Changing the distance metric in indexes like HNSW (Hierarchical Navigable Small World) or IVF (Inverted File Index) directly impacts how the index organizes and searches data, often requiring a full rebuild and altering performance characteristics. Here’s how:
Rebuilding the Index Most vector indexes, including HNSW and IVF, precompute relationships between data points during construction based on the chosen distance metric. For example, IVF partitions data into clusters using centroids optimized for a specific metric (e.g., Euclidean distance). Switching to a metric like cosine similarity would invalidate these precomputed clusters, as the geometric assumptions (e.g., spherical clusters for cosine) no longer align. Similarly, HNSW builds a graph where edges connect neighbors based on proximity under the original metric. Changing the metric would break these connections, making the graph ineffective for traversal. Rebuilding the index is typically mandatory unless the implementation explicitly supports metric-swapping (rare in practice).
Performance Implications The choice of metric affects both search speed and accuracy. For instance, metrics like Manhattan (L1) might produce different neighbor rankings compared to Euclidean (L2), leading to variations in recall rates. Computationally, some metrics are cheaper (e.g., squared L2 avoids a square root) or require preprocessing (e.g., normalizing vectors for cosine similarity). HNSW’s greedy graph traversal might also behave differently: a metric that violates the triangle inequality (e.g., Jaccard) could cause the search to explore more nodes, increasing latency. IVF’s performance depends on how well the clusters align with the query distribution under the new metric—poor alignment forces more exhaustive searches across clusters.
Examples and Practical Considerations For IVF, using a metric like angular distance (equivalent to cosine) instead of L2 would require normalizing vectors during clustering, altering centroid positions. If the index isn’t rebuilt, queries would incorrectly assume non-normalized data, reducing accuracy. In HNSW, a metric like inner product might prioritize direction over magnitude, causing the graph to prioritize different neighbors. Some libraries (e.g., FAISS) allow overriding the distance function at query time, but this risks silent failures if the index wasn’t built with compatible preprocessing (e.g., normalization). Always rebuild the index when changing metrics to ensure structural consistency with the new similarity measure.