🧬 Embedding Similarity

Embedding Similarity#

Measuring how close two items are in a learned embedding space.

Important

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What it is#

Embedding similarity is how we measure the closeness of two objects once they have been turned into embedding vectors: similar objects should have vectors that are close, so a similarity (or distance) score on the vectors becomes a proxy for how alike the objects are. It is the operation that makes embeddings useful in practice — search, recommendation and clustering are all “find the nearby vectors” at heart.

Similarity measures#

cosine similarity#

The most common choice for semantic vectors. It measures the angle between two vectors and ignores their magnitude, so it compares direction (meaning) rather than length:

\[\operatorname{cosine}(u, v) = \frac{u \cdot v}{\lVert u\rVert\,\lVert v\rVert} \quad\in\; [-1, 1],\]

where 1 means identical direction, 0 means unrelated and −1 means opposite.

other measures#

Dot product — like cosine but sensitive to magnitude; common inside neural networks (attention, matrix factorisation).
Euclidean distance (L2) — straight-line distance; smaller is more similar.
Manhattan distance (L1) — sum of absolute coordinate differences.
Jaccard similarity — for sparse sets rather than dense vectors.
Mahalanobis distance — accounts for feature covariance.

Why it matters#

Reducing “are these two things alike?” to a number on vectors is what powers semantic search, “people who liked this also liked that” recommendations, face and image retrieval, and clustering or anomaly detection in embedding space.

In practice#

import numpy as np
from sklearn.metrics.pairwise import cosine_similarity

u = np.array([[0.1, 0.8, 0.5]])
v = np.array([[0.2, 0.7, 0.4]])

score = cosine_similarity(u, v)[0, 0]
print(f"cosine similarity: {score:.2f}")   # ~0.99  ->  very similar

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