LangChain / RAG / Vector DBs · Lesson

Measuring Embedding Similarity

Understand the distance and similarity metrics that power vector search and how to choose the right one.

Measuring Embedding Similarity is a free LangChain / RAG / Vector DBs lesson on CoddyKit — lesson 4 of 4. You can read the complete lesson below for free — then practise it hands-on in the browser with a built-in code editor and a 24/7 AI tutor. It is part of the LangChain / RAG / Vector DBs learning path, one of 4 lessons in the course, and your progress syncs across the web and the CoddyKit app.

From Vectors to Meaning

An embedding maps text to a list of numbers in high-dimensional space. Texts with similar meaning land close together. To rank results we need a way to measure that closeness.

Cosine Similarity

Cosine similarity measures the angle between two vectors, ignoring their length. It ranges from -1 (opposite) to 1 (identical direction).

import numpy as np

def cosine(a, b):
    a, b = np.array(a), np.array(b)
    return a.dot(b) / (np.linalg.norm(a) * np.linalg.norm(b))

print(cosine([1, 0], [1, 1]))  # ~0.707

Euclidean Distance

Euclidean (L2) distance is the straight-line distance between two points. Smaller means more similar. Unlike cosine, it is sensitive to magnitude.

import numpy as np

def l2(a, b):
    return np.linalg.norm(np.array(a) - np.array(b))

print(l2([0, 0], [3, 4]))  # 5.0

Dot Product

The dot product multiplies matching dimensions and sums them. For normalized vectors it equals cosine similarity, which is why many stores normalize first.

import numpy as np

def dot(a, b):
    return float(np.array(a).dot(np.array(b)))

print(dot([1, 2, 3], [4, 5, 6]))  # 32.0

Normalization

Dividing a vector by its length gives a unit vector. After normalization, dot product and cosine similarity become equivalent, simplifying the math.

import numpy as np

def normalize(v):
    v = np.array(v, dtype=float)
    return v / np.linalg.norm(v)

print(normalize([3, 4]))  # [0.6 0.8]

Choosing a Metric

Most modern text embedding models are trained for cosine similarity. Use cosine unless your provider documentation recommends otherwise.

Cosine: direction matters, length ignored
L2: absolute position matters
Dot: cosine on normalized data

Similarity vs. Distance

Beware the inversion: higher cosine = more similar, but higher L2 = less similar. Vector stores expose this difference, sometimes returning a score you must interpret.

Why High Dimensions Help

Embeddings often have hundreds or thousands of dimensions. More dimensions give the model room to separate subtle differences in meaning, at the cost of more storage and compute.

Setting Metric in a Store

When creating a collection you declare the metric. Many libraries default to cosine.

import chromadb

client = chromadb.Client()
col = client.create_collection(
    name="docs",
    metadata={"hnsw:space": "cosine"}
)

Ranking Search Results

Search computes the chosen metric between the query embedding and every stored vector, then returns the top-k closest. The metric directly shapes which documents win.

query_vec = embed("refund policy")
scored = [(cosine(query_vec, d.vec), d) for d in docs]
scored.sort(reverse=True)
top3 = scored[:3]

Pitfall: Mixing Models

Vectors from different embedding models live in different spaces and are not comparable. Always embed your query with the same model you used to index the documents.

Quick Check

Test your grasp of similarity metrics.

Recap

You explored how similarity is measured:

Cosine compares direction (most common for text)
Euclidean compares position
Dot product equals cosine on normalized vectors
Always query and index with the same model

Frequently asked questions

Is the “Measuring Embedding Similarity” lesson free?

Yes — the full text of “Measuring Embedding Similarity” is free to read here on the web, and the LangChain / RAG / Vector DBs course includes 4 lessons in total. To practise it interactively (a built-in code editor and a 24/7 AI tutor) and unlock the rest of the LangChain / RAG / Vector DBs course, upgrade to CoddyKit PRO.

What will I learn in “Measuring Embedding Similarity”?

Understand the distance and similarity metrics that power vector search and how to choose the right one. You practise LangChain / RAG / Vector DBs with hands-on code you run directly in the browser, and a 24/7 AI tutor answers your questions as you work through the lesson.

Do I need any experience to start LangChain / RAG / Vector DBs?

No prior experience is required. LangChain / RAG / Vector DBs on CoddyKit is structured for beginners through advanced learners; this is — lesson 4 of 4, so you can start here or from the beginning and move at your own pace.

How long does the “Measuring Embedding Similarity” lesson take?

Most CoddyKit lessons take about 5–10 minutes. Each one is bite-sized and interactive, so you make steady progress and pick up exactly where you left off across the web and the app.

Can I write and run code in this LangChain / RAG / Vector DBs lesson?

Yes. Every LangChain / RAG / Vector DBs lesson includes a built-in code editor, so you write and run real code right in your browser and get instant AI feedback — no local setup required.

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