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Classic question but there's more surface area than you think.
Start by clarifying the problem scope and constraints, then outline the K-means algorithm steps: initialization, assignment, update, and convergence. Implement the algorithm efficiently, discussing trade-offs in initialization methods and distance metrics, and validate with a simple example.
Pro tip: Mention K-means++ initialization and the elbow method for choosing K, as these demonstrate practical maturity beyond basic implementation.
Ask about data size, dimensionality, distance metric, and whether K is given. Confirm if the implementation should be optimized for performance or readability.
Describe the standard K-means steps: initialize centroids, assign points to nearest centroid, update centroids, repeat until convergence. Mention convergence criteria (e.g., centroid movement threshold).
Write pseudocode or actual code for assignment and update steps. Use efficient data structures (e.g., numpy arrays) and vectorized operations where possible.
Compare initialization methods (random vs. K-means++), distance metrics (Euclidean vs. others), and stopping criteria. Mention scalability and potential issues like empty clusters.
Test on a small dataset with known clusters, check convergence, and discuss how to evaluate clustering quality (e.g., inertia, silhouette score).
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