This thesis is devoted to new data-driven methods for the analysis of problems in epilepsy and Dengue epidemics. The notion of dimensionality reduction will be important throughout the thesis and in the two problems we study. 

Our first contribution is a joint work with Cláudio M. Queiroz (Brain Institute, UFRN), Nathan Kutz (University of Washington) and Roberto I. Oliveira (IMPA), and it deals with a seizure detection problem. We develop a SVD-based method to explore the degree of synchronization before, during and after  seizures in a Temporal Lobe Epilepsy experimental (animal) model. With our methodology we build a seizure detection algorithm based on synchronization thresholds that significantly improves the state of the art. From the neurobiological viewpoint, we have found considerably low levels of brain synchronization during seizures and higher synchronous activity after seizures, which have important consequences.

Our second contribution, joint with Pedro D. Maia (Weill Cornell Medicine) and Nathan Kutz (UW), deals with the analysis of climate time series and their relationship with Dengue epidemic outbreaks. Local climate conditions play a major role in the development of the mosquito population responsible for transmitting Dengue Fever.  We apply dimensionality reduction techniques and machine-learning algorithms to climate time series data and analyze their connection to the occurrence of Dengue outbreaks for seven major cities in Brazil. Specifically, we have identified two key variables and a period during the annual cycle that are highly predictive of epidemic outbreaks. Critical temperature and precipitation signatures may vary significantly from city to city, suggesting that the interplay between climate variables and Dengue outbreaks is more complex than generally appreciated.