Premium
A new third‐order calibration method with application for analysis of four‐way data arrays
Author(s) -
Fu HaiYan,
Wu HaiLong,
Yu YongJie,
Yu LiLi,
Zhang ShuRong,
Nie JinFang,
Li ShuFang,
Yu RuQin
Publication year - 2011
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.1386
Subject(s) - third order , computer science , constraint (computer aided design) , calibration , algorithm , convergence (economics) , rate of convergence , mathematical optimization , data mining , key (lock) , mathematics , statistics , philosophy , geometry , theology , computer security , economics , economic growth
A novel third‐order calibration algorithm, alternating weighted residue constraint quadrilinear decomposition (AWRCQLD) based on pseudo‐fully stretched matrix forms of quadrilinear model, was developed for the quantitative analysis of four‐way data arrays. The AWRCQLD algorithm is based on the new scheme that introduces four unique constraint parts to improve the quality of four‐way PARAFAC algorithm. The tested results demonstrated that the AWRCQLD algorithm has the advantage of faster convergence rate and being insensitive to the excess component number adopted in the model compared with four‐way PARAFAC. Moreover, simulated data and real experimental data were analyzed to explore the third‐order advantage over the second‐order counterpart. The results showed that third‐order calibration methods possess third‐order advantages which allow more inherent information to be obtained from four‐way data, so it can improve the resolving and quantitative capability in contrast with second‐order calibration especially in high collinear systems. Copyright © 2011 John Wiley & Sons, Ltd.