摘要:

AbstractThe use of continuum regression (CR) for the identification of finite impulse response (FIR) dynamic models is investigated. CR encompasses the methods of principal component regression (PCR), partial least squares (PLS) and multiple linear regression (MLR). PCR and MLR are at the two extremes of the continuum. In PCR and PLS, cross‐validation is used to determine the optimum number of factors or ‘latent variables’ to retain in the regression model. CR allows one to vary themethodin addition. Cross‐validation then determines both the optimum method and the number of latent variables. The CR ‘prediction error surface’—a function of the method and number of latent variables—is elucidated. The optimal model is defined as the minimum of this surface. Among the cases studied, the optimal model usually comes from the region of the continuum between PCR and PLS. Few derive from the region between PLS and MLR. It is also demonstrated that FIR models identified by CR have frequency domain properties similar to those id

ISSN:0886-9383    

DOI:10.1002/cem.1180070102

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

摘要:

AbstractHigh‐performance liquid chromatography with diode array detection (HPLC––DAD) is used to characterize mixtures from chlorophylladegradation experiments. Overlapping chromatographic peaks are resolved by means of the heuristic evolving latent projections (HELP) method. The HELP method is a self‐modelling curve resolution method. No assumptions are made about spectral and/or chromatographic peak shape. In the first step the method establishes the real noise level in the data by use of the so‐called zero‐component regions. This information is used to reveal selective chromatographic information and the number of chemical species at every retention time in unresolved chromatographic peaks. Utilising the selective chromatographic regions in combination with the zero‐concentration windows, unique resolution into concentration profiles and spectra of the pure chemical species is accomplished. HPLC–DAD data from six chlorophylladegradation experiments were analysed. Consistent results were obtained even with very similar spectra for six or seven overlapping chem

ISSN:0886-9383    

DOI:10.1002/cem.1180070103

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

摘要:

AbstractA fast and memory‐saving PLS regression algorithm for matrices with large numbers of objects is presented. It is called the kernel algorithm for PLS. Long (meaning having many objects,N) matricesX(N×K) andY(N×M) are condensed into a small (K×K) square ‘kernel’ matrixXTYYTXof size equal to the number ofX‐variables. Using this kernel matrixXTYYTXtogether with the small covariance matricesXTX(K×K),XTY(K×M) andYTY(M×M), it is possible to estimate all necessary parameters for a complete PLS regression solution with some statistical diagnostics. The new developments are presented in equation form. A comparison of consumed floating point operations is given for the kernel and the classical PLS algorithm. As appendices, a condensed matrix algebra version of the kernel algorithm is given together with th

ISSN:0886-9383    

DOI:10.1002/cem.1180070104

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

摘要:

AbstractFor efficient handling of very large data arrays, pretreatment by compression is mandatory. In the present paper B‐spline methods are described as good candidates for such data array compression. The mathematical relation between the maximum entropy method for compression of data tables and the B‐spline of zeroth degree is described together with the generalization of B‐spline compression tonth‐order data array tables in matrix and tensor

ISSN:0886-9383    

DOI:10.1002/cem.1180070105

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

ISSN:0886-9383    

DOI:10.1002/cem.1180070106

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

ISSN:0886-9383    

DOI:10.1002/cem.1180070101

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY