Simon Rudkin’s research focuses on the information which is held within data and the ability to use that information for societal benefit. Much of Simon’s research focuses on the development of Topological Data Analysis (TDA) for understanding data in the social sciences and humanities. His work has considered applications in the UK, China, Europe, and the USA. Topics covered include the health impacts of supermarkets, regional productivity, the digital economy, and finance. He welcomes applications for PhD research on any application where the improved use of statistical methodologies may answer research questions as yet not fully understood.

TDA views data as points in multi-dimensional space and permits the construction of metrics thereupon. Much of Simon’s work uses the Ball Mapper algorithm to produce visualisations and metrics that represent the joint distribution of the characteristics of each data point. The space is covered by a set of balls which represent points with similar characteristics. Balls may then be coloured according to functions on the data points within the ball. For example, the function may be the average value of an outcome of interest. Consequently, it becomes possible to talk about joint-density across the space, identify subspaces where outcomes are observably different and conduct localised statistical analyses. All which is needed for an application to be of interest is a series of continuous variables with non-missing data for at least 100 data points.

Examples of projects which fit the remit of extracting information from data using TDA include:

1. Considering local authorities in the United Kingdom as defined by their socio-economic characteristics and then mapping further metrics such as deprivation indices, unemployment, cultural attitudes and digital economy access. Diving deeper into smaller spatial aggregations offers additional scope to target policy.
2. Viewing the growth trajectories of regions from one, or more, time series to ask whether the path followed by the region significantly affects the outcomes experienced for that region. For example, a consideration of the historic attraction of inward investment and the impact on the well-being of the region.
3. Considering the characteristics of constituencies and/or council wards and the voting behaviours therein. Interesting extensions may then include the incidence of government expenditure, trajectories of development and relationships with well-being.
4. Viewing each data point in a multi-dimensional space of historic values and appraising the extent to which future values are defined by the trajectory followed. Examples here include regional unemployment, educational outcomes, and technology adoption. Including covariates and multi-variate trajectories offer ready extensions for exploration.

For potential PhD students with deeper understanding of programming and data science, there are opportunities to extend the TDA methodology set which would also make for interesting PhD research.

Simon also welcomes applications in wider data science and statistical analyses where there is a clearly defined research question to explore.

If you would like to discuss more, please use the contacts on the contact tab.

Simon's present work is focused on the development of Topological Data Analysis (TDA) tools for applications in the social sciences and humanities. TDA is broken down into two strands, visualisation and dynamics, with both united by the view that data can be understood as points in multi-dimensional space. That is data is captured as a point cloud. TDA tools then measure the shapes created by the points and capture the way in which the point cloud changes over time. Information is then revealed on the joint distribution of the variables which define the co-ordinates of each point and on the distribution of outcomes associated with the points. Where the points are defined by the lags of one or more time series information about trajectories and periodicities may also be extracted from the shape of the point cloud. Suggested applications may be found on the Research Interests tab, whilst the publications list shows many examples of TDA in action.

Simon has also worked in multi-level modelling, quantile regression and on treatment effects. 

Uniting all of Simon's work is the belief that through the considered applications of statistical tools humans may learn more about the workings of the economy and society. Howsoever the data is analysed, explainability and interpretability must be central to the methodological approach.