive model for PARAFAC decomposition of a tensor},\n year = {2017},\n pages = {1115-1119},\n 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.},\n 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},\n doi = {10.23919/EUSIPCO.2017.8081381},\n issn = {2076-1465},\n month = {Aug},\n url = {https://www.eurasip.org/proceedings/eusipco/eusipco2017/papers/1570342730.pdf},\n}\n\n","author_short":["Shi, M.","Zhang, J.","Hu, B.","Wang, B.","Lu, Q."],"key":"8081381","id":"8081381","bibbaseid":"shi-zhang-hu-wang-lu-convergenceaccelerationofalternatingleastsquareswithamatrixpolynomialpredictivemodelforparafacdecompositionofatensor-2017","role":"author","urls":{"Paper":"https://www.eurasip.org/proceedings/eusipco/eusipco2017/papers/1570342730.pdf"},"keyword":["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"],"metadata":{"authorlinks":{}},"downloads":0},"bibtype":"inproceedings","biburl":"https://raw.githubusercontent.com/Roznn/EUSIPCO/main/eusipco2017url.bib","creationDate":"2021-02-13T16:38:25.630Z","downloads":0,"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"],"search_terms":["convergence","acceleration","alternating","squares","matrix","polynomial","predictive","model","parafac","decomposition","tensor","shi","zhang","hu","wang","lu"],"title":"Convergence acceleration of alternating least squares with a matrix polynomial predictive model for PARAFAC decomposition of a tensor","year":2017,"dataSources":["2MNbFYjMYTD6z7ExY","uP2aT6Qs8sfZJ6s8b"]}