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Combining network analysis and persistent homology for classifying behavior of time series

Program in Applied Mathematics Colloquium

Combining network analysis and persistent homology for classifying behavior of time series
Series: Program in Applied Mathematics Colloquium
Location: ONLINE
Presenter: Elizabeth Munch, Dept of Computational Mathematics, Science, and Engineering, Michigan State University

Abstract:  Persistent homology, the flagship method of topological data analysis, can be used to provide a quantitative summary of the shape of data.  One way to pass data to this method is to start with a finite, discrete metric space (whether or not it arises from a Euclidean embedding) and to study the resulting filtration of the Rips complex.  In this talk, we will discuss several available methods for turning time series data into a a discrete metric space, including the Takens embedding, $k$-nearest neighbor networks, and ordinal partition networks.  Combined with persistent homology and machine learning methods, we show how this can be used to classify behavior in time series in both synthetic and experimental data.

Zoom:     https://arizona.zoom.us/j/91826900125   

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