Fig. 1
From: MultiMAP: dimensionality reduction and integration of multimodal data
Schematic of MultiMAP. a MultiMAP takes any number of datasets, including those of differing dimensions, recovers geodesic distances on a single latent manifold on which all data lie, constructs a neighborhood graph (MultiGraph) on the manifold, and then projects the data into a single low-dimensional embedding. Integrated analysis and visualization can be performed on the embedding or graph. Variables are discussed in Methods. Xi is dataset i, xji is a point in Xi, M is the shared manifold, B(xi2) is a ball on M centered at xi2, Xij is the ambient space of M in the coordinate space with data containing points from datasets i and j, gij is the metric of M in the space Xij, μ is the membership function of the fuzzy simplicial set on the manifold, ν is the membership function of the fuzzy simplicial set in the low-dimensional space. b In the field of cell atlas technologies, encompassing single-cell genomics and spatial technologies, MultiMAP can be applied to integrate across different omics modalities, species, individuals, batches, and normal/perturbed states