## 2 Background and Related Work
### Data-Driven Analysis and Modeling of Articulatory Data  
With the increase of the data available from different technologies supporting speech production studies, as is the case for RT-MRI [32; 33], it is paramount to pursue methods that enable its systematic quantitative assessment through unsupervised approaches. These novel approaches can take advantage of the data not only to provide a wider view over the existing diversity (e.g., among speakers), but also to apply unsupervised methods that profit from the amount of data to model the phenomena. To this end, the literature already proposes several data-driven methods for processing and analysis of different data supporting speech studies (e.g., [34; 35; 36]).  
Considering articulatory data extracted from RT-MRI, the authors have explored data-driven approaches to determine critical articulators from vocal tract data extracted from RT-MRI [4; 37], expanding an approach proposed for EMA [38]. One notable aspect of the methods conveyed in [PERSON] et al. [4] is that, even though the method considers statistical modeling for the different sounds, the consideration of tract variables aligned with the articulatory phonology framework [39], as grounds for the method, yields results that maintain a connection to the tract anatomy (e.g., constrictions on the tongue tip and body) and are, hence, more interpretable towards a critical discussion of the outcomes and animproved knowledge of speech production. Nevertheless, while this provides valuable information for a wide range of sounds in an unsupervised manner, it is still not able to provide it over time, since it relies on a single vocal tract configuration to represent each sound, often taken at the middle of its production. While this may be adequate to grasp which articulators play a key role in producing each sound (e.g., the tongue body and velum for vowels), how these unfold over the duration of a vowel is key for further understanding the subtlety of the underlying dynamics and coordination.  
In a recent work, [PERSON] et al. [5] propose a novel data-driven approach exploring how vocal tract data extracted from RT-MRI can be tackled by modeling the dynamics of speech production based on multiple repetitions of each sound. In their method, they adopt generalized additive mixed models (GAMMs) applied to vocal tract aperture functions, along with validations of the resulting models using functional linear mixed models (FLMMs) at 20% and 80% of the vowel interval. Overall, these methods model vocal tract aperture over time for given sounds, and they can be useful to gain insight into how sounds are produced, considering data from multiple speakers at once. One aspect deserving particular attention is the interpretability of the results obtained with these data-driven methods, to ensure that by using GAMMs and FLMMs we do not lose sight of the vocal tract anatomy. It is important to interpret the results in light of articulatory changes and not in some unknown variable space resulting from the data-driven process. To achieve this goal, the authors establish a correspondence between data points on the tract aperture functions and anatomical regions and apply this principle to all speakers and repetitions. This allows both an alignment of the tract anatomy among speakers and a subsequent interpretation of how the resulting GAMMs relate to the vocal tract configuration. Given the shown potential of GAMMs as a method to model articulatory data extracted from RT-MRI data, it is important to assess if it can be applied to the study of nasal vowels, particularly to jointly address data from multiple speakers, as described in the following sections.