Fig. 1

Cross-Modality Optimal Transport (CMOT): CMOT is a computational approach to infer missing modalities for existing single-cell modalities. It has three main steps: A Alignment (optional), B Optimal Transport, and (C) k-Nearest Neighbors inference. CMOT inputs two multi-modalities \(X\) and \(Y\) (source), where the cells in \(X\) and \(Y\) need not be completely corresponding. The cell-to-cell correspondence information between \(X\) and \(Y\) can be specified through \(p\). CMOT aligns \(X\) and \(Y\) using non-linear manifold alignment (NMA) onto a common low-dimensional latent space if cells in \(X\), \(Y\) do not have complete correspondence. Then, CMOT uses optimal transport (OT) to map the cells in source \(Y\) to the cells in target \(\widehat{Y}\), where \(Y\) and \(\widehat{Y}\) share modalities. CMOT minimizes the cost of transportation by finding the Wasserstein distance between cells in \(Y\) and \(\widehat{Y}\) which is further regularized by prior knowledge or induced cell clusters and entropy of transport. Finally, CMOT infers the missing modality \(\widehat{X}\) for cells in \(\widehat{Y}\) using k-Nearest Neighbors (kNN). It calculates a weighted average of the k-nearest mapped cells in Y for every cell in \(\widehat{Y}\), using their values from \(X\), and infers \(\widehat{X}\)