Acceleration of the alternating least squares algorithm for principal components analysis

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 (...

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Veröffentlicht in:Computational statistics & data analysis Jg. 55; H. 1; S. 143 - 153
Hauptverfasser: Kuroda, Masahiro, Mori, Yuichi, Iizuka, Masaya, Sakakihara, Michio
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 2011
Elsevier
Schriftenreihe:Computational Statistics & Data Analysis
Schlagworte:
Acceleration
Acceleration of convergence
Algorithms
Alternating least squares algorithm
Alternating least squares algorithm Vector [epsilon] algorithm Acceleration of convergence PRINCIPALS PRINCALS
Convergence
Exact sciences and technology
General topics
Least squares method
Mathematical analysis
Mathematical models
Mathematics
Multivariate analysis
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
PRINCALS
Principal component analysis
PRINCIPALS
Probability and statistics
Sciences and techniques of general use
Statistics
Vector [formula omitted] algorithm
Vector ε algorithm
Alternating least squares algorithm
PRINCIPALS
PRINCALS
Acceleration of convergence
Data analysis
Convergence acceleration
Estimation
Iterative method
Iteration
Multivariate analysis
Algorithm
Convergence
Convergence speed
Selection problem
Numerical analysis
Statistical computation
Least squares method
Algorithm analysis
Principal component analysis
Variable selection
ISSN:0167-9473, 1872-7352
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2010.06.001