Cyclic subspace regression with analysis of wavelength-selection criteria

Common methods of building linear calibration models are principal componen t regression (PCR), partial least squares (PLS), and least squares (LS). Re cently, the method of cyclic subspace regression (CSR) has been presented a nd shown to provide PCR, PLS, LS and other related intermediate regressions with one algorithm. When forming a linear model with spectral data for qua ntitative analysis, prediction results can be adversely affected by respons es that do not conform well to the Linear model proposed. Wavelength select ion can be used to eliminate wavelengths where such problem responses occur . It has recently been reported that CSR regression vectors can be formed b y summing weighted eigenvectors where weights are determined from the hat m atrix, singular values, and eigenvectors characterizing the sample space. I nvestigation of these weights shows that wavelength selection based on load ing vectors can be misleading. Specifically, by using CSR it is shown that a small weight for an eigenvector can annihilate a large peak in a loading vector. In this study, correlograms an used with CSR regression vectors and eigenvector weights as wavelength-selection criteria. It is demonstrated t hat even though a model generated by LS for a wavelength subset produces su bstantially reduced prediction errors relative to PCR and PLS, CSR weight p lots show that the LS model overfits and should not be used. Simulated situ ations containing spectral regions with excess noise or nonlinear responses are examined to study the effectiveness of wavelengh selection based on th e previously listed criteria. Near infrared spectra of gasoline samples wit h several known properties are also studied. (C) 1999 Elsevier Science B.V. All rights reserved.