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.
