Force directed graphs vs. diffusion maps vs. t-SNE vs UMAP

Question

Can you help me with a conceptual explanation of how force directed graph drawings work compared to other methods in the context of dimensionality reduction for visualization purposes?

In particular, I'm interested in comparisons with diffusion maps, and t-SNE (or similar non-linear methods like UMAP). While I've found a lot of explanations of PCA, t-SNE, and UMAP, I've not found much on force directed graphs and diffusion maps.

Answer 1

A recent preprint provides some intuition on this topic, comparing t-SNE, UMAP, Force-directed graphs (FDGs; the ForceAtlas2 FA2 implementation), and diffusion maps (Laplacian eigenmaps here). In particular they show that under certain parameterisations that change "the balance between the attractive and the repulsive forces" t-SNE embeddings may correspond to those of UMAP, FA2, or diffusion maps.