## 6 Discussion  
In comparison to former works, as reviewed in the related works, one strong point of our methodology is that we do not assume the patient to be a static entity, which might distort the interpretation of the actual state of a patient. In the work of [22], for example, the patient characterization will not correspond to its latest months of CPAP use but, rather, to the most prominent patterns of use as observed in her/his, say, two years of use, i.e., a given patient might be referred to as being fully adapted to using the equipment when she/he just started to struggle in carrying out the therapy due to external factors that took place in recent times, causing prejudice to the proper evaluation of adherence. We also exceed in introducing a more granular 8-classes characterization statistically and visually  
Figure 9: GMM characterization of two patients from the CPAP use dataset. The first patient in plot (**a**) and its corresponding sliding-window characterization in plot (**c**). The second patient in plot (**b**) characterized in plot (**d**).  
verified; since each of our components encompassed a set of 30-day series with distinct and similar numerical properties, as demonstrated in Section 5, we advocate that the proposed cluster-based characterization is more comprehensive than that of previous works. This allegation is supported by ample statistics and by our set of extracted snippets, which has a cardinality larger than that of any dataset used in the similar analysis that we reviewed; that is, we count on a strong support to our findings.  
Another advance of our methodology is that we do not resort to aggregation to simplify the analysis of a given patient's series. This way, we avoid the loss of information due to aggregation [15; 16] and the misconception of providing a number holding no referential to the most usual 30-day-long patterns found in a real database. For example, if one verifies that the average of a patient's series is 5 h/night, it is possible that the physician will consider the patient to have high adherence to the treatment, which makes sense from an initial perspective. However, if we take the classes' average and standard deviation presented in Table 2, it is possible that this patient is behaving in any one of classes 1 through 5, i.e., by considering a real clinical database, we found out that the average of a time series can lead to a total misconception of what is really happening.  
Furthermore, from our investigation and by inspecting the state of the art, we verified that there is no agreement with respect to the number of characterizations (cluster/classes) of patients in the field of OSA and CPAP therapy. As reported in the related works, existing works report from four up to seven classes, diverging even for the same research team over different datasets [22; 24]. This variability, while not desired, does not invalidate the investigations carried out; nevertheless, it is evidence that there is not a definitive answer to the problem of cluster-based patient characterization. Possibly, this variability comes from peculiarities of the cohort being studied to the specific variable considered under each methodology, algorithmic traits, and even different interpretations of the results. As a result, one conclusion of ours is that the methodologies are more relevant than the presented results; and that each context in which they are to be employed must perform specific cluster analysis in accordance with the data nature and the needs of the analytic application. Regardless, the state of the art reinforces the importance and impact of research in ACPA monitoring and adherence, which ranges from preventing or working towards the prevention of cardiovascular diseases [47] to the study of improving neurocognitive response through OSA treatment [48]. Thus, our work sets new pathways for research on ACPA and OSA, directing further investigation with techniques beyond Gaussian mixture modeling in future works.