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A Convex Relaxation Approach to the Affine Subspace Clustering Problem

  • Francesco Silvestri
  • Gerhard Reinelt
  • Christoph Schnörr
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9358)

Abstract

Prototypical data clustering is known to suffer from poor initializations. Recently, a semidefinite relaxation has been proposed to overcome this issue and to enable the use of convex programming instead of ad-hoc procedures. Unfortunately, this relaxation does not extend to the more involved case where clusters are defined by parametric models, and where the computation of means has to be replaced by parametric regression. In this paper, we provide a novel convex relaxation approach to this more involved problem class that is relevant to many scenarios of unsupervised data analysis. Our approach applies, in particular, to data sets where assumptions of model recovery through sparse regularization, like the independent subspace model, do not hold. Our mathematical analysis enables to distinguish scenarios where the relaxation is tight enough and scenarios where the approach breaks down.

Notes

Acknowledgement

Authors gratefully acknowledge support by the DFG, grant GRK 1653.

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Copyright information

© Springer International Publishing Switzerland 2015

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Francesco Silvestri
    • 1
    • 2
  • Gerhard Reinelt
    • 1
  • Christoph Schnörr
    • 2
  1. 1.Discrete and Combinatorial Optimization GroupHeidelberg UniversityHeidelbergGermany
  2. 2.IPA and HCIHeidelberg UniversityHeidelbergGermany

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