Inference of Ancestral Recombination Graphs through Topological Data Analysis
Fig 1
(A) Topological data analysis aims to infer the topological features (e.g. loops, voids, etc.) of an unknown space from a finite set of sampled points. (B) Persistent homology, a tool of TDA, builds simplicial complexes (generalizations of networks that include higher dimensional elements like triangles and tetraheadra), by taking balls of radius ϵ centred on the sampled points. Points are connected in the simplicial complex if the corresponding balls intersect. This construction is known as Vitoris-Rips complex. Persistent homology tracks how the topological features of Vietoris-Rips complexes change with ϵ. (C) Barcodes are suitable representations of persistent homology. Each interval in the barcode represents the range of ϵ across which a particular topological feature (for instance, a loop) is present in the inferred topology. In this figure, the barcode of the first persistent homology, that tracks the presence of loops, is shown. The two intervals in the barcode correspond to the two loops present in the original space.