LEADER 05369nam 22006614a 450 001 9910830068003321 005 20230617002015.0 010 $a1-280-27462-X 010 $a9786610274628 010 $a0-470-01211-0 010 $a0-470-01210-2 035 $a(CKB)1000000000354415 035 $a(EBL)232671 035 $a(OCoLC)475938741 035 $a(SSID)ssj0000206871 035 $a(PQKBManifestationID)11168989 035 $a(PQKBTitleCode)TC0000206871 035 $a(PQKBWorkID)10228640 035 $a(PQKB)11025481 035 $a(MiAaPQ)EBC232671 035 $a(EXLCZ)991000000000354415 100 $a20031223d2004 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMulti-way analysis with applications in the chemical sciences$b[electronic resource] /$fAge Smilde, Rasmus Bro, and Paul Geladi 210 $aChichester, West Sussex, England ;$aHoboken, NJ $cJ. Wiley$dc2004 215 $a1 online resource (397 p.) 300 $aDescription based upon print version of record. 311 $a0-471-98691-7 320 $aIncludes bibliographical references (p. [351]-369) and index. 327 $aMulti-way Analysis with Applications in the Chemical Sciences; CONTENTS; Foreword; Preface; Nomenclature and Conventions; 1 Introduction; 1.1 What is multi-way analysis?; 1.2 Conceptual aspects of multi-way data analysis; 1.3 Hierarchy of multivariate data structures in chemistry; 1.4 Principal component analysis and PARAFAC; 1.5 Summary; 2 Array definitions and properties; 2.1 Introduction; 2.2 Rows, columns and tubes; frontal, lateral and horizontal slices; 2.3 Elementary operations; 2.4 Linearity concepts; 2.5 Rank of two-way arrays; 2.6 Rank of three-way arrays 327 $a2.7 Algebra of multi-way analysis2.8 Summary; Appendix 2.A; 3 Two-way component and regression models; 3.1 Models for two-way one-block data analysis: component models; 3.2 Models for two-way two-block data analysis: regression models; 3.3 Summary; Appendix 3.A: some PCA results; Appendix 3.B: PLS algorithms; 4 Three-way component and regression models; 4.1 Historical introduction to multi-way models; 4.2 Models for three-way one-block data: three-way component models; 4.3 Models for three-way two-block data: three-way regression models; 4.4 Summary 327 $aAppendix 4.A: alternative notation for the PARAFAC modelAppendix 4.B: alternative notations for the Tucker3 model; 5 Some properties of three-way component models; 5.1 Relationships between three-way component models; 5.2 Rotational freedom and uniqueness in three-way component models; 5.3 Properties of Tucker3 models; 5.4 Degeneracy problem in PARAFAC models; 5.5 Summary; 6 Algorithms; 6.1 Introduction; 6.2 Optimization techniques; 6.3 PARAFAC algorithms; 6.4 Tucker3 algorithms; 6.5 Tucker2 and Tucker1 algorithms; 6.6 Multi-linear partial least squares regression 327 $a6.7 Multi-way covariates regression models6.8 Core rotation in Tucker3 models; 6.9 Handling missing data; 6.10 Imposing non-negativity; 6.11 Summary; Appendix 6.A: closed-form solution for the PARAFAC model; Appendix 6.B: proof that the weights in trilinear PLS1 can be obtained from a singular value decomposition; 7 Validation and diagnostics; 7.1 What is validation?; 7.2 Test-set and cross-validation; 7.3 Selecting which model to use; 7.4 Selecting the number of components; 7.5 Residual and influence analysis; 7.6 Summary; 8 Visualization; 8.1 Introduction 327 $a8.2 History of plotting in three-way analysis8.3 History of plotting in chemical three-way analysis; 8.4 Scree plots; 8.5 Line plots; 8.6 Scatter plots; 8.7 Problems with scatter plots; 8.8 Image analysis; 8.9 Dendrograms; 8.10 Visualizing the Tucker core array; 8.11 Joint plots; 8.12 Residual plots; 8.13 Leverage plots; 8.14 Visualization of large data sets; 8.15 Summary; 9 Preprocessing; 9.1 Background; 9.2 Two-way centering; 9.3 Two-way scaling; 9.4 Simultaneous two-way centering and scaling; 9.5 Three-way preprocessing; 9.6 Summary; Appendix 9.A: other types of preprocessing 327 $aAppendix 9.B: geometric view of centering 330 $aThis book is an introduction to the field of multi-way analysis for chemists and chemometricians. Its emphasis is on the ideas behind the method and its pratical applications. Sufficient mathematical background is given to provide a solid understanding of the ideas behind the method. There are currently no other books on the market which deal with this method from the viewpoint of its applications in chemistry. Applicable in many areas of chemistry.No comparable volume currently available.The field is becoming increasingly important. 606 $aChemistry$xStatistical methods 606 $aMultivariate analysis 615 0$aChemistry$xStatistical methods. 615 0$aMultivariate analysis. 676 $a540.1519535 676 $a540.72 676 $a540/.72 700 $aSmilde$b Age K$0855361 701 $aBro$b Rasmus$0696535 701 $aGeladi$b Paul$0855362 712 02$aWiley Online Library (Servicio en línea) 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830068003321 996 $aMulti-way analysis with applications in the chemical sciences$94117035 997 $aUNINA