While we know this (see the Advanced Matrix Factorization Jungle Page.), Christian really wanted to get to the bottom of this in writing. Thank you !
This closed form solution makes it more like a subspace clustering algorithm, from the Jungle page
Here is the derivation: k-Means Clustering Is Matrix Factorization by Christian Bauckhage
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.Related:
- Sunday Morning Insight: Relax, no need to round: integrality of clustering formulations
- Sunday Morning Insight: Why You Should Care About Phase Transitions in Clustering
Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.
No comments:
Post a Comment