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Microsoft·Machine Learning Engineer·Technical Phone Screen·Senior

Senior
Jun 2026

Summary

Microsoft ML Engineer technical screen, pretty much just one meaty coding question about implementing K-Means from scratch. No fluff, they went straight into the algorithm and then pushed on complexity analysis as a follow-up.

Questions Asked (1)

Q1

Implement K-Means clustering from scratch without using any libraries. Your solution should cover centroid initialization, assigning points to the nearest centroid using Euclidean distance, updating centroids as the mean of assigned points, and a convergence check. Follow-up: what is the time complexity in terms of n (points), k (clusters), d (dimensions), and i (iterations)?

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

I started with random initialization and worked through the assignment and update steps without too much trouble, but the convergence criterion tripped me up a bit.

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AI HintsAI Generated

Suggested Approach

Start by outlining the K-Means algorithm steps: initialization, assignment, update, and convergence. Then implement each step in code, ensuring clarity and efficiency. Finally, analyze the time complexity by breaking down the cost of each step.

Pro tip: Mention that while random initialization is common, K-Means++ improves convergence and reduces the chance of poor local minima. Also, note that the convergence check can be based on centroid movement or objective function change.

1. Initialize centroids

Choose k initial centroids, either randomly from the data points or using K-Means++ for better initialization.

2. Assign points to nearest centroid

For each point, compute Euclidean distance to all centroids and assign it to the closest one.

3. Update centroids

Recompute each centroid as the mean of all points assigned to it. Handle empty clusters by reinitializing or removing them.

4. Check convergence

Repeat steps 2-3 until centroids no longer change significantly or a maximum number of iterations is reached.

5. Analyze time complexity

Derive the complexity: O(n*k*d*i) for assignment and update, considering distance computations and mean calculations.

Key Points to Mention

  • Euclidean distance calculation: sqrt(sum((x_i - c_j)^2)) for d dimensions.
  • Assignment step: for each point, compute distance to all k centroids, O(n*k*d).
  • Update step: compute mean of assigned points, O(n*d) total per iteration.
  • Convergence criteria: centroids unchanged or change below threshold, or max iterations.
  • Time complexity: O(n*k*d*i) overall, where i is number of iterations.
  • Space complexity: O(n*d + k*d) for storing data and centroids.
  • Handling empty clusters: reassign to farthest point or reinitialize randomly.
  • K-Means++ initialization for better convergence.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.