Hit Rate at K

Recommender SystemsMetrics & Evaluation

Easy

Hit rate at K measures the fraction of users whose first k recommendations contain at least one relevant item. A user contributes one hit regardless of how many relevant items appear.

\operatorname{HR@K} = \frac{1}{|U|}\sum_{u \in U}\mathbb{1}(R_u^{(K)} \cap G_u \ne \varnothing)

The sum examines every user. For each user, the indicator contributes 1 when the first k recommendations share at least one item with that user's ground-truth relevant items; otherwise it contributes 0. Divide the total hits by the number of users. Return 0.0 when there are no users.

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Examples

Input: recommendations = [[1, 2, 3], [4, 5, 6], [7, 8, 9]], ground_truth = [[1], [10], [7]], k = 3

Output: 0.6667

Explanation: Users 0 and 2 have at least one relevant item in their first three recommendations.

Input: recommendations = [[10, 1, 2, 3], [10, 4, 5, 6]], ground_truth = [[1], [4]], k = 1

Output: 0.0000

Hint 1

Convert each first-k slice and corresponding ground-truth list to sets.

Hint 2

A nonempty set intersection contributes one hit.

Requirements

Inspect only the first k recommendations for each user.
Count at most one hit per user.
Divide the hit count by the number of users.
Return 0.0 when there are no users.

Constraints

recommendations and ground_truth contain the same number of user lists.
k is positive.
Time limit: 300 ms.

Try Similar Problems

Precision Recall At K Mean Average Precision Ndcg Top K Recommendations Catalog Coverage

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