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Multi-way analysis with applications in the chemical sciences [[electronic resource] /] / Age Smilde, Rasmus Bro, and Paul Geladi
| Multi-way analysis with applications in the chemical sciences [[electronic resource] /] / Age Smilde, Rasmus Bro, and Paul Geladi |
| Autore | Smilde Age K |
| Pubbl/distr/stampa | Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2004 |
| Descrizione fisica | 1 online resource (397 p.) |
| Disciplina |
540.1519535
540.72 540/.72 |
| Altri autori (Persone) |
BroRasmus
GeladiPaul |
| Soggetto topico |
Chemistry - Statistical methods
Multivariate analysis |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-27462-X
9786610274628 0-470-01211-0 0-470-01210-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Multi-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
2.7 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 Appendix 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 6.7 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 8.2 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 Appendix 9.B: geometric view of centering |
| Record Nr. | UNINA-9910143442703321 |
Smilde Age K
|
||
| Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Multi-way analysis with applications in the chemical sciences [[electronic resource] /] / Age Smilde, Rasmus Bro, and Paul Geladi
| Multi-way analysis with applications in the chemical sciences [[electronic resource] /] / Age Smilde, Rasmus Bro, and Paul Geladi |
| Autore | Smilde Age K |
| Pubbl/distr/stampa | Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2004 |
| Descrizione fisica | 1 online resource (397 p.) |
| Disciplina |
540.1519535
540.72 540/.72 |
| Altri autori (Persone) |
BroRasmus
GeladiPaul |
| Soggetto topico |
Chemistry - Statistical methods
Multivariate analysis |
| ISBN |
1-280-27462-X
9786610274628 0-470-01211-0 0-470-01210-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Multi-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
2.7 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 Appendix 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 6.7 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 8.2 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 Appendix 9.B: geometric view of centering |
| Record Nr. | UNINA-9910830068003321 |
|
Smilde Age K
|
||
| Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Multi-way analysis with applications in the chemical sciences [[electronic resource] /] / Age Smilde, Rasmus Bro, and Paul Geladi
| Multi-way analysis with applications in the chemical sciences [[electronic resource] /] / Age Smilde, Rasmus Bro, and Paul Geladi |
| Autore | Smilde Age K |
| Pubbl/distr/stampa | Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2004 |
| Descrizione fisica | 1 online resource (397 p.) |
| Disciplina |
540.1519535
540.72 540/.72 |
| Altri autori (Persone) |
BroRasmus
GeladiPaul |
| Soggetto topico |
Chemistry - Statistical methods
Multivariate analysis |
| ISBN |
1-280-27462-X
9786610274628 0-470-01211-0 0-470-01210-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Multi-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
2.7 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 Appendix 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 6.7 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 8.2 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 Appendix 9.B: geometric view of centering |
| Record Nr. | UNINA-9910840574803321 |
|
Smilde Age K
|
||
| Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||