  The JWST will deliver large data sets of high-quality spectral data over the
0.6-28 $\mu$m range. It will combine sensitivity, spectral and spatial
resolution. Specific tools are required to provide efficient scientific
analysis of such large data sets. Our aim is to illustrate the potential of
unsupervised learning methods to get insights into chemical variations in the
populations that carry the aromatic infrared bands (AIBs), more specifically
PAH species and carbonaceous very small grains (VSGs). We present a method
based on linear fitting and blind signal separation (BSS) for extracting
representative spectra for a spectral data set. The method is fast and robust,
which ensures its applicability to JWST spectral cubes. We tested this method
on a sample of ISO-SWS data, which resemble most closely the JWST spectra in
terms of spectral resolution and coverage. Four representative spectra were
extracted. Their main characteristics appear consistent with previous studies
with populations dominated by cationic PAHs, neutral PAHs, evaporating VSGs,
and large ionized PAHs, known as the PAH$^x$ population. In addition, the 3
$\mu$m range, which is considered here for the first time in a BSS method,
reveals the presence of aliphatics connected to neutral PAHs. Each
representative spectrum is found to carry second-order spectral signatures
(e.g. small bands), which are connected with the underlying chemical diversity
of populations. However, the precise attribution of theses signatures remains
limited by the combined small size and heterogeneity of the sample of
astronomical spectra available in this study. The upcoming JWST data will allow
us to overcome this limitation. The large data sets of hyperspectral images
provided by JWST analysed with the proposed method, which is fast and robust,
will open promising perspectives for our understanding of the chemical
evolution of the AIB carriers.
