### Abstract

Principal components analysis (PCA) is a popular descriptive multivariate method for handling quantitative data and it can be extended to deal with qualitative data and mixed measurement level data. The existing algorithms for extended PCA are PRINCIPALS of Young et al. (1978) and PRINCALS of Gifi (1989) in which the alternating least squares algorithm is utilized. These algorithms based on the least squares estimation may require many iterations in their application to very large data sets and variable selection problems and may take a long time to converge. In this paper, we derive a new iterative algorithm for accelerating the convergence of PRINCIPALS and PRINCALS by using the vector ε algorithm of Wynn (1962). The proposed acceleration algorithm speeds up the convergence of the sequence of the parameter estimates obtained from PRINCIPALS or PRINCALS. Numerical experiments illustrate the potential of the proposed acceleration algorithm.

Original language | English |
---|---|

Pages (from-to) | 143-153 |

Number of pages | 11 |

Journal | Computational Statistics and Data Analysis |

Volume | 55 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2011 |

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### Keywords

- Acceleration of convergence
- Alternating least squares algorithm
- PRINCALS
- PRINCIPALS
- Vector ε algorithm

### ASJC Scopus subject areas

- Computational Mathematics
- Computational Theory and Mathematics
- Statistics and Probability
- Applied Mathematics

### Cite this

*Computational Statistics and Data Analysis*,

*55*(1), 143-153. https://doi.org/10.1016/j.csda.2010.06.001

**Acceleration of the alternating least squares algorithm for principal components analysis.** / Kuroda, Masahiro; Mori, Yuichi; Iizuka, Masaya; Sakakihara, Michio.

Research output: Contribution to journal › Article

*Computational Statistics and Data Analysis*, vol. 55, no. 1, pp. 143-153. https://doi.org/10.1016/j.csda.2010.06.001

}

TY - JOUR

T1 - Acceleration of the alternating least squares algorithm for principal components analysis

AU - Kuroda, Masahiro

AU - Mori, Yuichi

AU - Iizuka, Masaya

AU - Sakakihara, Michio

PY - 2011/1/1

Y1 - 2011/1/1

N2 - Principal components analysis (PCA) is a popular descriptive multivariate method for handling quantitative data and it can be extended to deal with qualitative data and mixed measurement level data. The existing algorithms for extended PCA are PRINCIPALS of Young et al. (1978) and PRINCALS of Gifi (1989) in which the alternating least squares algorithm is utilized. These algorithms based on the least squares estimation may require many iterations in their application to very large data sets and variable selection problems and may take a long time to converge. In this paper, we derive a new iterative algorithm for accelerating the convergence of PRINCIPALS and PRINCALS by using the vector ε algorithm of Wynn (1962). The proposed acceleration algorithm speeds up the convergence of the sequence of the parameter estimates obtained from PRINCIPALS or PRINCALS. Numerical experiments illustrate the potential of the proposed acceleration algorithm.

AB - Principal components analysis (PCA) is a popular descriptive multivariate method for handling quantitative data and it can be extended to deal with qualitative data and mixed measurement level data. The existing algorithms for extended PCA are PRINCIPALS of Young et al. (1978) and PRINCALS of Gifi (1989) in which the alternating least squares algorithm is utilized. These algorithms based on the least squares estimation may require many iterations in their application to very large data sets and variable selection problems and may take a long time to converge. In this paper, we derive a new iterative algorithm for accelerating the convergence of PRINCIPALS and PRINCALS by using the vector ε algorithm of Wynn (1962). The proposed acceleration algorithm speeds up the convergence of the sequence of the parameter estimates obtained from PRINCIPALS or PRINCALS. Numerical experiments illustrate the potential of the proposed acceleration algorithm.

KW - Acceleration of convergence

KW - Alternating least squares algorithm

KW - PRINCALS

KW - PRINCIPALS

KW - Vector ε algorithm

UR - http://www.scopus.com/inward/record.url?scp=77956395014&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77956395014&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2010.06.001

DO - 10.1016/j.csda.2010.06.001

M3 - Article

AN - SCOPUS:77956395014

VL - 55

SP - 143

EP - 153

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

IS - 1

ER -