Journal
COMPUTATIONAL STATISTICS & DATA ANALYSIS
Volume 55, Issue 1, Pages 143-153Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.csda.2010.06.001
Keywords
Alternating least squares algorithm; Vector epsilon algorithm; Acceleration of convergence; PRINCIPALS; PRINCALS
Funding
- Japan Society for the Promotion of Science (JSPS) [20500263]
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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 epsilon 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. (C) 2010 Elsevier B.V. All rights reserved.
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