Custom Similarity Metric Coding | Dataford Interview Questions

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Problem

TELUS Digital AI Community uses vector representations when evaluating semantic similarity. Implement a custom weighted cosine similarity metric that gives each vector dimension a configurable importance.

Formal Specification

Write weighted_similarity(a, b, weights) to accept three lists of equal length containing real numbers. For each dimension i, weights[i] must be nonnegative. Compute:

similarity = Σ(weights[i] * a[i] * b[i]) / (sqrt(Σ(weights[i] * a[i]^2)) * sqrt(Σ(weights[i] * b[i]^2)))

Return a Python float. Dimensions with weight 0 must not affect the result. If either weighted vector has zero magnitude, return 0.0 instead of raising an error. The result should be in [-1.0, 1.0] for valid inputs.

Constraints

1 <= len(a) = len(b) = len(weights) <= 10^5
-10^6 <= a[i], b[i] <= 10^6
0 <= weights[i] <= 10^6
At least one weight is positive
Inputs contain finite numeric values

Function Signature

def weighted_similarity(a, b, weights):