Topological Data Analysis Ball Mapper for the Social Sciences methods@manchester

A methods@manchester workshop

18 November | 10-3pm | Alliance Manchester Business School

This workshop introduces the Topological Data Analysis Ball Mapper algorithm as a model free tool for visualising data and is led by Dr Simon Rudkin. Dr Rudkin is a member of the University of Manchester's Cathie Marsh Institute for Social Research (CMI) and his work has pioneered application of Ball Mapper in the social sciences. The workshop will showcase the strengths of the algorithm and the research opportunities available for exploitation.

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.

This 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. Examples will be provided with UK Census data.

Full Details

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.

The workshop will be conducted using R and Python. Data and code files will be shared with participants via GitHub. R users will need the package BallMapper on their computer. Python users will need the PyBallMapper library. For those who would like to look at their own data, support will be given during the practical elements of the workshop.

Not sure if your data is suitable?

We have a one-hour virtual pre-session for participants who would like to know more about the suitability of their data for visualising with Ball Mapper. This session is on Monday 10 November at 4-5pm.

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 on suitability of data are also welcomed.

References

Anscombe, F. J. (1973). Graphs in statistical analysis. The American Statistician, 27(1), 17-21.

Otway, A., & Rudkin, S. (2024). The Shape of Left-Behindedness: The 2019 UK General Election and Britain's Changing Electoral Geography. Available at SSRN 4877434.

Dłotko, P. (2019). Ball mapper: A shape summary for topological data analysis. arXiv preprint arXiv:1901.07410.

Dłotko, P., Qiu, W., & Rudkin, S. T. (2024). Financial ratios and stock returns reappraised through a topological data analysis lens. The European Journal of Finance, 30(1), 53-77.

Qiu, W., Rudkin, S., & Dłotko, P. (2020). Refining understanding of corporate failure through a topological data analysis mapping of Altman’s Z-score model. Expert Systems with Applications, 156, 113475.

Rudkin, S., Barros, L., Dłotko, P., & Qiu, W. (2024). An economic topology of the Brexit vote. Regional Studies, 58(3), 601-618.

Rudkin, S., & Dlotko, P. (2024). A topology of inclusion: European regions and the digital divide. In 2024 Fourth International Conference on Digital Data Processing (DDP) (pp. 123-128). IEEE.

Rudkin, S., Rudkin, W., & Dłotko, P. (2025). Return trajectory and the forecastability of Bitcoin returns. Financial Review, 60(2), 509-539.

Rudkin, S., & Webber, D. J. (2023). Regional growth paths and regional resilience. Available at SSRN 4333276.

Tubadji, A., & Rudkin, S. (2025). Cultural gravity and redistribution of growth through migration: Cohesion lessons from spatial econometrics and topological data analysis. Papers in Regional Science, 104(1), 100064.