A0904
Title: Topological data analysis of time-series data
Authors: Jae-Hun Jung - POSTECH (Korea, South) [presenting]
Abstract: Time-series data analysis is found in various applications that deal with sequential data over a given interval of, e.g. time. Time-series data analysis is discussed based on topological data analysis (TDA). The commonly used TDA method for time-series data analysis utilizes embedding techniques such as sliding window embedding. With sliding window embedding, the given data points are translated into the point cloud in the embedding space, and the method of persistent homology is applied to the obtained point cloud. Some examples of time-series data analysis with TDA are first shown. Then, the recent work of exact and fast multi-parameter persistent homology (EMPH) theory will be introduced. The EMPH method is based on the Fourier transform of the data and the exact persistent barcodes. The EMPH is highly advantageous for time-series data analysis because its computational complexity is as low as O(Nlog N) and provides various topological inferences almost in no time.
