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A Note on the Use of the Partial Least-Squares Method for Multivariate Calibration

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Abstract:

The multivariate calibration problem is a problem of predicting the concentration in an unknown sample, c un, from the response vector of an unknown sample, r un (J responses). The predicting equation can be arranged in the form



ĉ un = r un T R + c.       (1)



R + is the pseudo-inverse of the calibration set matrix of responses, R, whose column indices correspond to the J sensors or wavelengths and row indices correspond to the I samples (individuals), and c is the vector of concentrations for the I samples of the analyte in each of the calibration samples. Derivation of Eq. 1 is described in Ref. 1. The PLS regression involves solution of the predicting equation.

Keywords: Multivariate calibration; PLS; Regression; Singular value decomposition

Document Type: Short Communication

DOI: http://dx.doi.org/10.1366/0003702884429481

Affiliations: 1: Center for Process Analytical Chemistry, and Laboratory for Chemometrics, Department of Chemistry BG-10, University of Washington, Seattle, Washington 98195; on leave from Nuclear Research Center-Negev, P.O. Box 9001 Beer-Sheva 84190 Israel 2: Center for Process Analytical Chemistry, and Laboratory for Chemometrics, Department of Chemistry BG-10, University of Washington, Seattle, Washington 98195

Publication date: November 1, 1988

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