Hugo Åkesson: Topological data analysis - the main idea

Abstract.

Topological data analysis is a relatively young, growing field. In data analysis, a common goal is to find clusters in your data. Note that a cluster can essentially be thought of as a connected component, after "clumping together" very nearby points. Using tools from algebraic topology, a connected component is actually a 0-dimensional hole, in a sense. So why be satisfied by looking at just the 0-dimensional holes in your space? Enter, topological data analysis.