How do inverted file (IVF) indexes work in vector databases, and what role do clustering centroids play in the search process?

Inverted file (IVF) indexes are a core component of vector databases designed to accelerate similarity searches. They work by partitioning a large dataset of vectors into smaller, manageable clusters, each associated with a representative “centroid” vector. During a search, IVF narrows the scope of comparisons by focusing only on clusters likely to contain relevant results, reducing computational overhead. Clustering centroids act as anchors for these partitions, enabling the system to quickly identify candidate clusters for a query.

The process starts with clustering algorithms like k-means to generate centroids. For example, if a database contains 1 million image embeddings, k-means might group them into 1,024 clusters, each with a centroid representing the average of its assigned vectors. During indexing, every vector is assigned to the cluster whose centroid is closest to it. This creates an inverted index structure: instead of mapping terms to documents (as in text search), it maps centroids to the vectors in their clusters. When a query vector is submitted, the system computes distances between the query and all centroids, selects the nearest n clusters (e.g., the top 10), and searches only within those. This avoids scanning all 1 million vectors, drastically speeding up the search.

Clustering centroids directly influence the trade-off between search speed and accuracy. Increasing the number of clusters (e.g., from 1,024 to 4,096) reduces the number of vectors per cluster, which speeds up individual cluster searches but requires checking more centroids. Conversely, probing more clusters during a query (e.g., checking 50 instead of 10) improves recall but increases latency. Developers often tune parameters like the number of clusters and the probe count to balance these factors. For instance, in a recommendation system, using IVF with 2,048 clusters and probing the top 20 might achieve sub-second latency while retaining 95% accuracy compared to an exhaustive search. This makes IVF a practical solution for scaling similarity search in applications like image retrieval or semantic text matching.