ALBATROSS: fAst fiLtration BAsed geomeTRy via stOchastic Sub-Sampling
What are the intrinsic patterns that shape distributions of biological data? Often, we use analysis techniques that assume that our data come from a flat Euclidean space (e.g., PCA, tSNE, and eigenvector decomposition). However biological data often looks like it has been sampled from a space with some curvature. In this talk, I will build some intuition for curved spaces, particularly spaces with negative curvature, i.e. Hyperbolic spaces, and discuss why these geometries might be better frameworks than Euclidean or flat space to analyze biological data. In addition, I will introduce a new statistical topological data analysis (TDA) protocol to detect geometric structure in biological data and determine whether your data comes from a curved or flat space. This statistical protocol reduces TDA’s memory requirements and makes it possible for scientists with modest computing resources to infer the underlying geometry of their data. Finally, I will demonstrate this protocol by mapping the topology of functional correlations for the entire human cortex, something that was previously infeasible.