Cosine Similarity
Beginner
The problem, from first principles
Two vectors can be far apart in distance yet point in the same direction (a document and a copy of it repeated ten times). Cosine similarity compares only direction, ignoring length, which is why it is the default way to compare embeddings.
From theory to code
Implement cosine_similarity(a, b) for two one-dimensional vectors.
Constraints
aandbare one-dimensional float arrays of equal length.- Return a Python
floatin[-1, 1]. - If either vector has zero length, return
0.0rather than dividing by zero.
Hints
Open one at a time. Each gives away a little more than the last.
Hint 1
The dot product measures alignment; dividing by both norms removes the effect of length.
Hint 2
np.linalg.norm(v) gives a vector's length.
Keywords
mathematicslinear-algebrasimilarity
Python
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