German Conference on Pattern Recognition

Pattern Recognition pp 67-78

A Convex Relaxation Approach to the Affine Subspace Clustering Problem

  • Francesco Silvestri
  • Gerhard Reinelt
  • Christoph Schnörr
Conference paper

DOI: 10.1007/978-3-319-24947-6_6

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9358)
Cite this paper as:
Silvestri F., Reinelt G., Schnörr C. (2015) A Convex Relaxation Approach to the Affine Subspace Clustering Problem. In: Gall J., Gehler P., Leibe B. (eds) Pattern Recognition. Lecture Notes in Computer Science, vol 9358. Springer, Cham

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.

Copyright information

© Springer International Publishing Switzerland 2015

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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