Implement robust k-means from scratch
Company: Microsoft
Role: Data Scientist
Category: Machine Learning
Difficulty: hard
Interview Round: Onsite
Implement k-means clustering from scratch and make it production-robust.
Requirements:
- Function: kmeans(X, k, init="k-means++", max_iter=300, tol=1e-4, random_state=0, n_init=10) → (centers, labels, inertia).
- Inputs: X is an (n×d) float matrix; no ML libraries; vectorize where possible.
- Initialization: Implement k-means++ seeding; run n_init independent restarts; return the run with minimal inertia.
- Convergence: Stop when relative change in inertia < tol for two consecutive iterations.
- Empty clusters: Must handle by splitting the cluster with highest within-cluster variance at the furthest point from its centroid (describe and implement).
- Numerical stability: Discuss and implement safe handling for NaNs/Infs and feature scaling; support optional standardization.
- Complexity: Analyze time and space in terms of n, d, k; propose mini-batch k-means variant and when it helps.
- Evaluation: Describe how you would pick k (e.g., silhouette score, gap statistic) and test stability across seeds.
- Tests: Provide unit tests covering tiny degenerate cases (n<k, duplicate points), high-dimensional sparse-like data, and convergence behavior.
Quick Answer: This question evaluates implementation and engineering competency in K-Means clustering, covering numerical stability, edge-case handling (empty clusters, NaNs/Infs), initialization strategies, convergence criteria, complexity analysis, evaluation methods for selecting k, and unit testing; it targets the Machine Learning domain, specifically unsupervised clustering and algorithmic implementation. It is commonly asked to assess both practical application (writing production-ready, vectorized code and testable algorithms) and conceptual understanding (trade-offs in initialization, convergence, computational complexity, and evaluation metrics), demonstrating the ability to deliver robust, scalable clustering solutions.