Embeddings & Similarity Search • Dimensionality Reduction (PCA, UMAP)Easy⏱️ ~2 min
What is Dimensionality Reduction and Why Do We Need It?
Dimensionality reduction maps high dimensional data to a lower dimensional space while preserving the structure that matters for downstream tasks. In production ML systems, vectors are everywhere: 512 to 1536 dimensional text or image embeddings, hundreds of engineered features for ranking, tens of thousands of sparse features after hashing. These high dimensional vectors are expensive to store, index, and compare.
Consider a real world vector search service for a product catalog serving 40,000 queries per second at p95 latency under 50 milliseconds. The catalog has 50 million items, each with a 768 dimensional float32 embedding. Raw storage for these vectors is 768 times 4 bytes, about 3 kilobytes per item, totaling roughly 150 gigabytes. Building an Approximate Nearest Neighbor (ANN) index on 768 dimensions is slower and memory intensive.
Applying dimensionality reduction offline to project from 768 to 128 dimensions slashes storage to about 25 gigabytes for 50 million items. Index construction time drops by 2 to 4 times because distance computations become cheaper. Measured p95 query latency can drop from 20 milliseconds to 7 to 10 milliseconds at the same recall@10, with recall loss kept under 1 percent when the target dimension k is chosen by cross validating downstream retrieval metrics rather than only explained variance.
💡 Key Takeaways
•High dimensional vectors are expensive to store (768D float32 = 3KB per item), index, and compare at scale with millions or billions of items
•Dimensionality reduction cuts memory by 6x or more (150GB to 25GB for 50M items) and speeds up index construction by 2 to 4 times
•Query latency can drop significantly (20ms to 7 to 10ms p95) while maintaining recall loss under 1 percent with proper k selection
•The technique improves signal to noise ratio by discarding low variance directions dominated by noise
•Common use cases include vector search for product catalogs, recommendation systems, and feature compression for ranking models
•Choose target dimension k by cross validating end to end metrics like recall@10 or NDCG, not just explained variance thresholds
📌 Examples
Product catalog vector search: 50M items with 768D embeddings reduced to 128D, serving 40K QPS with p95 latency dropping from 20ms to 7-10ms
Network bandwidth optimization: Apply PCA before transmitting embeddings to reduce payload size from 3KB to 512 bytes per vector
ANN index compression: 100M vectors at 256D quantized with 8 bits per code uses 1.6GB RAM resident storage, enabling sub 10ms queries