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Subspace Least Squares Multidimensional Scaling

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Scale Space and Variational Methods in Computer Vision (SSVM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10302))

Abstract

Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the analysis and reconstruction of non-rigid shapes. In this regard, MDS can be thought of as a shape from metric algorithm, consisting of finding a configuration of points in the Euclidean space that realize, as isometrically as possible, some given distance structure. In the present work we cast the least squares variant of MDS (LS-MDS) in the spectral domain. This uncovers a multiresolution property of distance scaling which speeds up the optimization by a significant amount, while producing comparable, and sometimes even better, embeddings.

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Notes

  1. 1.

    Note also that (1) is not differentiable everywhere.

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Acknowledgement

This research was supported by the ERC StG grant no. 335491 and the ERC StG grant no. 307048 (COMET). Part of this research was carried out during a stay with Intel Perceptual Computing Group, Haifa, Israel.

Author information

Authors and Affiliations

  1. Technion, Haifa, Israel

    Amit Boyarski & Alex M. Bronstein

  2. Tel-Aviv University, Tel Aviv, Israel

    Alex M. Bronstein & Michael M. Bronstein

  3. Intel Perceptual Computing, Haifa, Israel

    Alex M. Bronstein & Michael M. Bronstein

  4. University of Lugano, Lugano, Switzerland

    Michael M. Bronstein

Authors
  1. Amit Boyarski
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  2. Alex M. Bronstein
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  3. Michael M. Bronstein
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Corresponding author

Correspondence to Amit Boyarski .

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Editors and Affiliations

  1. University of Copenhagen , Copenhagen, Denmark

    François Lauze

  2. Technical University of Denmark , Kongens Lyngby, Denmark

    Yiqiu Dong

  3. Technical University of Denmark , Kongens Lyngby, Denmark

    Anders Bjorholm Dahl

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Boyarski, A., Bronstein, A.M., Bronstein, M.M. (2017). Subspace Least Squares Multidimensional Scaling. In: Lauze, F., Dong, Y., Dahl, A. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2017. Lecture Notes in Computer Science(), vol 10302. Springer, Cham. https://doi.org/10.1007/978-3-319-58771-4_54

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  • DOI: https://doi.org/10.1007/978-3-319-58771-4_54

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58770-7

  • Online ISBN: 978-3-319-58771-4

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