Learning Cost Functions for Optimal Transport

scConfluence : single-cell diagonal integration with regularized Inverse Optimal Transport on weakly connected features

“…transport plan, between point clouds based on their relative positions (see Methods). rIOT aims at addressing the inverse problem by inferring the relative positions of points based on a given transport plan 32 . scConfluence makes an innovative use of both OT and rIOT by first solving an OT problem leveraging weakly connected features ( Y ( p, p ′) and Y ( p ′, p ) ) to find a transport plan P ( p, p ′) across modalities and then using rIOT on P ( p, p ′) to adjust the cell embeddings inferred by AE ( p ) and AE ( p ′) .…”

“…Regularized Inverse Optimal Transport (rIOT) 32 refers to the problem of learning a pairwise dissimilarity matrix from a given transport plan P ∈ ∏ ( n 1 , n 2 ), with a certain regularization on C. In our case, it can be formalized as the following convex optimization problem: where Q ε ( a , b ) is the balanced optimal transport plan achieving the optimum in and R is a user-defined regularization. In our case, we want this regularization to force points coupled by P to completely overlap.…”

“…Here, we propose scConfluence, a novel diagonal integration method combining uncoupled autoencoders, which reduce the dimensionality of the original data to a shared latent space and account for potential batch effects, together with regularized Inverse Optimal Transport (rIOT) 32 , which aligns cells across modalities in the shared latent space by leveraging weakly connected features. By employing rIOT to ensure modality alignment, scConfluence can independently process the complete set of original features through autoencoders while utilizing only the connected features for aligning cell embeddings.…”