Chapter 1: Similarity Search

Introduction

Similarity search is the foundation of retrieval in RAG systems. It finds documents whose vector representations are closest to the query vector.

Distance Metrics

Cosine Similarity

import numpy as np

def cosine_similarity(a, b):
    return np.dot(a, b) / (np.linalg.norm(a) * np.linalg.norm(b))

# Range: -1 to 1 (1 = identical)

Euclidean Distance

def euclidean_distance(a, b):
    return np.linalg.norm(a - b)

# Range: 0 to infinity (0 = identical)

Inner Product (Dot Product)

def inner_product(a, b):
    return np.dot(a, b)

# For normalized vectors, equivalent to cosine

Top-K Retrieval

from langchain.vectorstores import Chroma

# Create retriever
retriever = vectorstore.as_retriever(
    search_type="similarity",
    search_kwargs={"k": 5}  # Return top 5 results
)

# Retrieve
docs = retriever.get_relevant_documents("What is RAG?")

Score Thresholds

Filter by minimum similarity:

retriever = vectorstore.as_retriever(
    search_type="similarity_score_threshold",
    search_kwargs={
        "score_threshold": 0.7,  # Minimum similarity
        "k": 10
    }
)

Maximum Marginal Relevance (MMR)

Balance relevance with diversity:

retriever = vectorstore.as_retriever(
    search_type="mmr",
    search_kwargs={
        "k": 5,
        "fetch_k": 20,        # Fetch more candidates
        "lambda_mult": 0.7    # 1=relevance, 0=diversity
    }
)

Comparison

Method	Best For	Trade-off
Similarity	General use	May have redundant results
Threshold	Quality filtering	May return few results
MMR	Diverse results	Slightly lower relevance

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Next Steps

Continue to Chapter 2: Hybrid Search.