"algo-rec-cf"

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}
}