Cosine Similarity for Embeddings | Dataford Interview Questions

Scotiabank may compare embedding vectors to rank semantically related content, such as matching a customer query with relevant Scotia mobile app help content. Implement cosine similarity for two high-dimensional vectors.

Given two equal-length lists of numbers, compute:

similarity = (A · B) / (||A|| × ||B||)

Return a floating-point value in the range [-1.0, 1.0]. If either vector has zero magnitude, return 0.0, because cosine similarity is undefined for a zero vector.

Formal Specification

Implement cosine_similarity(a, b), where a and b are non-empty lists of integers or floating-point values with the same length. Return the cosine similarity as a float. Do not modify either input list.

Constraints

1 <= len(a) = len(b) <= 100000
-10^6 <= a[i], b[i] <= 10^6
Inputs contain only finite numeric values
Input vectors must not be modified

Function Signature

def cosine_similarity(a, b):

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