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A.I. Kavaler
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Hyperbolic Interpolation-Based t-SNE
Introducing a Novel Algorithm for Accelerating Hyperbolic t-SNE
Hyperbolic t-SNE extends t-SNE to hyperbolic space, making it well suited for visualizing hierarchical datasets. However, its computational cost remains a barrier to scaling. This thesis introduces HIt-SNE, a method that accelerates hyperbolic t-SNE. It does so by adapting the interpolation-based strategy behind FIt-SNE to hyperbolic geometry. The approach reformulates the underlying gradient computation and partitions the embedding space using a hyperbolic tiling. Distant interactions are then approximated through local interpolation, while an exact correction term preserves accuracy for nearby points. We analyze the runtime and accuracy of the resulting algorithm and evaluate it on real-world datasets. We find that our algorithm substantially reduces computational cost relative to the exact method, while keeping approximation error within a controllable range. These results suggest that interpolation-based acceleration is a promising direction for making hyperbolic dimensionality reduction more scalable.
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Hyperbolic t-SNE extends t-SNE to hyperbolic space, making it well suited for visualizing hierarchical datasets. However, its computational cost remains a barrier to scaling. This thesis introduces HIt-SNE, a method that accelerates hyperbolic t-SNE. It does so by adapting the interpolation-based strategy behind FIt-SNE to hyperbolic geometry. The approach reformulates the underlying gradient computation and partitions the embedding space using a hyperbolic tiling. Distant interactions are then approximated through local interpolation, while an exact correction term preserves accuracy for nearby points. We analyze the runtime and accuracy of the resulting algorithm and evaluate it on real-world datasets. We find that our algorithm substantially reduces computational cost relative to the exact method, while keeping approximation error within a controllable range. These results suggest that interpolation-based acceleration is a promising direction for making hyperbolic dimensionality reduction more scalable.