A0204
Title: Topological low dimensional learning of high dimensional time series
Authors: Tullia Padellini - Sapienza University of Rome (Italy) [presenting]
Pierpaolo Brutti - University of Rome - Sapienza (Italy)
Abstract: As the complexity and the dimension of available data increases, so does the need to characterize them through lower dimensional structures. Topological features are gaining momentum in this quest for insights on the data, as they provide an interpretable description of the connectivity structure of data. We introduce a new topological statistic, the Persistence Flamelet, tailored for high dimensional time series, where we need to summarize data at each time point, as well as their evolution in time. The proposal allows us for visualization of the evolution of hidden structures in the data, and also provides a quantitative measure of their relevance in explaining the data (persistence). After assessing its theoretical properties, such as convergence and stability, we show the performance of this new tool in visualisation as well as in inferential challenges. Focusing on EEG data, whose dependency structure is especially complicated due to the unclear spatial propagation of the signal, we show how topological information can be exploited to explain and recover groups in the observed subjects.
