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On the self‐weighted alternating trilinear decomposition algorithm—the property of being insensitive to excess factors used in calculation
Author(s) -
Chen ZengPing,
Wu HaiLong,
Yu RuQin
Publication year - 2001
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.633
Subject(s) - chemometrics , property (philosophy) , constraint (computer aided design) , decomposition , iterative method , algorithm , computer science , chemistry , mathematics , chromatography , philosophy , geometry , organic chemistry , epistemology
PARAFAC is well known as an iterative trilinear decomposition method. In practice, an accurate estimation of the number of underlying factors is required; otherwise it is difficult to guarantee the chemical meaning of the results obtained. The absence of a versatile chemometric method for factor estimation has often caused problems for analysts. With the advent of ATLD followed by SWATLD, the above relatively strict constraint can be relaxed. Experiments have shown that the profiles of the underlying factors can be extracted by ATLD (Wu et al. , J. Chemometrics 1998; 12 : 1) and SWATLD (Chen et al. , Chemometrics Intell. Lab. Syst . 2000; 52: 75) as long as the number of factors used in calculation is no less than the number of actual factors. In other words, an overestimation of the number of factors will not affect the obtainment of chemically meaningful results by SWATLD and ATLD. In this paper the authors provide some simple mathematical explanations of this valuable property of SWATLD. Along with these explanations, some other properties of SWATLD as well as some guidelines for designing new trilinear decomposition methods are also discussed. Copyright © 2001 John Wiley & Sons, Ltd.