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Understading HNSW — Hierarchical Navigable Small World
- HNSW (Hierarchical Navigable Small World) is crucial for fast approximate nearest neighbor searches in modern vector databases and recommendation systems, offering high recall rates.
- Traditional methods for nearest neighbor searches are limited by linear time complexity for large datasets.
- Tree-based approaches like k-d trees suffer from the curse of dimensionality, limiting their effectiveness in high-dimensional spaces.
- Locality-sensitive hashing (LSH) methods offer sub-linear search times but may require maintaining multiple hash tables with high memory overhead.
- Product quantization techniques compress high-dimensional vectors for memory efficiency, though they introduce computational overhead and accuracy losses.
- Graph-based approaches, like HNSW, combine local connectivity with long-range connections for efficient navigation in high-dimensional spaces.
- HNSW addresses scalability challenges by creating hub nodes with long-range connections, enabling logarithmic search complexity.
- The algorithm draws from small world network theory and skip list hierarchical structures to achieve efficient search operations.
- HNSW's construction involves multiple layers with exponential layer assignment, balancing search efficiency and construction complexity.
- Key parameters like M, mL, Mmax0, and efConstruction impact HNSW's performance and scalability across different datasets.
- Challenges include local minima traps, distance metric assumptions, and limitations in high-dimensional spaces, influencing HNSW's applicability.
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