Cosine Similarity From Scratch | Dataford Interview Questions

Your question is Cosine Similarity From Scratch. Start with the requirements on the right.

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Problem

Cognizant Neuro AI may compare embedding vectors to identify semantically similar text. Implement cosine similarity from scratch using only Python's built-in operations.

Given two non-empty vectors a and b of equal length, return their cosine similarity:

similarity = (a · b) / (||a|| × ||b||)

The dot product is the sum of pairwise products, and each norm is the square root of the sum of squared components. If either vector is a zero vector, return 0.0 because its direction is undefined.

Formal Specification

Input: Two lists of integers or floating-point numbers, a and b, with equal non-zero lengths.
Output: A floating-point number in the range [-1.0, 1.0], subject to normal floating-point precision.
Do not use NumPy, scikit-learn, or other vector libraries.

Constraints

1 <= len(a) = len(b) <= 10^5
-10^6 <= a[i], b[i] <= 10^6
Both vectors are non-empty and have equal lengths
Inputs contain finite integers or floating-point values

Function Signature

def cosine_similarity(a, b):