Speaker: Mikael Vejdemo-Johansson, College of Staten Island
Title: Topological Data Analysis
Topological Data Analysis (TDA) is a fast-growing area of research and applications, drawing from algebraic topology to create tools for data analysis, learning and statistics that are independent of embedding, robust against deformations and compact in representation.
Fundamentally, the idea is that any data set has an intrinsic shape, and that this shape carries much if not all the information of interest to users of the data. By partially encoding the geometry in constructing a topological structure on the data set itself, homology can be used to extract shape descriptors carrying topological information. The lowest-dimensional of these, 0-homology, comes out as a variation of hierarchical clustering, and higher dimensional descriptors capture more intricate details of the shape of data.
In this talk, we will be defining and describing persistent homology and its close relative persistent cohomology, and demonstrate how both can be used to extract information from datasets from visual cognition, imaging, motion capture, and other applications.