Recommender Systems

Recommender systems serve two primary purposes: predicting user preferences (A) — modeling what users are likely to enjoy based on historical data and patterns; and suggesting relevant items to users (C) — providing actionable recommendations. These two work hand-in-hand: prediction is the internal mechanism, while suggestion is the user-facing output. Clustering users (B) and extracting patterns (D) are techniques used to achieve these goals, not purposes themselves.

The three main recommender system architectures are: Collaborative filtering (A) — recommendations based on user-item interaction patterns ("users like you also liked…"); Content-based filtering (B) — recommendations based on item features ("since you liked X, try Y which has similar attributes"); Hybrid systems (C) — combine both approaches to overcome individual limitations. Dimensionality reduction (D) is a technique used within recommenders (e.g., matrix factorization), not a recommender type itself.

Collaborative filtering is fundamentally about leveraging the wisdom of the crowd. It relies on: User-item interaction data (A) — who interacted with what; Explicit feedback (B) — ratings, likes, reviews that directly signal preferences; Identifying patterns in user behaviour (D) — finding correlations like "users who bought A also bought B." The key distinguishing feature: collaborative filtering does not need to know anything about item content (C) — it works purely from interaction patterns. It could recommend movies without knowing genres, or books without reading them.

Content-based systems recommend items similar to what a user has liked before, based on intrinsic item attributes. They use: User profiles (A) — a model of what features the user prefers (e.g., "likes action movies with high budgets"); Item features (A) — attributes like genre, director, keywords; Similarity between items (B) — computing how close two items are in feature space. Social network relationships (C) and user-to-user similarity (D) are hallmarks of collaborative filtering, not content-based approaches.

The cold-start problem specifically refers to the challenge of making recommendations when there's no prior data for new entities. This includes: Lack of interaction data (A) — the general formulation of the problem; New users (B) — no history means no basis for collaborative filtering; New items (C) — no ratings means they can't be recommended via collaborative methods. Sparse matrices (D) is a related but distinct challenge that affects all recommender systems, not just cold-start scenarios. Sparsity is about having some data but not much; cold-start is about having none.

Content-based systems suffer from over-specialization or the filter bubble (A). If you only watch action movies, the system will only recommend more action movies — it can't suggest a documentary or romance film that might surprise you. This happens because recommendations are based purely on matching past preferences. Options B and C describe collaborative filtering problems (need many users, sparse matrices). Option D is false — content-based systems can recommend popular items if they match the user's profile.

Nearest-neighbor (k-NN) collaborative filtering is a classic approach. The workflow: Find similar users or items (A) — identify neighbors with similar taste or consumption patterns. Compute similarity metrics (B, C) — cosine similarity and Pearson correlation are two common measures to quantify how alike two users/items are. Predict ratings (D) — estimate what a user will rate an item by averaging the ratings from similar neighbors, weighted by similarity. This is memory-based collaborative filtering — it keeps all the data and computes on-the-fly.

The long tail refers to the distribution of item popularity: a few blockbusters (the "head") get most attention, while a vast number of niche items (the "tail") each get little. Good recommenders help users discover less popular items (A) that match their niche interests (B), increasing recommendation diversity (D). This is valuable because it surfaces hidden gems and serves diverse tastes. Option C describes the head (popular items), not the tail. Think of Netflix recommending an obscure indie film you'd never find browsing the homepage.

Using the formula R_xi = Σ Sim(x,y) × R_yi / Σ Sim(x,y): First, find users who rated movie 4: users 1, 5, and 6. Compute similarity between user 3 and each (using cosine similarity on commonly rated movies). User 1: common movie {2} → similarity ≈ 1.0. User 5: common movies {2, 6} → similarity ≈ 0.923. User 6: common movies {2, 6} → similarity ≈ 0.965. Top 2 most similar: users 1 and 6. Both rated movie 4 as 3. Prediction = (1.0×3 + 0.965×3) / (1.0 + 0.965) ≈ 5.895/1.965 ≈ 3.0.

RMSE (Root Mean Squared Error) = √(Σ(predicted - actual)² / n). A is true — squaring errors means a 2-point error contributes 4 to the sum, while a 4-point error contributes 16, so large errors are penalized quadratically. B is true — RMSE is in the same units as the target, so you can't compare RMSE across datasets measured in different units (e.g., dollars vs. kilograms). C is false — RMSE is always non-negative (≥ 0) because it's a square root of squared terms. D is true — unlike MSE (squared units), RMSE is in the original units, making it interpretable.