Modern science and technology generate data at an unprecedented rate. A major challenge is that this data is often complex, high dimensional and may include temporal and/or spatial information. The 'shape' of the data can be important but it is difficult to extract and quantify it using standard machine learning or statistical techniques. For example, an image of blood vessels near a tumour looks very different to an image of healthy blood vessels; statistics alone cannot quantify this difference. New shape analysis methods are required.
Thanks to funding from the Engineering and Physical Sciences Research Council (EPSRC), a newly created centre combining scientists in Oxford, Swansea and Liverpool will study the shape of data through the development of new mathematics and algorithms, and build on existing data science techniques in order to obtain and interpret the shape of data. A theoretical field of mathematics that enables the study of shapes is geometry and topology. The ability to quantify the shape of complicated objects is only possible with advanced mathematics and algorithms. The field known as topological data analysis (TDA), enables one to use methods of topology and geometry to study the shape of data. In particular, a method within TDA known as persistent homology provides a summary of the shape of the data (e.g. features such as holes) at multiple scales. A key success of persistent homology is the ability to provide robust results, even if the data are noisy. There are theoretical and computational challenges in the application of these algorithms to large scale, real-world data.
The aim of this centre is to build on current persistent homology tools, extending them theoretically, computationally, and adapting them for practical applications. The Oxford team led by Heather Harrington and Ulrike Tillmann together with Helen Byrne, Peter Grindrod and Gesine Reinert is composed of experts in pure and applied mathematics, computer scientists, and statisticians whose combined expertise covers cutting edge pure mathematics, mathematical modelling, algorithm design and data analysis. This core team will in turn work closely with collaborators in a range of scientific and industrial domains.