A General Kernel Framework for Non-CND Distance Measures Using |D|-Dimensional Sparse Landmark Embeddings
The paper claims its SLE kernel can make standard PSD kernels work with arbitrary distance measures, without requiring CND geometry.
It embeds each input as a sparse landmark vector built from compactly supported bump functions centered on the training points. The authors say this preserves positive semi-definiteness while keeping the resulting kernel matrices tractable and well-conditioned. They give guarantees for PSD behavior, sparsity, stability, and universal approximation. Tests using geodesic and Wasserstein distances are reported to match or beat domain-specific baselines on prediction and uncertainty.
ArXiv · AI/CL/LG's note
It embeds each input as a sparse landmark vector built from compactly supported bump functions centered on the training points. The authors say this preserves positive semi-definiteness while keeping the resulting kernel matrices tractable and well-conditioned. They give guarantees for PSD behavior, sparsity, stability, and universal approximation. Tests using geodesic and Wasserstein distances are reported to match or beat domain-specific baselines on prediction and uncertainty.
ArXiv · AI/CL/LG's note
score 4