An adapted version of the element-wise weighted total least squares method for applications in chemometrics
An adapted version of the element-wise weighted total least squares method for applications in chemometrics
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.
EW-TLS, MLPCA, Rank reduction, Measurement errors
40-46
Schuermans, Mieke
7852110e-167e-4c51-8b9c-2520b439e889
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
Van Huffel, Sabine
8814fa15-3922-4a5a-9ba5-c2ea63ceeaf7
January 2007
Schuermans, Mieke
7852110e-167e-4c51-8b9c-2520b439e889
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
Van Huffel, Sabine
8814fa15-3922-4a5a-9ba5-c2ea63ceeaf7
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), .
Abstract
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.
More information
Published date: January 2007
Keywords:
EW-TLS, MLPCA, Rank reduction, Measurement errors
Organisations:
Southampton Wireless Group
Identifiers
Local EPrints ID: 263422
URI: http://eprints.soton.ac.uk/id/eprint/263422
PURE UUID: fc8c8653-d703-43c2-abbd-2ea5820007f3
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Date deposited: 13 Feb 2007
Last modified: 14 Mar 2024 07:31
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Contributors
Author:
Mieke Schuermans
Author:
Ivan Markovsky
Author:
Sabine Van Huffel
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