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Residual bilinearization. Part 1: Theory and algorithms
Author(s) -
Öhman Jerker,
Geladi Paul,
Wold Svante
Publication year - 1990
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.1180040109
Subject(s) - residual , matrix (chemical analysis) , mathematics , rank (graph theory) , algorithm , data matrix , partial least squares regression , calibration , total least squares , least squares function approximation , statistics , combinatorics , chemistry , chromatography , singular value decomposition , clade , biochemistry , gene , phylogenetic tree , estimator
When using hyphenated methods in analytical chemistry, the data obtained for each sample are given as a matrix. When a regression equation is set up between an unknown sample (a matrix) and a calibration set (a stack of matrices), the residual is a matrix R . The regression equation is usually solved by minimizing the sum of squares of R . If the sample contains some constituent not calibrated for, this approach is not valid. In this paper an algorithm is presented which partitions R into one matrix of low rank corresponding to the unknown constituents, and one random noise matrix to which the least squares restrictions are applied. Properties and possible applications of the algorithm are also discussed. In Part 2 of this work an example from HPLC with diode array detection is presented and the results are compared with generalized rank annihilation factor analysis (GRAFA).