English

k-Means Clustering Is Matrix Factorization

Machine Learning 2015-12-24 v1

Abstract

We show that the objective function of conventional k-means clustering can be expressed as the Frobenius norm of the difference of a data matrix and a low rank approximation of that data matrix. In short, we show that k-means clustering is a matrix factorization problem. These notes are meant as a reference and intended to provide a guided tour towards a result that is often mentioned but seldom made explicit in the literature.

Keywords

Cite

@article{arxiv.1512.07548,
  title  = {k-Means Clustering Is Matrix Factorization},
  author = {Christian Bauckhage},
  journal= {arXiv preprint arXiv:1512.07548},
  year   = {2015}
}
R2 v1 2026-06-22T12:16:54.120Z