Locally weighted regression

T. Naes, T. Isaksson and B. Kowalski, Locally weighted regression in NIR analysis. Anal. Chem., 2 (1990) 664-673. 

Local flux-density profile, 23 816 Localized molecular orbital (LMO) calculations, 10 633 Locally weighted regression, 6 53 Local oscillator (LO), 23 142, 143 Local toxicity, 25 202 Locard Exchange Principle, 12 99 Lochett, W., 11 8... 

Naes, T., Isaksson, T., Kowalski, B. R. Anal. Chem. 62, 1990, 664—673. Locally weighted regression and scatter correction for near-infrared reflectance data. 

Barton, F.E., II, Shenk, J.S., Westerhaus, M.O. and Funk, D.B. (2000) The development of near infrared wheat quality models by locally weighted regressions. Journal of Near Infrared Spectroscopy 8, 201-208. 

Since the work of Baxter et al. [75,76] around 1990, we have not found many more recent applications and it was not until 2003 that Felipe-Sotelo et al. [77] presented another application. They considered a problem where a major element (Fe) caused spectral and chemical interferences on a minor element (Cr), which had to be quantified in natural waters. They demonstrated that linear PLS handled (eventual) nonlinearities since polynomial PLS and locally weighted regression (nonlinear models) did not outperform its results. Further, it was found that linear PLS was able to model three typical effects which currently occur in ETAAS peak shift, peak enhancement (depletion) and random noise. 

Solow, A.R. (1988) Detecting changes through time in the variance of a long-term hemispheric temperature record an application of robust locally weighted regression. J.Climate 1,290-296. 

Cleveland WS, Robust locally weighted regression and smoothing scatterplots, J. Amer. Stat. Assoc., 74 829-836, 1979. 

Cleveland, W.S. and Devlin, S.J. (1988) Locally weighted regression An approach to regression analysis by local fitting. J. Am. Stat. Assoc. 83, 596-610. 

Two other techniques of calibration equation computation have recently been used by NIR workers, locally weighted regression (LWR) and artificial neural nets. 

W. Cleveland and E. Grosse [1990] Fortran Routines for Locally-Weighted Regression, LOESS Program Source and Documentation, www.nethb.org. 

The locally weighted regression (LWR) philosophy assumes that the data can be efficiently modeled over a short span with linear methods. The first step in LWR is to determine the N samples that are most similar with the unknown sample to be analyzed. Similarity can be defined by distance between samples in the spectral space [25] by projections into the principal component space [26] and by employing estimates of the property of interest [27]. Once the N nearest standards are determined, either PLS or PCR is employed to calculate the calibration model. 

T. Naes and T. Isaksson, Locally Weighted Regression of Diffuse Near Infrared Transmittance Spectroscopy, A/ / Z. Spectros., 46 34-43 (1992). 

Z. Wang, T. Isaksson, and B. R. Kowalski, New Approach for Distance Measurement in Locally Weighted Regression, AnaZ. Chem., 66 249-260 (1994). 

T. Ntes and T. Isaksson, Locally weighted regression in diffuse near infrared transmittance spectroscopy. 

Nonlinear Calibration Approaches Spectral data can respond nonlinearly to process perturbations due to deviations of the Lambert-Beer law, to the nonlinear characteristics of light detectors or to interactions among analytes. Sources of nonlinear behavior and techniques for the detection of important nonlinear effects in spectral responses have been discussed in the literature [25, 76]. In order to cope with the nonlinear features of spectral data sets, different approaches have been applied to build calibration models. These calibration approaches have almost always been based on NN models and locally weighted regression (LWR) models. 

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