I got the core loop down fine: initialize centroids, assign points by nearest Euclidean distance, recompute means, repeat.
Start by clarifying the problem and assumptions (e.g., Euclidean distance, random initialization). Then outline the K-Means algorithm steps and implement the fit method with proper initialization, iterative assignment and update, and convergence check. Finally, discuss trade-offs and potential improvements.
Pro tip: Mention that you would use K-Means++ initialization to improve convergence and avoid poor local minima, and discuss how to handle empty clusters by reassigning them to the farthest points.
Confirm the distance metric (typically Euclidean), initialization method, convergence criteria, and whether to return inertia or other metrics. Also discuss input data types and scalability considerations.
Choose an initialization strategy: random selection from data points or K-Means++ for better convergence. Explain the trade-offs and why K-Means++ is often preferred.
Iteratively assign each point to the nearest centroid, then recompute centroids as the mean of assigned points. Handle edge cases like empty clusters by reassigning them to the farthest points from their centroids.
Stop when centroid assignments no longer change or when the change in centroid positions falls below a tolerance. Also consider a maximum number of iterations to prevent infinite loops.
Return final centroids and cluster assignments. Discuss computational complexity (O(n*k*d*i)), scalability, and potential improvements like Mini-Batch K-Means for large datasets.
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