摘要:

AbstractThe growing awareness of the need for non‐deterministic and distribution‐free (soft) models combined with an iterative algorithm for finding latent variables led to the construction of partial least squares models. There have been separate developments in the humanistic and the natural sciences, with stress on different aspects and a different terminology. The historical development is described and some key topics are explai

ISSN:0886-9383    

DOI:10.1002/cem.1180020403

出版商:John Wiley&Sons, Ltd.    

年代:1988

数据来源: WILEY

摘要:

AbstractMany analytical instruments now produce one‐, two‐ orn‐dimensional arrays of data that must be used for the analysis of samples. An integrated approach to linear calibration of such instruments is presented from a tensorial point of view. The data produced by these instruments are seen as the components of a first‐, second‐ ornth‐order tensor respectively. In this first paper, concepts of linear multivariate calibration are developed in the framework of first‐order tensors, and it is shown that the problem of calibration is equivalent to finding the contravariant vector corresponding to the analyte being calibrated. A model of the subspace spanned by the variance in the calibration must be built to compute the contravarian vectors. It is shown that the only difference between methods such as least squares, principal components regression, latent root regression, ridge regression and partial least squres resides in the choice

ISSN:0886-9383    

DOI:10.1002/cem.1180020404

出版商:John Wiley&Sons, Ltd.    

年代:1988

数据来源: WILEY

摘要:

AbstractTensorial calibration provides a useful approach to calibration in general. For calibration of instruments that produce two‐dimensional (second‐order) arrays of data per sample, tensoial concepts are as natural a way of solving the calibration problem as vectorial concepts are for the multivariate problem. Similarly, for third‐ and higher‐order data, the tensorial description of calibration is also useful. This paper introduces second‐order calibration from a tensorial point of view. Univariate, multivariate and bilinear approaches to calibration are presented. The generalized rank annihilation method (GRAM) is described from the tensorial perspective, and it is shown that GRAM is equivalent to finding a second‐order tensorial base that spans both tensors (calibration and unknown) with respective diagonal component matrices. GRAM uses asinglecalibration sample for multicomponent analysis even in the presence of interference. Second‐order bilinear calibration is extended tomultiplecalibration samples where the effect of collineariti

ISSN:0886-9383    

DOI:10.1002/cem.1180020405

出版商:John Wiley&Sons, Ltd.    

年代:1988

数据来源: WILEY

摘要:

AbstractPartial least squares regression (PLS) is proposed for solving ir pollution source apportionment problems as an alternative method to the frequently used chemical mass balance technique. A discriminant PLS is used to calculate linear mixing proportions for a synthetic ambient aerosol data set where the truth is known. Without sacrificing orthogonality of the source profiles, PLS can resolve the emission sources and accurately predict the emission source contributions. Further extensions of the PLS approach to environmental receptor modelling are discussed.

ISSN:0886-9383    

DOI:10.1002/cem.1180020406

出版商:John Wiley&Sons, Ltd.    

年代:1988

数据来源: WILEY

ISSN:0886-9383    

DOI:10.1002/cem.1180020407

出版商:John Wiley&Sons, Ltd.    

年代:1988

数据来源: WILEY

ISSN:0886-9383    

DOI:10.1002/cem.1180020409

出版商:John Wiley&Sons, Ltd.    

年代:1988

数据来源: WILEY

ISSN:0886-9383    

DOI:10.1002/cem.1180020410

出版商:John Wiley&Sons, Ltd.    

年代:1988

数据来源: WILEY

ISSN:0886-9383    

DOI:10.1002/cem.1180020402

出版商:John Wiley&Sons, Ltd.    

年代:1988

数据来源: WILEY