The kernel of graph indices for vector search
Existing graph-based indexing methods (e.g., HNSW, DiskANN) rely on the Euclidean space assumption and thus struggle to support general metric or non-metric similarities—such as inner-product similarity—limiting their applicability. Method: This paper introduces the Support Vector Graph (SVG) framework, the first to integrate kernel methods and support vector machines into graph index construction, enabling unified indexing over both metric and non-metric spaces. We further propose SVG-L0, an ℓ₀-sparse variant with formal navigability guarantees and self-tuning capability—eliminating the need for manual candidate set selection or heuristic rules. Contribution/Results: Theoretical analysis shows that HNSW, DiskANN, and related methods are special cases of SVG. Experiments demonstrate that SVG-L0 achieves significantly improved search efficiency while maintaining low out-degree, establishing the first learning-based graph indexing paradigm for vector retrieval that combines theoretical rigor with broad practical applicability.