PhD defense of Clément Pealat

M. Clément PEALAT defends his PhD Tuesday March 22th 2022, entitled: "Modélisation du flux de patients aux urgences liés aux maladies respiratoires par analyse géométrique de séries temporelles".

Summary:

Every year, during the winter period, hospitals are deeply impacted by the arrival of winter viruses. These winter viruses, influenza and RSV, are difficult to anticipate. Indeed, these epidemic phenomena are not perfectly periodic and have an impact mainly on the length of stay of patients rather than on the number of arrivals. It is therefore not possible to anticipate these epidemics by directly analyzing the number of patients arriving in the emergency department per day. A posteriori, in order to have an image of the epidemic, PCR tests are carried out on the hospital’s patients. In addition, a patient arriving at the emergency department is immediately classified according to his symptoms. We then propose to gather the positive PCR tests and the number of arrivals per symptom via time series clustering. This highlights the symptoms related to viruses. Thus, to anticipate an arrival of an epidemic in a near future, we can use the number of arrivals for the virus marker symptoms rather than the total number of arrivals at the emergency department. To achieve this clustering, we propose an innovative method based on a geometric representation of time series. In particular, we highlight the efficiency of using the Riemmannian geometry applied to the Grassmann manifold (via a representation on the Stiefel manifold) to analyze time series.