Skip to main navigationSkip to main content
The University of Southampton
Joining the dots: from data to insight

Witness Complexes for Time Series Analysis, Nikki Sanderson (University of Colorado) Seminar

JTD Seminar
14:00 - 16:00
30 October 2017
Building 58, Room 1023, Lecture Room G, University of Southampton, Highfield Campus, SO17 1BJ

For more information regarding this seminar, please email Professor Jacek Brodzki at .

Event details

Time series analysis relying upon statistics and frequency analyses makes restrictive assumptions about the underlying data - i.e. nonlinearity, non-stationarity. We believe topological data analysis (TDA) can be of benefit in these situations. Yet time series do not necessarily have interesting topology in their own right. The process of delay coordinate reconstruction ``unfolds” a scalar time-series into a point cloud in Rm. We can then compute the persistent homology of the reconstructed data to obtain a topological signature. With the ultimate goal of online regime shift detection in mind, we choose to use the witness complex - a sparse simplicial complex - for these computations. Topologically accurate delay reconstruction requires appropriate choices for the dimension m and time delay. We introduce novel witness relations that incorporate time and improve the robustness of the resulting homology with respect to choice of delay. These new relations seek to inhibit data points from witnessing landmarks traveling in dissimilar directions, as these can create false connections. We explore how these relations simultaneously address challenges that arise when dealing with non-uniform samples of strange attractors from chaotic dynamical systems.

Speaker information

Nikki Sanderson, University of Colorado, Boulder. Nikki's research interests are Computational Topology, Dynamical Systems, Shape Spaces & Computational Mechanics.

Privacy Settings