What is the computational complexity of K-Means?

Updated May 16, 2026

Short answer

K-Means complexity is O(n × k × i × d), where n is data points, k clusters, i iterations, and d dimensions.

Deep explanation

Each iteration computes distance from every point to every centroid. This scales linearly with dataset size but can become expensive for large n, k, or d. Optimizations include vectorization, KD-trees (limited usefulness), and mini-batch K-Means.

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