Increasing the number of centroids in an Inverted File (IVF) index directly impacts search speed and recall by altering how the dataset is partitioned and searched. IVF works by dividing data into clusters using centroids, and during a query, only the nearest clusters are scanned. More centroids mean smaller clusters and a finer partitioning of the data, which introduces trade-offs between computational overhead during the initial centroid lookup and the efficiency of searching within clusters. The relationship between centroids, search speed, and recall depends on how many clusters are probed per query and the quality of the clustering.
Search Speed Implications With more centroids, the initial step of finding the closest clusters to a query becomes slower because the system must compare the query vector against a larger set of centroids. For example, with 1M vectors split into 100 centroids, each cluster contains ~10k vectors. If the index uses 1,000 centroids, each cluster holds ~1k vectors. Probing 10 clusters in the first case searches 100k vectors, while probing 10 clusters in the second case scans only 10k vectors—reducing in-cluster search time. However, the increased centroid count raises the cost of the initial nearest-centroid lookup, which scales with the number of centroids. If the system probes the same number of clusters regardless of centroid count, search speed may improve due to smaller cluster sizes. But if the system probes more clusters to maintain recall (e.g., 100 clusters for 1,000 centroids), the total search time could increase due to both the larger centroid lookup and the larger number of clusters scanned.
Recall Implications Recall depends on whether the true nearest neighbors reside in the clusters probed. More centroids can improve recall if the finer partitioning better isolates relevant vectors. For instance, in a dataset with varied subclusters, 1,000 centroids might group similar items more accurately than 100, increasing the chance that probing a few clusters captures the correct neighbors. However, if the number of probed clusters remains fixed (e.g., 10), higher centroid counts reduce the total data scanned, which risks missing neighbors spread across unprobed clusters. For example, probing 10 clusters out of 1,000 covers 1% of the data, whereas 10 clusters out of 100 covers 10%. To maintain recall with more centroids, the system must probe more clusters, offsetting potential speed gains. Additionally, poorly trained centroids (e.g., due to insufficient iterations in k-means) can degrade recall, as clusters may not align with the data’s natural groupings.
Balancing Trade-offs The optimal number of centroids depends on the dataset and use case. For high-dimensional data with clear clusters, more centroids may improve speed and recall by reducing in-cluster search time and better isolating neighbors. For example, image retrieval systems often use large centroid counts (e.g., 4,096) to handle fine-grained visual patterns. However, for datasets with uniform distributions or limited compute resources, fewer centroids reduce initial lookup overhead. Tuning requires testing: measure recall against search latency while adjusting both centroid count and the number of clusters probed. Libraries like FAISS recommend starting with centroids set to sqrt(N) (e.g., 1,000 for 1M vectors) and scaling based on empirical performance.