TY - GEN

T1 - Initial value selection for the alternating least squares algorithm

AU - Kuroda, Masahiro

AU - Mori, Yuichi

AU - Iizuka, Masaya

N1 - Funding Information:
Acknowledgments The authors would like to thank the editor and referees for their valuable comments and helpful suggestions. This work was supported by JSPS KAKENHI Grant Number JP16K00061.
Publisher Copyright:
© Springer Nature Singapore Pte Ltd 2020.

PY - 2020

Y1 - 2020

N2 - The alternating least squares (ALS) algorithm is a popular computational algorithm for obtaining least squares solutions minimizing the loss functions in nonlinear multivariate analysis with optimal scaling (NMVA). The ALS algorithm is a simple computational procedure and has a stable convergence property, while the algorithm only guarantees local convergence. In order to avoid finding a local minimum of a loss function, the most commonly used method is to start the ALS algorithm with various random initial values. Such random initialization ALS algorithm tries to find the least squares solution that globally minimizes the loss function. However, the drawback of the random initialization ALS algorithm with multiple runs is to take a huge number of iterations and long computation time. For these problems, we consider initial value selection for selecting an initial value leading to a global minimum of the loss function. The proposed procedure enables efficiently selecting an initial value of the ALS algorithm. Furthermore, we can increase the computation speed when applying the vector ε acceleration for the ALS algorithm to the initial value selection procedure and the least squares estimation in NMVA.

AB - The alternating least squares (ALS) algorithm is a popular computational algorithm for obtaining least squares solutions minimizing the loss functions in nonlinear multivariate analysis with optimal scaling (NMVA). The ALS algorithm is a simple computational procedure and has a stable convergence property, while the algorithm only guarantees local convergence. In order to avoid finding a local minimum of a loss function, the most commonly used method is to start the ALS algorithm with various random initial values. Such random initialization ALS algorithm tries to find the least squares solution that globally minimizes the loss function. However, the drawback of the random initialization ALS algorithm with multiple runs is to take a huge number of iterations and long computation time. For these problems, we consider initial value selection for selecting an initial value leading to a global minimum of the loss function. The proposed procedure enables efficiently selecting an initial value of the ALS algorithm. Furthermore, we can increase the computation speed when applying the vector ε acceleration for the ALS algorithm to the initial value selection procedure and the least squares estimation in NMVA.

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U2 - 10.1007/978-981-15-3311-2_18

DO - 10.1007/978-981-15-3311-2_18

M3 - Conference contribution

AN - SCOPUS:85092188078

SN - 9789811533105

T3 - Studies in Classification, Data Analysis, and Knowledge Organization

SP - 227

EP - 239

BT - Advanced Studies in Classification and Data Science, IFCS 2017

A2 - Imaizumi, Tadashi

A2 - Okada, Akinori

A2 - Miyamoto, Sadaaki

A2 - Sakaori, Fumitake

A2 - Yamamoto, Yoshiro

A2 - Vichi, Maurizio

PB - Springer Science and Business Media Deutschland GmbH

T2 - Biennial Conference of the International Federation of Classification Societies, IFCS 2017

Y2 - 8 August 2017 through 10 August 2017

ER -