THE EFFECT OF HETEROSCEDASTIC NOISE ON THE CHEMOMETRIC MODELING OF FREQUENCY-DOMAIN DATA

The structure of noise in a dataset and, in particular, whether it is homoscedastic or heteroscedastic, can significantly affect the propert ies of multivariate calibration models. This is particularly true when the data are subjected to a nonlinear transformation prior to the for mation of the model. The problems of mathematical modelling in the fre quency domain in the presence of heteroscedastic noise are demonstrate d using simple, illustrative, synthesised datasets and partial least s quares regression. The heteroscedasticity spreads signal-dependent inf ormation throughout the spectrum of the signal, removing the localisat ion seen with band-limited signals with homoscedastic noise. Heterosce dasticity significantly reduces the scope for efficient variable selec tion to allow modelling on a reduced variable set, with consequences f or the production of sparse models which generalise well according to the parsimony principle. However, significant modelling can take place purely on the noise components even when the frequency range of the s ignal has been completely excluded. Optimal denoising schemes will ben eficially take into account the noise structure of a dataset. (C) 1998 Elsevier Science B.V. All rights reserved.