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2015

k-Means Clustering Is Matrix Factorization

Bauckhage, Christian

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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.

k-Means Clustering Is Matrix Factorization · Around

Built on

The Elements of Statistical Learning
Hastie, T., Tibshirani, R., Friedman, J.: · 2001
Earlier work this paper cites.
Information Theory, Inference, & Learning Algorithms
MacKay, D.: · 2003
Earlier work this paper cites.
On the Equivalence of Nonnegative Matrix Factorization and Spectral Clustering
Ding, C., He, X., Simon, H.: · 2005
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