Acceleration of the alternating least squares algorithm for principal components analysis

Authors:
Masahiro Kuroda;Yuichi Mori;Masaya Iizuka;Michio Sakakihara
Affiliations:
Department of Socio-Information, Okayama University of Science, 1-1 Ridaicho, Kita-ku, Okayama 700-0005, Japan;Department of Socio-Information, Okayama University of Science, 1-1 Ridaicho, Kita-ku, Okayama 700-0005, Japan;Graduate School of Environmental Science, Okayama University 1-1-1 Tsushima-naka, Kita-ku, Okayama 700-8530, Japan;Department of Information Science, Okayama University of Science, 1-1 Ridaicho, Kita-ku, Okayama 700-0005, Japan
Venue:
Computational Statistics & Data Analysis
Year:
2011

Citing 5
Cited 0

Principal component analysis based on a subset of variables: variable selection and sensitivity analysis

MSI '00 Proceedings of the conference, volume III (in honor of Professor Minoru Siotani on his 70th birthday on Multivariate statistical analysis
Accelerating the convergence of the EM algorithm using the vector ε algorithm

Computational Statistics & Data Analysis
Acceleration of the EM algorithm using the vector epsilon algorithm

Computational Statistics
Convergence of the sequence of parameters generated by alternating least squares algorithms

Computational Statistics & Data Analysis
Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems

Computational Statistics & Data Analysis

Quantified Score

Hi-index	0.03

Visualization

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 @e 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.