An Approach to Bridge Topology and Machine Learning

Topological data analysis looks at data from a rather unique angle. Good news: it may provide additional information to traditional machine learning, hence benefiting downstream applications. Bad news: Let K be the social network over topologists and machine learners, then betti0(K)=2. Why this means they didn’t talk to each other will become apparent as we go over some basics of topological data analysis, specifically persistent homology. The rest of the talk will focus on our effort to bring persistent homology into mainstream machine learning. We will discuss our proposed solution to two important issues. First, persistent homology lands us in the space of persistence diagrams, which is not a vector space and thus unwieldy for machine learning. Second, persistent homology requires O(n^3) or worse computation time. At the end of day, our goal is to give data scientists a topological tool that they can happily use on their data without having to sit in this very talk.