Lastly, we found that when working with sizable bridge datasets, the large number of atoms (single cells in the bridge dataset) created a substantial computational burden. Motivated by a similar problem addressed by Laplacian Eigenmaps42, we compute the graph laplacian for the multi-omic dataset, and calculate an eigendecomposition, thereby reducing the dimensionality from the number of atoms to the number of selected eigenvectors (Supplementary Methods). We then utilize these eigenvectors to transform the learned dictionary representations into the same lower-dimensional space, substantially increasing the efficiency of our bridge integration procedure.
