HackerPapers

arXiv:1512.07548stat.ML

k-Means Clustering Is Matrix Factorization

Christian Bauckhage

Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.

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.

arXiv comments
Journal reference
DOI
Subjects
stat.MLMachine Learning (Statistics)

On Hacker News

Linked by 1 identifiable commenter in 1 comment across 1 thread, from Mar 2020 to Mar 2020. Found in 1 HN submission from Mar 2020 to Mar 2020. Open submission discussions.

Comments linking this paper, per year.

Discussed in comments1 thread

  1. Separability, SVD and low-rank approximation of 2D image processing filters 1 comment

    • Good stuff. A lot of clustering methods can be viewed as matrix factorization (see, e.g., https://arxiv.org/abs/1512.07548) so it would be interesting to see if you could spend more computation on the creating the low dimensional approximation to achieve a better result. E.g.…

      noelwelshView on HNParent context

Submitted to Hacker News

Connected through shared HN threads, not inferred similarity or a recommendation.