Item Coverage

1. Definition

• Item Coverage measures how many unique items from the catalog a recommender system is able to recommend across users.
• It tells you how much of the item space is being explored, rather than just recommending the same “popular” items to everyone.

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2. Formula

Let:

• $I$ = set of all items in the catalog.
• $R(u)$ = set of items recommended to user $u$.
• $U$ = set of all users.

Then:

$\text{Item Coverage} = \frac{|\bigcup_{u \in U} R(u)|}{|I|}$

• Numerator = number of distinct recommended items across all users.
• Denominator = total number of items in the system.

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3. Example

Suppose:

• Catalog = 100 items.
• System recommends 10 items to each of 20 users.
• Across all recommendations, only 30 distinct items appear.

$\text{Item Coverage} = \frac{30}{100} = 0.3 \; (30\%)$

This means the system is using only 30% of the available catalog.

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4. Intuition

• High coverage → system is diverse, explores the catalog, helps users discover “long-tail” items.
• Low coverage → system sticks to a small subset (often the most popular items).

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5. Variants

• User Coverage: fraction of users who receive at least one “good” recommendation.
• Catalog Coverage: same as item coverage, but sometimes weighted by popularity or relevance.
• Top-N Coverage: item coverage restricted to top-N recommendations per user.

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6. Trade-offs

• Accuracy vs Coverage:
  • A system might achieve high accuracy by always recommending a few popular items → low coverage.
  • Improving coverage often reduces accuracy slightly but increases novelty and fairness.
• In practice, recommender evaluation often balances precision and coverage.

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Summary:
Item Coverage = fraction of items from the catalog that appear in at least one recommendation list across users. It measures how broadly a recommender system explores the catalog, complementing accuracy metrics by capturing diversity and novelty.