A Finslerian Approach for Embedding Directed Data
Many datasets carry an intrinsic directionality: citations point backward in time, cells differentiate along lineages, and traffic follows preferred routes. Spectral embedding methods, including most of their extensions to directed graphs, discard this information: they symmetrize the data and map it into a Euclidean space where asymmetry cannot be represented. We instead model directed data as sampled from a Finsler manifold, whose distance depends on the direction of travel, and study the kernel operator built from this asymmetric distance. Through a moment expansion of this operator, we show that its symmetric and antisymmetric parts separate geometry from direction. As the bandwidth o...
| Authors | Gwendal Debaussart-Joniec, Théau Blanchard, Argyris Kalogeratos |
|---|---|
| Primary category | stat.ML |
| Published | 29 September 2026 |
| Last updated at source | 29 September 2026 |
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