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Algorithms for DEDICOM: acceleration, deceleration, or neither?
Author(s) -
Takane Yoshio,
Zhang Zhidong
Publication year - 2009
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.1230
Subject(s) - monotonic function , convergence (economics) , eigenvalues and eigenvectors , computation , extrapolation , acceleration , algorithm , polynomial , simple (philosophy) , matrix (chemical analysis) , mathematics , computer science , decomposition , mathematical optimization , mathematical analysis , philosophy , physics , materials science , epistemology , quantum mechanics , classical mechanics , economics , composite material , economic growth , ecology , biology
Takane's original algorithm for DEDICOM (DEcomposition into DIrectional COMponents) was proposed more than two decades ago. There have been a couple of significant developments since then: Kiers et al .'s modification to ensure monotonic convergence of the algorithm, and Jennrich's recommendation to use the modified algorithm only when Takane's original algorithm violates the monotonicity. In this paper, we argue that neither of these modifications is essential, drawing a close relationship between Takane's algorithm and the simultaneous power method for obtaining dominant eigenvalues and vectors of a symmetric matrix. By ignoring monotonicity, we can develop a much more efficient algorithm by simple modifications of Takane's original algorithm, as demonstrated in this paper. More specifically, we incorporate the minimum polynomial extrapolation (MPE) method to accelerate the convergence of Takane's algorithm, and show that it significantly cuts down the computation time. Copyright © 2009 John Wiley & Sons, Ltd.