Relax, No Need to Round: Integrality of Clustering Formulations

@article{Awasthi2015RelaxNN,
  title={Relax, No Need to Round: Integrality of Clustering Formulations},
  author={P. Awasthi and A. Bandeira and M. Charikar and R. Krishnaswamy and S. Villar and Rachel Ward},
  journal={ArXiv},
  year={2015},
  volume={abs/1408.4045}
}
  • P. Awasthi, A. Bandeira, +3 authors Rachel Ward
  • Published 2015
  • Mathematics, Computer Science
  • ArXiv
  • We study exact recovery conditions for convex relaxations of point cloud clustering problems, focusing on two of the most common optimization problems for unsupervised clustering: k-means and k-median clustering. Motivations for focusing on convex relaxations are: (a) they come with a certificate of optimality, and (b) they are generic tools which are relatively parameter-free, not tailored to specific assumptions over the input. More precisely, we consider the distributional setting where… CONTINUE READING
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    References

    SHOWING 1-2 OF 2 REFERENCES
    Relax, no need to round: Integrality of clustering formulations
    • 2014
    CVX: Matlab software for disciplined convex programming, version
    • 2014