Beyond Unimodal Bases: Pullback Geometry for Multimodal Data
Data-driven Riemannian geometry provides nonlinear interpolation and geometric representations of high-dimensional data. For these operations to be statistically meaningful, paths between observations should preferentially traverse high-likelihood regions. Existing scalable pullback constructions typically use a unimodal Gaussian latent distribution, assuming that the data reside close to a single manifold. For multimodal data, mapping separated modes or local structures into one Gaussian region can require substantial transport deformation and compromise the resulting geometry. We introduce a pullback geometry for data supported on mixtures of manifolds. Using a latent Gaussian mixture, ...
| Authors | Honglei Brinkmann, Lucas Ng, Georgios Batzolis et al. |
|---|---|
| Primary category | cs.LG |
| Published | 30 September 2026 |
| Last updated at source | 30 September 2026 |
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