Process analytic technologies (PAT) are routinely used to rapidly assess quality properties in many
industrial sectors. The performance of PAT-based models is, however, highly related to their
ability to pre-process the spectra and select key wavebands. Amongst the modeling methodolo-
gies for PAT, partial least squares (PLS) (Wold, Sjöström and Eriksson, 2001) and interval partial
least squares (iPLS) (Nørgaard et al., 2000) models coupled with well-known chemometric pre-
processing approaches are the most widespread due to their ease of use and interpretability. As
an alternative to classical pre-processing approaches, wavelet transforms (Mallat, 1989) provide a
fast framework for feature extraction by convulsion of fixed filters with the original signal.
The proposed Multiscale interval Partial Least Squares (MS-iPLS) methodology aims to combine
the ability of wavelet transforms for feature extraction with those of iPLS for feature selection. To
achieve this, MS-iPLS makes use of wavelet transforms to decompose the spectrum into wavelet
coefficients at different time-frequency scales, and, afterward, the relevant wavelet coefficients
are selected using either Forward addition or Backward elimination algorithms for iPLS. As the
wavelet filters are linear, the MS-iPLS model can also be equivalently expressed in the original spec-
tral domain, and thus, the standard PLS approaches can be applied for the sake of interpretability
and feature analysis.
In this study, 10 MS-iPLS models variants were constructed using five types of wavelet transforms
and two iPLS selection algorithms and compared against 27 PLS benchmarks variants using differ-
ent chemometric pre-processing and interval selection algorithms. The models were compared in
two case studies, addressing a regression problem and a classification problem with real data.
The results show that MS-iPLS models can either match or overcome the performance of the PLS
benchmark models. For the regression problem, the PLS benchmark models were able to attain
the lowest root mean squared error (RMSE), but their performance range was also wider, from an
average RMSE of 0.11 (best model) to 2.46 (worst model), with most models being on the lower
end. In contrast, the MS-iPLS models were consistently on the upper end, with an average RMSE
ranging from 0.13 (best model) to 0.50 (worst model).
In the classification problem, MS-iPLS attained the best performance with an average accuracy of
92.7%, while the best PLS benchmark model had an average accuracy of 89.0%.
Similarly to the PLS benchmarks models, MS-iPLS still requires an exhaustive search for the op-
timal wavelet transform for each case study. However, with MS-iPLS the number of models to
explore was significantly reduced (by a factor of 3, i.e., 1/3) without compromising on performance
or interpretability.