  In the first two papers of this series (Rhea et al. 2020; Rhea et al. 2021),
we demonstrated the dynamism of machine learning applied to optical spectral
analysis by using neural networks to extract kinematic parameters and
emission-line ratios directly from the spectra observed by the SITELLE
instrument located at the Canada-France-Hawai'i Telescope. In this third
installment, we develop a framework using a convolutional neural network
trained on synthetic spectra to determine the number of line-of-sight
components present in the SN3 filter (656--683nm) spectral range of SITELLE. We
compare this methodology to standard practice using Bayesian Inference. Our
results demonstrate that a neural network approach returns more accurate
results and uses less computational resources over a range of spectral
resolutions. Furthermore, we apply the network to SITELLE observations of the
merging galaxy system NGC2207/IC2163. We find that the closest interacting
sector and the central regions of the galaxies are best characterized by two
line-of-sight components while the outskirts and spiral arms are
well-constrained by a single component. Determining the number of resolvable
components is crucial in disentangling different galactic components in merging
systems and properly extracting their respective kinematics.
