Acceleration of the alternating least squares algorithm for principal components analysis

Masahiro Kuroda, Yuichi Mori, Masaya Iizuka, Michio Sakakihara

Research output: Contribution to journalArticle

24 Citations (Scopus)

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 languageEnglish
Pages (from-to)143-153
Number of pages11
JournalComputational Statistics and Data Analysis
Volume55
Issue number1
DOIs
Publication statusPublished - Jan 1 2011

Fingerprint

Alternating Least Squares
Least Square Algorithm
Principal component analysis
Principal Component Analysis
Least Squares Estimation
Variable Selection
Large Data Sets
Iterative Algorithm
Speedup
Numerical Experiment
Converge
Iteration
Estimate

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

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

In: Computational Statistics and Data Analysis, Vol. 55, No. 1, 01.01.2011, p. 143-153.

Research output: Contribution to journalArticle

Kuroda, Masahiro ; Mori, Yuichi ; Iizuka, Masaya ; Sakakihara, Michio. / Acceleration of the alternating least squares algorithm for principal components analysis. In: Computational Statistics and Data Analysis. 2011 ; Vol. 55, No. 1. pp. 143-153.
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