Seminar by Dr. Brittany Terese Fasy
※講演者の都合により日時が変更となりました．
This seminar has been rescheduled as follows.
- Date&Time
- Tue 5th June 2014, 13:30-15:00
- Location
- Seminar Room 5 (3F, D313), Institute of Statistical Mathematics
- Speaker
- Brittany Terese Fasy (Dept. of Computer Science, Tulane University)
- Title
- Stochastic Convergence of Persistence Landscapes and Silhouettes
- Abstract
- Persistent homology is a widely used tool in Topological Data Analysis that encodes multi-scale topological information as a multi-set of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly to a random sample of diagrams. Instead, we can summarize the persistent homology with the persistence landscape, which converts a diagram into a well-behaved real-valued function. We investigate the statistical properties of landscapes, such as weak convergence of the average landscapes and convergence of the bootstrap. In addition, we introduce an alternate functional summary of persistent homology, which we call the silhouette, and derive an analogous statistical theory.
