Persistence Images: A Stable Vector Representation of Persistent Homology

Understand

Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery.

• One such tool is persistent homology, which provides a multiscale description of the homological features within a dataset.
• A useful representation of this homological information is a persistence diagram (PD).
• Efforts have been made to map PDs into spaces with additional structure valuable to machine learning tasks.