In this study, a novel unsupervised classification framework for time series of medical nature is presented. This framework is based on the intersection of machine learning, Hilbert Spaces algebra, and signal theory. The methodology is illustrated through the resolution of three biomedical engineering problems: neuronal activity tracking, protein functional classification, and non-invasive diagnosis of atrial flutter (AFL). The results indicate that the proposed algorithms exhibit high proficiency in solving these tasks and demonstrate robustness in identifying damaged neuronal units while tracking healthy ones. Moreover, the application of the framework in protein functional classification provides a new perspective for the development of pharmaceutical products and personalised medicine. Additionally, the controlled environment of the framework in AFL simulation problem underscores the algorithm's ability to encode information efficiently. These results offer valuable insights into the potential of this framework and lay the groundwork for future studies.Clinical relevance- The framework proposed in this study has the potential to yield novel insights into the effects of newly implanted electrodes in the brain. Furthermore, the categorization of proteins by function could facilitate the development of personalised and efficient medicines, ultimately reducing both time and cost. The simulation of atrial flutter also demonstrates the framework's ability to encode information for arrhythmia diagnosis and treatment, which has the potential to lead to improved patient outcomes.