Geodesics in fibered latent spaces: A geometric approach to learning correspondences between conditions
This work addresses the problem of integrating multiple biological datasets for researchers in computational biology, though it appears incremental as it builds on existing geometric and latent space methods.
The paper tackles the problem of learning correspondences between samples from different conditions by introducing a geometric framework and network architecture that models the latent space as a fiber bundle with a pull-back metric, resulting in diffeomorphism flows between fibers. It demonstrates this approach on MNIST and Olivetti datasets and benchmarks it for batch correction in biological data integration.
This work introduces a geometric framework and a novel network architecture for creating correspondences between samples of different conditions. Under this formalism, the latent space is a fiber bundle stratified into a base space encoding conditions, and a fiber space encoding the variations within conditions. Furthermore, this latent space is endowed with a natural pull-back metric. The correspondences between conditions are obtained by minimizing an energy functional, resulting in diffeomorphism flows between fibers. We illustrate this approach using MNIST and Olivetti and benchmark its performances on the task of batch correction, which is the problem of integrating multiple biological datasets together.