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}
}