I’m interested in the capabilities of Topological Data Analysis, most specifically in the context of preforming functions which are done with deep learning algorithms. I’m especially interested in the possibility of categorizing unlabeled data. This obviously opens up many, many possible topics, but this topic was the last one open in the TDA area so I jumped on it. I would love to explore and hopefully build upon speech recognition through a topological approach. I plan to read the paper provided in the sign-up sheet as well as papers on TDA by Robert Ghrist which motivate and describe the idea of persistence and the application of different simplicial complexes to understanding structure in data.
This stuff seems super exciting, but is going to require a lot of thinking. Which is good, right?
Philipp
February 20, 2018 — 00:49
This topic is exciting! Efficient categorization and clustering of unlabeled data is a huge problem and persistence is a powerful tool to aid in the process, and, (arguably equally as important), it is a fun thing to ponder on. It is always interesting how mathematics are able to help us better understand things as we usually subjectively perceive as lying in deep in the space of humanities, such as music and written text. Good luck with your project!