Theory and computation of vineyards and vineyard modules

Topological Data Analysis is an exciting new area of research in data science providing insights into the shape of data. Within Topological Data Analysis the mathematical object of vineyards capture information about how this shape of changes over time-varying data. Vineyards have been effective in diverse applications with dynamic data from analysis fMRI scans to music classification, but their power is hampered by the lack of algorithms to compute their algebraic and geometrical structures, and the lack of statistical tools that can utilise the information contained in these structures. This project addresses this important gap through theory development as well as mathematically informed algorithm design and implementation. The project will create accessible tools for data scientists to use for dynamic point clouds and for the analysis of shapes.