# Improved Conic Reformulations for K-means Clustering

arXiv: https://arxiv.org/abs/1706.07105 · HTML: https://mlsanity.com/paper/1706.07105/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2017.

## Built on by (most cited first, 1 of 1)

- [Sketch-and-solve approaches to k-means clustering by semidefinite programming](https://mlsanity.com/paper/2211.15744/) (2022)

## Abstract (arXiv)

In this paper, we show that the popular K-means clustering problem can equivalently be reformulated as a conic program of polynomial size. The arising convex optimization problem is NP-hard, but amenable to a tractable semidefinite programming (SDP) relaxation that is tighter than the current SDP relaxation schemes in the literature. In contrast to the existing schemes, our proposed SDP formulation gives rise to solutions that can be leveraged to identify the clusters. We devise a new approximation algorithm for K-means clustering that utilizes the improved formulation and empirically illustrate its superiority over the state-of-the-art solution schemes.