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Partial least-squares regression: a tutorial

Partial least-squares regression: a tutorial,10.1016/0003-2670(86)80028-9,Analytica Chimica Acta,PAUL GELADI,BRUCE R. KOWALSKI

Partial least-squares regression: a tutorial   (Citations: 1020)
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SUMMARY A tutorial on the partial least-squares (PLS) regression method is provided. Weak points in some other regression methods are outlined and PLS is developed as a remedy for those weaknesses. An algorithm for a predictive PLS and some practical hints for its use are given. The partial least-squares regression method (PLS) is gaining importance in many fields of chemistry; analytical, physical, clinical chemistry and indus- trial process control can benefit from the use of the method. The pioneering work in PLS was done in the late sixties by H. Wold in the field of econo- metrics. The use of the PLS method for chemical applications was pioneered by the groups of S. Wold and H. Martens in the late seventies after an initial application by Kowalski et al. ( 11. In spite of the large amount of literature that emerged from these groups, most articles describing PLS give algorithms and theory that are incomplete and often difficult to understand. Two recent articles (2, 31 show that PLS is a good alternative to the more classical multiple linear regression and principal component regression methods because it is more robust. Robust means that the model parameters do not change very much when new calibration samples are taken from the total population. This article is meant as a tutorial. The reader is referred to texts on linear algebra (4, 51 if needed. The two most complete articles on PLS available at present are by S. Wold et al. (4, 61. The nomenclature used in Kowalski (6) will be used here. Furthermore, all vectors will be column vectors. The corre- sponding row vectors will be designated as transposed vectors. The notation will be kept as rigorous as possible. Table 1 lists the notation used. The paragraphs on multiple linear regression, principal component analysis and principal component regression are included because they are necessary for a good understanding of PLS. They do not represent a complete treatment of these subjects.
Journal: Analytica Chimica Acta - ANAL CHIM ACTA , vol. 185, no. 1, pp. 1-17, 1986
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