A0903
Title: Trajectory inference with varifold distances
Authors: Elodie Maignant - Zuse Institute Berlin (Germany) [presenting]
Christoph von Tycowicz - Zuse Institute Berlin (Germany)
Tim Conrad - Zuse Institue Berlin (Germany)
Abstract: The focus is on a tree inference problem motivated by the problem, known as trajectory inference, in single-cell genomics of reordering a population of cells sampled from a dynamic process according to their progression in the process. If the process is differentiation, this amounts to reconstructing the corresponding differentiation tree. One way of doing this in practice is to estimate the shortest-path distance between nodes based on cell similarities observed in sequencing data. Recent sequencing techniques make it possible to measure two types of data: Gene expression levels and RNA velocity, a vector that predicts changes in gene expression. The data then consist of a discrete vector field on a (subset of a) Euclidean space of dimension equal to the number of genes under consideration. By integrating this velocity field, the evolution of gene expression levels is traced in each single cell from some initial stage to its current stage, and using varifold distances between the curves thus obtained, a similarity measure is defined between nodes which is proven to approximate the shortest-path distance in a tree that is isomorphic to the differentiation tree.
