Vector Databases & Embeddings

# WORKED EXAMPLE — find the most similar items by MEANING
# Plain Python, no libraries. Each item is a tiny "embedding" (a list of numbers).
# We score every item against the query with COSINE similarity, then return the top-k.

import math

# A toy collection: id -> embedding vector.
# Think of these as 3 numbers describing each thing ("sporty", "fruity", "techy").
items = {
    "apple":   [0.9, 0.1, 0.0],   # very fruity
    "banana":  [0.8, 0.2, 0.0],   # fruity
    "laptop":  [0.0, 0.1, 0.9]
...

# 🎯 YOUR TURN #1 — return the IDs of the top-k nearest neighbours
# Fill in the blanks marked with ___

import math

items = {
    "dog":   [0.9, 0.1, 0.0],
    "cat":   [0.8, 0.2, 0.0],
    "car":   [0.0, 0.1, 0.9],
    "truck": [0.1, 0.0, 0.9],
}

def dot(a, b):
    return sum(x * y for x, y in zip(a, b))

def norm(a):
    return math.sqrt(sum(x * x for x in a))

def cosine_similarity(a, b):
    # 👉 cosine = dot(a, b) divided by (norm(a) * norm(b))
    return ___ / (norm(a) * norm(b))

def t
...

# 🎯 YOUR TURN #2 — normalise a vector, then search with the right metric
# Fill in the blanks marked with ___

import math

def norm(a):
    return math.sqrt(sum(x * x for x in a))

def normalize(a):
    n = norm(a)
    # 👉 divide every component by the length so the vector has length 1.0
    return [x / ___ for x in a]

# After L2-normalising both vectors, the DOT PRODUCT equals the COSINE similarity.
def dot(a, b):
    return sum(x * y for x, y in zip(a, b))

items = {
    "red":   normalize
...

# FAISS — Facebook AI Similarity Search (an indexing LIBRARY, not a server)
# Read-only example: this needs 'pip install faiss-cpu numpy' and won't run in the box.

import numpy as np
import faiss

dim = 64                                  # embedding dimension
vectors = np.random.randn(1000, dim).astype("float32")
faiss.normalize_L2(vectors)               # normalise so inner product = cosine

# IndexFlatIP = brute force (exact) with inner product.
index = faiss.IndexFlatIP(dim)
index.add(vecto
...

# ChromaDB — an embedding database with built-in storage + METADATA FILTERING
# Read-only example: needs 'pip install chromadb'.

import chromadb

client = chromadb.Client()
collection = client.create_collection("articles")

# Chroma can embed text for you; here we pass our own vectors to stay explicit.
collection.add(
    ids=["a1", "a2", "a3"],
    embeddings=[[0.9, 0.1, 0.0], [0.0, 0.1, 0.9], [0.85, 0.15, 0.0]],
    metadatas=[{"topic": "fruit"}, {"topic": "tech"}, {"topic": "fruit"}],
    do
...