What methods can be used to estimate the storage size of an index before building it (based on number of vectors, dimension, and chosen index type)?

To estimate the storage size of a vector index before building it, you can use calculations based on the number of vectors, their dimensions, and the index type. The key is to understand how the index structure stores data and whether it uses compression or additional metadata. Here’s a breakdown of common methods for different index types:

1. Flat Index (Exhaustive Search): For a flat index, which stores vectors without compression, the storage size is straightforward to calculate. Each vector is stored as a sequence of floating-point numbers (typically 4 bytes per value). Multiply the number of vectors by the dimension and by 4 bytes to get the total size. For example, 1 million 256-dimensional vectors would require 1,000,000 × 256 × 4 bytes = 1,024 MB. Flat indexes have minimal overhead but scale linearly with data size, making them impractical for very large datasets. Some implementations may add metadata (e.g., IDs), but this is often negligible compared to vector data.

2. Inverted File (IVF) or HNSW (Hierarchical Navigable Small World): These indexes introduce additional structures. For IVF, vectors are grouped into clusters, and the index stores cluster centroids and inverted lists mapping clusters to vectors. Storage includes the centroids (calculated as number of clusters × dimensions × 4 bytes) and the inverted lists (approximately number of vectors × 4 bytes for cluster IDs). HNSW, a graph-based index, stores layers of nodes and edges. Each node (vector) has links to neighbors, and the total size depends on the average number of edges per node (e.g., vectors × edges_per_node × 4 bytes). For example, 1 million vectors with 32 edges each would add 1,000,000 × 32 × 4 = 128 MB to the base vector storage. These structures increase storage but enable faster search.

3. Product Quantization (PQ) or Compressed Indexes: PQ reduces storage by splitting vectors into subvectors and quantizing each into a code from a small codebook. The total size is number of vectors × (number of subvectors × bytes_per_code). For example, 1 million vectors split into 8 subvectors with 1-byte codes (256 centroids per subvector) would require 1,000,000 × 8 × 1 = 8 MB, plus the codebook (negligible for large datasets). Hybrid indexes like IVF-PQ combine clustering with compression: IVF cluster metadata + PQ-compressed vectors. Always factor in trade-offs: PQ saves space but adds approximation error, while HNSW/IVF improve speed at the cost of higher memory. Tools like FAISS provide formulas for these estimates, and testing with sample data can refine predictions.