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Advanced 22 min readModule: Module 10: Vector Embeddings & Vector Databases (pgvector, Pinecone)

Vector Embeddings & Vector Databases (pgvector)

Convert unstructured text into mathematical vector embeddings and execute nearest neighbor searches with pgvector.

What You Will Learn in This Lesson

  • Dense vector embeddings (e.g. 1536-dimensional float arrays)
  • Distance metrics: Cosine Similarity, Euclidean Distance (L2), Dot Product
  • Storing and indexing vectors in PostgreSQL using the pgvector HNSW index

Introduction & Core Concept

Vector embeddings transform words, sentences, and documents into high-dimensional numerical vectors where semantically similar texts are placed close together in vector space.
WHY DOES THIS MATTER IN THE REAL WORLD?

Vector search finds relevant answers even when the user uses completely different vocabulary ('car' matches 'automobile' and 'vehicle').

Semantic Cosine Similarity Calculation

python
python
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import numpy as np
 
def cosine_similarity(v1, v2):
    return np.dot(v1, v2) / (np.linalg.norm(v1) * np.linalg.norm(v2))
 
v_html = np.array([0.90, 0.15, 0.05])
v_css = np.array([0.88, 0.18, 0.04])
v_quantum = np.array([0.05, 0.85, 0.70])
 
print("HTML vs CSS Similarity:", cosine_similarity(v_html, v_css))
print("HTML vs Quantum Similarity:", cosine_similarity(v_html, v_quantum))

Line-by-Line Technical Breakdown

1HNSW (Hierarchical Navigable Small World) indexes perform Approximate Nearest Neighbor (ANN) search in O(log n) time.

Try It Yourself (Interactive Editor)

Modify the code in real-time and click Run to test live browser output and console logs.

Intelligent Code Runner & Live Sandbox[PYTHON]
PYTHON SOURCE EDITOR
Interactive Live Code

Industry Best Practices & Professional Standards

  • Normalize vectors to unit length to make Dot Product equivalent to Cosine Similarity for 3x faster GPU searches.

Lesson Summary & Core Takeaways

  • Vector embeddings and vector databases enable semantic AI search across billions of documents.