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 m...