May the force be with you
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Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 9 of its 26 references that are in the map. First posted on arXiv 13 Aug 2022.
Builds on
9 of 26 references.
References · 9
- 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,349
- 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,898
- 2014A Tutorial on Principal Component Analysiscited by 141
- 2017Efficient Algorithms for t-distributed Stochastic Neighborhood Embeddingcited by 75
- 2021Theoretical Foundations of t-SNE for Visualizing High-Dimensional Clustered Datacited by 55
- 2017Clustering with t-SNE, provablycited by 51
- 2018An Analysis of the t-SNE Algorithm for Data Visualizationcited by 49
- 2019Heavy-tailed kernels reveal a finer cluster structure in t-SNE visualisationscited by 22
- 2021t-SNE, Forceful Colorings and Mean Field Limitscited by 10
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