Vector Space

What is a Vector Space?

A vector space is a mathematical model where items (words, documents, or products) are represented as vectors (lists of numbers). In search, this allows engines to calculate similarity between a query and documents using metrics like cosine similarity or dot product.

How It Works (quick)

• Representation: Each document/query → vector of term weights (TF-IDF, embeddings).
• Similarity: Compute cosine similarity (angle) or Euclidean distance.
• Indexing: Store vectors in specialized databases (e.g., FAISS, Pinecone).
• Hybrid search: Combine vector scores with keyword ranking (BM25).

Why It Matters in E-commerce

• Semantic search: Matches intent beyond exact keywords (“joggers” ↔ “sweatpants”).
• Personalization: Shopper profiles as vectors matched with products.
• Cross-language: Vectors allow matching queries across languages.

Best Practices

• Normalize vectors to unit length for cosine similarity.
• Use domain-tuned embeddings for catalog language.
• Combine with filters and facets for precision.
• Monitor drift: embeddings may age as catalog or language changes.

Summary

Vector spaces power semantic and hybrid search. They help shoppers find products even when they don’t use exact catalog terms.