An adapted version of the element-wise weighted total least squares method for applications in chemometrics
Schuermans, Mieke, Markovsky, Ivan and Van Huffel, Sabine (2007) An adapted version of the element-wise weighted total least squares method for applications in chemometrics. Chemometrics and Intelligent Laboratory Systems, 85, (1), 40-46.
The Maximum Likelihood PCA (MLPCA) method has been devised in chemometrics as a generalization of the well-known PCA method in order to derive consistent estimators in the presence of errors with known error distribution. For similar reasons, the Total Least Squares (TLS) method has been generalized in the field of computational mathematics and engineering to maintain consistency of the parameter estimates in linear models with measurement errors of known distribution. In a previous paper [M. Schuermans, I. Markovsky, P.D. Wentzell, S. Van Huffel, On the equivalance between total least squares and maximum likelihood PCA, Anal. Chim. Acta, 544 (2005), 254–267], the tight equivalences between MLPCA and Element-wise Weighted TLS (EW-TLS) have been explored. The purpose of this paper is to adapt the EW-TLS method in order to make it useful for problems in chemometrics. We will present a computationally efficient algorithm and compare this algorithm with the standard EW-TLS algorithm and the MLPCA algorithm in computation time and convergence behaviour on chemical data.
|Keywords:||EW-TLS; MLPCA; Rank reduction; Measurement errors|
|Divisions:||Faculty of Physical Sciences and Engineering > Electronics and Computer Science > Comms, Signal Processing & Control
|Date Deposited:||13 Feb 2007|
|Last Modified:||21 Aug 2012 03:45|
|Contributors:||Schuermans, Mieke (Author)
Markovsky, Ivan (Author)
Van Huffel, Sabine (Author)
|Further Information:||Google Scholar|
|ISI Citation Count:||1|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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