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Recommendation Systems • Collaborative Filtering (Matrix Factorization)Easy⏱️ ~2 min

What is Collaborative Filtering?

Definition
Collaborative filtering predicts user preferences by finding patterns in how groups of users interact with items. If users A and B both liked items 1, 2, and 3, and user A also liked item 4, then user B will probably like item 4 too. It works without knowing anything about the items themselves.
The Core Intuition
Collaborative filtering exploits a simple observation: people with similar tastes in the past will have similar tastes in the future. If you and I both gave 5 stars to The Shawshank Redemption, Pulp Fiction, and The Dark Knight, we probably have similar taste in movies. So if I loved Inception and you have not seen it, the system predicts you will like it too.
This is fundamentally different from content-based filtering, which would need to know that all these movies share features like "acclaimed directors" or "complex plots". Collaborative filtering does not need to understand why we have similar taste. It just needs to observe that we do.
User-Based vs Item-Based
User-based: Find users similar to you, see what they liked that you have not tried. The algorithm computes similarity between users based on their rating patterns. Similar users become your "neighborhood". Predictions come from what your neighbors rated highly. Problem: user profiles change rapidly as they rate more items, so neighborhoods shift constantly. Recomputing similarities is expensive.
Item-based: Find items similar to ones you liked. If you rated item A highly, find items that other users rated similarly to A. Item similarities are more stable than user similarities because item profiles change only when new ratings come in, while user profiles change with every new rating. This stability makes item-based collaborative filtering more practical for production.
The Sparsity Problem
With millions of users and millions of items, the rating matrix is enormous but almost entirely empty. A typical user rates maybe 0.01% of available items. Most user pairs have zero items rated in common, making similarity calculation meaningless. This sparsity is why simple nearest-neighbor collaborative filtering struggles at scale and why matrix factorization became the dominant approach.
💡 Key Insight: Collaborative filtering learns from behavior, not from content features. This is its strength and weakness. Strength: no need to engineer features or understand item content. Weakness: cannot recommend new items until users interact with them (cold start), and cannot explain why a recommendation was made.

💡 Key Takeaways

✓Core insight: users who agreed in the past will agree in the future. If 10,000 users who liked A also liked B, the 10,001st user who likes A will probably like B too

✓No understanding needed: CF detects patterns in behavior without knowing WHY users like things. Just matches patterns across users

✓User-based: find similar users, recommend what they liked. Item-based: find similar items to what you liked, recommend those

✓Item-based is more common in production because item similarities are stable (a movie stays similar to other movies) while user preferences shift

✓Works because preferences cluster: sci-fi fans like similar sci-fi, jazz listeners explore similar artists. Aggregate patterns are stable even when individuals are noisy

✓The rating matrix is sparse: most users rate few items. CF fills in the gaps by finding patterns across the known ratings

📌 Interview Tips

1When asked about MF vs deep learning: explain that matrix factorization remains highly effective for sparse interaction data and is 10-100x faster to train than neural approaches.

2For scalability questions: mention that k=64-128 dimensions is typical; storage is (users + items) × k instead of users × items, enabling billion-scale systems.

3When discussing trade-offs: explain that MF captures linear patterns efficiently but struggles with complex feature interactions that deep models handle.

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