| RESIDUAL BILINEARIZATION.PART 1:THEORY AND ALGORITHMS |
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| 作者姓名： | JERKER |
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| 作者单位： | JERKER (?)HMAN Department of Analytical Chemistry，University of Ume(?)，S-90187 Umea，SwedenPAUL GELADI SVANTE WOLD Research Group for Chemometrics，University of Ume(?).S-90187 Ume(?)，Sweden |
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| 摘 要： | When using hyphenated methods in analytical chemistry,the data obtained for each sample are given asa matrix.When a regression equation is set up between an unknown sample (a matrix) and a calibrationset (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 containssome constituent not calibrated for,this approach is not valid.In this paper an algorithm is presentedwhich partitions R into one matrix of low rank corresponding to the unknown constituents,and onerandom noise matrix to which the least squares restrictions are applied.Properties and possibleapplications of the algorithm are also discussed.In Part 2 of this work an example from HPLC with diode array detection is presented and the resultsare compared with generalized rank annihilation factor analysis (GRAFA).
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RESIDUAL BILINEARIZATION.PART 1:THEORY AND ALGORITHMS |
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| JERKER.RESIDUAL BILINEARIZATION.PART 1:THEORY AND ALGORITHMS[J].Journal of Geographical Sciences,1990(1). |
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| Authors: | JERKER |
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| Abstract: | 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). |
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| Keywords: | PLS Three-way matrices Calibration Residual bilinearization Background correction |
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