## 7 Conclusions  
We introduced an unsupervised machine-learning methodology based on a Gaussian Mixture Modeling (GMM) employed over a set of recurrent 30-day-long patterns (snippets) extracted from a database of CPAP use time series. We tested our methodology over a dataset provided by a French hospital that collects CPAP telemonitored data (hours of use per night) regarding over 2000 patients. As a result, we identified eight characteristic patient behaviors regarding CPAP use adherence as indicated by the GMM components. This procedure demonstrated success in classifying any 30-day-long period of CPAP use according to a frame of eight classes that progressively indicate more efficient adherence.  
Our approach is an alternative to the usually employed average-based aggregations, which can potentially lose important information, and that provide a number holding no referential magnitude to permit a proper interpretation. In addition, we demonstrated the use of our GMM-based classification combined with the classic method of sliding window; by considering 30-day-long periods, it becomes possible to simplify the entire time series of a given patient, providing less information but more promptly understandable patient behavior. Along with this investigation, we also collected evidence that, in the field of OSA and CPAP therapy, there is not a consensus on the number of classes to which the patients correspond, indicating that such unsupervised machine-learning analyses must pass through a new data fitting whenever the dataset or goals change significantly.  
We expect our contributions to support physicians in more precisely evaluating the adherence of patients to the CPAP therapy. This might take place as a computer-aided diagnosis system or as full-time monitoring that issues alarms when critical situations are detected. Such a monitoring system is highly needed as telemoitored equipment produces larger and larger data streams overcoming the capacity of physicians to timely inspect the conditions of the patients. As a last remark, we suggest that future work is to employ our methodology over other attributes produced during the treatment of OSA, mainly the Apnea-Hypopnea Index.  
Conceptualization, J.F.R.J., S.B., J.-L.P., G.S. and L.G.; methodology, J.F.R.J. and S.A.-Y.; software, J.F.R.J.; validation, G.S., S.B., J.-L.P. and L.G.; formal analysis, J.F.R.J.; investigation, J.F.R.J.; resources, S.A.-Y.; data curation, S.B., J.-L.P., L.G. and G.S.; writing--original draft preparation, J.F.R.J.; writing--review and editing, S.B., J.-L.P., L.G., G.S. and S.A.-Y.; visualization, J.F.R.J.; supervision, S.A.-Y.; project administration, J.F.R.J.; funding acquisition, S.A.-Y. All authors have read and agreed to the published version of the manuscript.  
This research was partially financed by the French agency Multidisciplinary Institute in Artificial Intelligence MIAI - Grenoble Alpes (Grant ANR-19-P3 IA0003) and the \"e-health and integrated care\" Chair of excellence from the Grenoble Alpes University Foundation and the French National Research Agency in the framework of the Investissements d'Avenir program (Grant ANR-15-IDEX-02); by the Canada First Research Excellence Fund (CFREF) through the Ocean Frontier Institute (OFI) at Dalhousie University, Halifax - NS, Canada; and by Brazilian agencies Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (2019/04461-9, 2018/17620-5, 2017/08376-0, and 2016/17078-0); Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (167967/2017-7, 305580/2017-5, 406550/2018-2, and 307946/2021-5); and Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES, Finance Code 001).  
The data used for the experiment is private and cannot be made available to the public due to privacy reasons. However, the neural network models produced during experiments are publicly available.  
The authors declare no conflict of interest.