Extensions of the partial least squares approach for the analysis of biomolecular interactions [Elektronische Ressource] / Nina Kirschbaum

Dissertationam Fachbereich Statistik der Universit¨at DortmundExtensions of the Partial LeastSquares approach for theanalysis of biomolecularinteractionsNina KirschbaumErstgutachter: Prof. Dr. W. UrferZweitgutachter: Prof. Dr. G. TrenklerTag der mund¨ lichen Prufung¨ : 02.07.2007Ort der Einreichung: DortmundJahr der Einreichung: 2007Contents1 Introduction 12 The multivariate multiple linear regression 122.1 General considerations . . . . . . . . . . . . . . . . . . . . . . 122.2 The regression model . . . . . . . . . . . . . . . . . . . . . . . 132.3 Ordinary Least Squares estimation . . . . . . . . . . . . . . . 152.4 Univariate linear regression as a special case . . . . . . . . . . 153 Methodology of Partial Least Squares regression 173.1 Basic idea of PLS regression . . . . . . . . . . . . . . . . . . . 173.2 The multivariate PLS algorithm . . . . . . . . . . . . . . . . . 203.2.1 Scaling and centering . . . . . . . . . . . . . . . . . . . 203.2.2 The decomposition models . . . . . . . . . . . . . . . . 213.2.3 Performance of the multivariate PLS algorithm . . . . 243.2.4 The computations of the multivariate algorithm . . . . 263.2.5 Considerationsconcerningthecomponentsofthealgo-rithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2.6 An alternative presentation of the multivariate PLSalgorithm . . . . . . . . . . . . . . . . . . . . . . . . . 403.2.