B0910
Title: Persistence surfaces: A new frequency specific topological summary for time series dependence structure
Authors: Anass El Yaagoubi Bourakna - King Abdullah University of Science and Technology (Saudi Arabia) [presenting]
Hernando Ombao - King Abdullah University of Science and Technology (KAUST) (Saudi Arabia)
Moo K Chung - University of Wisconsin-Madison (United States)
Abstract: Topological data analysis (TDA) has become a powerful approach over the last years, mainly because of its ability to capture the shape present in the geometry of the data at hand. However, TDA methods that rely on Rips or Morse filtrations produce highly variable results due to sensitivity to noise, regardless of the stability theorems that have been derived, which are too restrictive to be of practical importance when it comes to time series analysis. In many applications such as brain signals, the raw form of the data does not always display any geometrical form or shape. Nevertheless, by transforming the raw data into connectivity matrices, some geometrical information might be present in the underlying connectivity network, even if no apparent geometrical structure is present in the raw form of the data. We propose a new frequency-specific topological summary for analyzing time-series data. This new topological summary that we call persistence surface (PS) can be viewed as an extension of the popular persistence landscape (PL). All the statistical results that have been derived for the PL will hold for the PS due to its definition. We demonstrate that our approach is able to detect topological features in simulated data and provides new insights on existing datasets of brain signals using functional data analysis.
