##### Question You need to cluster users for a social product (e.g. Meta) to discover meaningful groups such as communities, interest groups, or usage segments. The data you have may be either, or both, of: - A **user feature table** — dense numeric/categorical features per user (age bucket, country, activity rate, topics engaged, embeddings, etc.). - A **social network graph** — nodes = users, edges = friendships / follows / messages / interactions, possibly **weighted and directed**. Answer the following: 1. **Traditional (feature-vector) clustering.** Which clustering algorithms would you consider (e.g. k-means, GMM, hierarchical, DBSCAN/HDBSCAN) and how would you choose among them? Describe preprocessing, distance/similarity choices, how you would pick the number of clusters, and how you would evaluate cluster quality. 2. **Social network / graph clustering.** If the core data is a social graph instead, what algorithms would you use for community detection, and how does this differ fundamentally from clustering a feature matrix? 3. **Directed and weighted graphs.** How do you handle direction and edge weights in graph clustering? 4. **Hybrid.** How would you combine graph structure and user features when both are available? 5. **Choosing the number of clusters and evaluating quality.** What metrics and validation strategy would you use for both the feature-vector and the graph case? 6. **Scale and operations.** What practical issues arise at millions of users (compute, dynamic graphs, cold-start, drift) and how would you handle them?