# On the Consistency of k-means++ algorithm

arXiv: https://arxiv.org/abs/1702.06120 · HTML: https://mlsanity.com/paper/1702.06120/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2017.

## Built on by (most cited first, 2 of 2)

- [Towards Continuous Consistency Axiom](https://mlsanity.com/paper/2202.06015/) (2022)
- [Are Easy Data Easy (for K-Means)](https://mlsanity.com/paper/2308.01926/) (2023)

## Abstract (arXiv)

We prove in this paper that the expected value of the objective function of the k-means++ algorithm for samples converges to population expected value. As k-means++, for samples, provides with constant factor approximation for k-means objectives, such an approximation can be achieved for the population with increase of the sample size. This result is of potential practical relevance when one is considering using subsampling when clustering large data sets (large data bases).