Contemporary research in biology and medicine generates huge amounts of data. Molecular data in particular poses difficulties in analysis. Often high-dimensional, it corresponds to complex biological systems, usually without a quantitative model. Novel techniques to extract molecular information are continually being realised – the ability to sequence cells on an individual level is one such example.
Topological data analysis (TDA) is a relatively new field in applied mathematics that aims to analyse the ‘shape’ of data with methods from algebraic topology and related fields. Studying the shape of data is not a new idea – clustering and dimensionality reduction is standard procedure with omics data. TDA encapsulates many of these existing techniques and pushes them further by leveraging deep ideas from mathematics to describe the topology of data in a robust way.
My current work focuses on applying methods from TDA to realise biologically relevant features from omics data. I am especially interested in using topological data analysis to understand the immune repertoire.