May the force be with you
This work offers a novel enhancement for users of force-based dimensionality reduction techniques, though it is incremental as it builds on existing methods.
The paper tackles the problem of extracting additional information from force-based dimensionality reduction methods by showing that the associated vector field provides high-quality insights, and proposes a refinement strategy using Morse theory, demonstrating efficiency on synthetic and real-life datasets with t-SNE.
Modern methods in dimensionality reduction are dominated by nonlinear attraction-repulsion force-based methods (this includes t-SNE, UMAP, ForceAtlas2, LargeVis, and many more). The purpose of this paper is to demonstrate that all such methods, by design, come with an additional feature that is being automatically computed along the way, namely the vector field associated with these forces. We show how this vector field gives additional high-quality information and propose a general refinement strategy based on ideas from Morse theory. The efficiency of these ideas is illustrated specifically using t-SNE on synthetic and real-life data sets.