PRE-SESSION Topological Data Analysis Ball Mapper for the Social Sciences

Led by Dr Simon Rudkin, whose work has pioneered application of Ball Mapper in the social sciences. Dr Rudkin is a member of the University of Manchester's Cathie Marsh Institute for Social Research (CMI).

Pre-cursor to full workshop

This one hour virtual pre-meeting is for participants who would like to know more about the suitability of their data for visualising with Ball Mapper, ahead of the in-person workshop on Tuesday 18 November.

The basic guide is that if you would be happy to draw a scatter plot with your variables, the construction of the point cloud makes sense. As a rule, the axis variables for the cloud should be ordinal and have sufficiently many different values. Email enquiries to Simon.Rudkin@manchester.ac.uk on suitability of data are also welcomed.

Introduction to the theory

The importance of data visualisation in statistical analysis is understood from Anscombe’s Quartet (Anscombe, 1973). In the example, four datasets with identical linear regression fits are plotted as scatter plots. The independent variable is on the horizontal axis and the dependent variable is on the vertical axis. By seeing the data, it is very clear that the linear regression is only appropriate for one of the four cases. Moreover, the datasets have identical means, standard deviations and correlation. The cautionary tale provided is often neglected in empirical work. The scatter plots that Anscombe (1973) uses are two-dimensional, but the lessons apply when the dataset has more variables.

The BallMapper algorithm is a tool of Topological Data Analysis (TDA) proposed in the original working paper of Dlotko (2019). TDA considers data as points in a multidimensional space, a point cloud. The TDA toolkit is developed to analyse the point cloud. The full workshop focuses on the use of TDA for data visualisation. Ball Mapper allows the user to understand the shape of their data in exactly the way the scatter plot allows the understanding of two-dimensional data. Because paper is inherently two-dimensional, it is necessary to apply a mapping to convert the multi-dimensional space into something that can be visualised in research. The Ball Mapper algorithm creates an abstract visualisation of multidimensional data. We will see how the visualisation is produced, and how the visualisations created by Ball Mapper are interpreted, in the full workshop. Examples will be provided with UK Census data.

The strength of the Ball Mapper algorithm for visualising data in the social sciences can be seen in Rudkin and Webber (2024), Rudkin et al. (2024), Otway and Rudkin (2024), Rudkin and Dlotko (2024), and Tubadji and Rudkin (2025). Examples from Finance with extensions of the visualisation algorithm include Qiu et al. (2020), Dlotko et al. (2024) and Rudkin et al. (2025). These examples give a flavour of the additional benefits the Ball Mapper algorithm can bring to your data.

Ready for the full workshop?

This is a pre-cursor to our full-day workshop on Topological Data Analysis Ball Mapper for the Social Sciences, running on Tuesday 18 November. Sign up for the full workshop here.