Interview questions · Tubi

Implement K-Means and compare with GMM

This question evaluates understanding and practical implementation of clustering algorithms, specifically K-Means centroid initialization, assignment and update mechanics, convergence criteria and edge-case handling, along with comparative knowledge of Gaussian Mixture Models and the Expectation-Maximization training framework.

Implement K-Means clustering from scratch for a dataset X of shape (n_samples, n_features) and a target number of clusters k.

Your implementation should:

initialize k centroids,
assign each point to its nearest centroid,
recompute centroids as the mean of assigned points,
repeat until convergence or a maximum number of iterations,
handle edge cases such as empty clusters,
and include a test or check for convergence, such as unchanged assignments, centroid movement below a tolerance, or non-increasing within-cluster loss.

After coding, answer these follow-up questions:

How does Gaussian Mixture Modeling differ from K-Means?
How would you train a Gaussian mixture model using the EM algorithm?
In what situations would you prefer GMM over K-Means?

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