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A global perspective on multivariate calibration methods
Author(s) -
Lang Patrick M.,
Kalivas John H.
Publication year - 1993
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.1180070303
Subject(s) - mathematics , variety (cybernetics) , perspective (graphical) , matrix (chemical analysis) , multivariate statistics , principal component analysis , calculus (dental) , algebra over a field , computer science , pure mathematics , statistics , geometry , medicine , dentistry , materials science , composite material
This paper consists of two distinct but related parts. In the first part a geometric theory of generalized inverses is presented and a methodology based on this theory is developed and applied to solve the K‐matrix and P‐matrix forms of Beer's law. It is shown that most currently accepted and practiced methods for solving these forms of Beer's law are just special cases of this geometric theory of generalized inverses. In addition, this geometric theory is used to explain why the current methods work and why they fail. In the second part a general methodology that includes as special cases least squares, principal component regression, partial least squares 1 and 2, continuum regression plus a variety of other described and undescribed methodologies is presented and then applied to solve the P‐matrix formulation of Beer's law. This general methodology, like the first, is also geometric in nature and relies on an understanding of projections. The main emphasis of this paper is one of perspective, which, if understood, provides the proper foundation for answering the general but extremely hard and possibly unanswerable question “what is the best method?”.