- Title: Persistent Homology of Complex Networks for Dynamic State Detection
- Authors: Audun Myers, Elizabeth Munch, and Firas Khasanweh
- Date Published: 8/21/19
- Publisher Info: American Physical Society, Physical Review E
- Link: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.100.022314
Signals obtained from sensors are ubiquitous in science and engineering. Typically, these signals represent a sequence of time-indexed measurements such as position or temperature. This resulting sequence is termed a time series, and often includes rich but hidden information about the process that generated the data. An important but difficult challenge for time series analysis is determining the characteristics of the underlying dynamical system, such as whether the system is operating in a periodic or chaotic regime. In this work, we utilize two methods that encode the time series as a network. One uses standard delay reconstruction techniques combined with local neighbor information to generate the k-nearest neighbor network; the other tracks short patterns in the time series and uses the transition information contained there for construction of the ordinal partition network. These networks are then analyzed using a shape measuring tool from the emerging field of topological data analysis called persistent homology. We compute several point summaries of the resulting persistence diagrams and show that they are capable of distinguishing between different dynamical regimes.