What is Topological Data Analysis Ball Mapper?

Speaker(s):

Simon Rudkin, University of Manchester

Abstract:

The value in visualising data early within the analysis cycle is well understood. Topological Data Analysis (TDA) is an emerging strand of data science which considers the shape of data. This session will show one methodology from the TDA toolkit which speaks to the benefits of visualising data. Taking an intuitive perspective, we will introduce Ball Mapper (TDABM) to view the joint distribution of multivariate datasets. All that is required are ordinal variables for which plotting a scatter plot would be logical. TDA considers data as a point cloud, the scatter plot being a 2-dimensional representation. TDABM enables the mapping of multi-dimensional point clouds. By mapping outcomes across the joint distribution, we may highlight regions of particular interest. TDABM then allows the user to link back to the data and identify exactly the data points involved. Examples will be taken from across the social sciences. Accompanying R code is provided.