Recall at K

Recall@K measures fraction of relevant items found in top-K — evaluating what percentage of all relevant items appear in the first K results, complementing precision by measuring coverage.

What Is Recall@K?

• Definition: Percentage of all relevant items that appear in top-K.
• Formula: R@K = (# relevant in top-K) / (total # relevant items).
• Range: 0 (no relevant items found) to 1 (all relevant items in top-K).

Example

Total relevant items: 20.
Top 10 results contain: 8 relevant items.
- Recall@10 = 8/20 = 0.4 (40% recall).

Why Recall@K?

• Coverage: Measures how many relevant items are found.
• Completeness: Important when users want comprehensive results.
• Complement to Precision: Precision = quality, Recall = coverage.

Precision vs. Recall Trade-off

• High Precision, Low Recall: Few results, mostly relevant (conservative).
• Low Precision, High Recall: Many results, some irrelevant (liberal).
• Balance: Need both for good ranking.

When Recall@K Matters

High Recall Important: Research, legal discovery, medical diagnosis (can't miss relevant items).
Low Recall OK: Quick search, single answer needed (precision more important).

Limitations

• Requires Knowing Total Relevant: Need to know how many relevant items exist.
• K-Dependent: Different K values give different scores.
• Ignores Position: Treats all top-K positions equally.

Applications: Search evaluation, recommendation evaluation, information retrieval, document retrieval.

Tools: scikit-learn, IR evaluation libraries.

Recall@K is essential for comprehensive retrieval — while precision measures quality, recall measures coverage, and both are needed to fully evaluate ranking systems.