Internal Seminar: 2nd Year PhD student

[Statistics & Probability Seminar]

2nd year PhD student talk: Yang Di

Effects of the sampling methods on Persistent Homology

Persistent homology is a method which captures the topological properties of point clouds. This method records the appearance and disappearance of the topological features as the parameter increases. The most commonly used summary of persistent homology are the barcode and the persistent diagram.  However, one of the most important issues with persistent homology is that a dataset with a large number of data points may exceed the capability of the computational program. Therefore, it is necessary to find effective sampling methods for selecting subsamples from the original dataset, which may contain a far large number of data points. In addition, it is important to explore the statistical properties of these sampling methods and the extent to which they capture the topological properties of the original data.