Collaborative Filtering

Overview

Collaborative filtering recommends items based on collective user behavior patterns. User-based CF finds similar users; item-based CF finds similar items. Computes in O(U² × I) for user-based or O(I² × U) for item-based where U=users, I=items.

When to Use

Trigger conditions:

• Building recommendations from user-item interaction data (ratings, clicks, purchases)
• Finding "users like you also liked" or "frequently bought together" patterns

When NOT to use:

• When you have no interaction data (cold start — use content-based filtering)
• When item features matter more than behavior patterns (use content-based)

Algorithm

IRON LAW: CF Requires SUFFICIENT Interaction Data
With sparse matrices (< 1% fill rate), similarity computation is
unreliable. Minimum viable: each user has rated 5+ items, each item
has 5+ ratings. Below this, fallback to content-based or popularity.

Phase 1: Input Validation

Load user-item interaction matrix. Check sparsity level and filter users/items below minimum interaction threshold. Gate: Matrix sparsity < 99%, minimum interaction thresholds met.

Phase 2: Core Algorithm

User-based CF:

1. Compute pairwise user similarity (cosine or Pearson correlation)
2. For target user, find top-K most similar users
3. Predict rating: weighted average of similar users' ratings

Item-based CF:

1. Compute pairwise item similarity from co-rating patterns
2. For target item, find top-K most similar items
3. Predict: weighted average of user's ratings on similar items

Phase 3: Verification

Hold out 20% of interactions for testing. Compute RMSE, MAE, or precision@K / recall@K. Gate: RMSE below baseline (global mean predictor).

Phase 4: Output

Return top-N recommendations with predicted scores.

Output Format

{
  "recommendations": [{"item_id": "123", "predicted_score": 4.2, "similar_items_used": 5}],
  "metadata": {"method": "item-based", "similarity": "cosine", "k_neighbors": 20, "sparsity": 0.97}
}

Examples

Sample I/O

Input: 5 users × 5 items rating matrix, target: user1, item5 Expected: Predicted rating based on weighted similarity of user1's rated items similar to item5

Edge Cases

Input	Expected	Why
New user, no ratings	Cannot recommend	Cold start — fallback to popularity
Item rated by all users	Low differentiation	High popularity ≠ personalized match
Single shared item	Unreliable similarity	Need multiple co-ratings for stable similarity

Gotchas

• Scalability: User-based CF with millions of users is O(U²). Use approximate nearest neighbors (LSH) or switch to item-based CF (item catalog is usually smaller).
• Popularity bias: Popular items have more co-ratings, inflating their similarity scores. Normalize by inverse popularity.
• Implicit vs explicit feedback: Clicks/views (implicit) need different treatment than ratings (explicit). Use confidence weighting for implicit data.
• Similarity metric matters: Cosine similarity ignores rating scale differences; Pearson correlation accounts for user rating biases. Choose based on data characteristics.
• Gray sheep: Users with unusual taste patterns have no similar peers. CF fails for them — consider hybrid approaches.

References

• For matrix factorization as a scalable alternative, see references/matrix-factorization.md
• For implicit feedback handling, see references/implicit-feedback.md