A tumour and a healthy blood vessel network look different, but standard statistics cannot capture that difference—only the shape of the data can. This project develops new mathematics and algorithms to extract and quantify the “shape” of complex, high-dimensional data, using a field called topological data analysis (TDA). The core tool, persistent homology, detects features like loops and holes in data at multiple scales, even when the data is noisy. Current TDA methods struggle with large, real-world datasets, so the team—mathematicians, computer scientists, and statisticians—will extend the theory, speed up the computations, and adapt them for practical use. If successful, the work could improve medical imaging (detecting tumours from blood vessel shape), accelerate materials design by analysing molecular structures, and enable real-time anomaly detection in security data. The research is fundamentally mathematical and computational, but its applications touch systems that quietly underpin healthcare, manufacturing, and public safety.
View original technical description
Modern science and technology generates data at an unprecedented rate. A major challenge is that this data is often complex, high dimensional, 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 tumor looks very different than an image of healthy blood vessels; statistics alone cannot quantify this shape because it is the shape that matters. The focus of this proposal is to 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 topology. The ability to compute the shape (its topology) of complicated shapes is only possible with advanced mathematics and algorithms. The field known as topological data analysis (TDA), enables one to use topology to study the shape of data, such as loops in a blood vessel network. In particular, an algorithm within TDA known as persistent homology, provides a topological 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 project is to build on current persistent homology tools, extending it theoretically, computationally, and adapting it for practical applications. Our core team is composed of experts in pure and applied mathematicians, computer scientists, and statisticians whose combined expertise covers cutting edge pure mathematics, mathematical modeling, algorithm design and data analysis. This core team will work closely with our collaborators in a range of scientific and industrial domains. Some of the application challenges we have set out include: Can we detect a tumor by looking at the shape of images of blood vessels? Can we design new materials by looking at the shape of molecules using topology? How can we design such molecules? Can we detect anomalies in security data? And importantly, how can we accelerate algorithms to obtain topological characteristics of data in real time?
Plain English summaries and category classifications on this site are generated by AI and may not perfectly reflect the original research.
Is something wrong? Let us know