Your question is Efficient Cosine Similarity. Start with the requirements on the right.
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Andela's machine learning systems may compare high-dimensional feature embeddings where most dimensions are zero. Given two sparse vectors, compute their cosine similarity without expanding them into dense arrays.
Represent each vector as a Python dictionary mapping a nonzero dimension index to its numeric value. Return the cosine similarity:
cosine_similarity(a, b) = (a · b) / (||a|| ||b||)
The dot product should include only dimensions present in both dictionaries. If either vector has zero magnitude, return 0.0.
Implement cosine_similarity(a, b), where a and b are dictionaries with integer keys and numeric values. Return a floating-point number. The input dictionaries contain only nonzero values, and their dimension ranges do not need to be identical.
Your solution should avoid iterating over the entire possible dimension range. Aim for time proportional to the number of stored nonzero entries, and use dictionary lookup for shared dimensions.
def cosine_similarity(a, b):