Visualizing high-dimensional data as continuous volumes instead of scattered points

Dimensionality reduction typically outputs discrete point clouds, which suffer from occlusion and fail to capture the continuous structure of underlying manifolds. Topo-GS repurposes 3D Gaussian Splatting as a volumetric reconstruction tool, optimizing Gaussians via geometric constraints derived from orthogonal Procrustes alignment and tangent-space covariance. The method adapts its loss function based on data topology—treating 1D curves and 2D surfaces differently—to preserve local structure. Experiments show Topo-GS converts scattered plots into smooth volumetric representations where projection artifacts appear as visible geometric distortion rather than artificial gaps, while maintaining topological fidelity comparable to discrete baselines.