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A Convex Relaxation Approach to the Affine Subspace Clustering Problem

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Pattern Recognition (DAGM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9358))

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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.

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Acknowledgement

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

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Authors and Affiliations

  1. Discrete and Combinatorial Optimization Group, Heidelberg University, Heidelberg, Germany

    Francesco Silvestri & Gerhard Reinelt

  2. IPA and HCI, Heidelberg University, Heidelberg, Germany

    Francesco Silvestri & Christoph Schnörr

Authors
  1. Francesco Silvestri
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  2. Gerhard Reinelt
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  3. Christoph Schnörr
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Corresponding author

Correspondence to Francesco Silvestri .

Editor information

Editors and Affiliations

  1. Institute of Computer Science III, University of Bonn, Bonn, Germany

    Juergen Gall

  2. MPI for Intelligent Systems, University of Tübingen, Tübingen, Germany

    Peter Gehler

  3. Computer Vision Group, Visual Computing Institute, RWTH Aachen, Aachen, Germany

    Bastian Leibe

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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. DAGM 2015. Lecture Notes in Computer Science(), vol 9358. Springer, Cham. https://doi.org/10.1007/978-3-319-24947-6_6

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  • DOI: https://doi.org/10.1007/978-3-319-24947-6_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24946-9

  • Online ISBN: 978-3-319-24947-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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