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SUMMARY:Witness complexes for time series analysis
DTSTART:20171004T130000
DTEND:20171004T140000
DTSTAMP:20260414T154754Z
UID:7ac454af12bd46a147700544c6f3f576778e73ba587a2c46c253b1b4
CATEGORIES:Conferences - Seminars
DESCRIPTION:Nikki Sanderson (Colorado)\nTime series analysis traditionally
  relies upon statistics and frequency analyses that make restrictive assum
 ptions about the data - i.e. nonlinearity\, non-stationarity. We believe t
 opological data analysis (TDA) can be of benefit in these situations. The 
 process of delay coordinate reconstruction ``unfolds” a scalar time-seri
 es into a point cloud in Rm. We can then compute the persistent homology 
 of the reconstructed data to obtain a topological signature. With the ulti
 mate goal of regime shift detection in mind\, we choose to use the witness
  complex - a sparse simplicial complex - for these computations. Topologic
 ally accurate delay reconstruction requires appropriate choices for the di
 mension m and time delay. We introduce novel witness relations that inco
 rporate time and improve the robustness of the resulting homology with res
 pect to choice of delay. The new relations seek to inhibit data points fro
 m witnessing landmarks traveling in dissimilar directions\, as these can c
 reate false connections. We explore how these relations can ameliorate add
 itional challenges that arise when dealing with non-uniform samples of str
 ange attractors.
LOCATION:Campus Biotech\, B1.05 Videoconference room
STATUS:CONFIRMED
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