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Combining Linear Dimension Reduction Subspaces

In: Recent Advances in Robust Statistics: Theory and Applications

Author

Listed:
  • Eero Liski

    (University of Tampere)

  • Klaus Nordhausen

    (University of Tampere
    University of Turku)

  • Hannu Oja

    (University of Turku)

  • Anne Ruiz-Gazen

    (Toulouse School of Economics)

Abstract

Dimensionality is a major concern in the analysis of large data sets. There are various well-known dimension reduction methods with different strengths and weaknesses. In practical situations it is difficult to decide which method to use as different methods emphasize different structures in the data. Like ensemble methods in statistical learning, several dimension reduction methods can be combined using an extension of the Crone and Crosby distance, a weighted distance between the subspaces that allows to combine subspaces of different dimensions. Some natural choices of weights are considered in detail. Based on the weighted distance we discuss the concept of averages of subspaces and how to combine various dimension reduction methods. The performance of the weighted distances and the combining approach is illustrated via simulations and a real data example.

Suggested Citation

  • Eero Liski & Klaus Nordhausen & Hannu Oja & Anne Ruiz-Gazen, 2016. "Combining Linear Dimension Reduction Subspaces," Springer Books, in: Claudio Agostinelli & Ayanendranath Basu & Peter Filzmoser & Diganta Mukherjee (ed.), Recent Advances in Robust Statistics: Theory and Applications, pages 131-149, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-3643-6_7
    DOI: 10.1007/978-81-322-3643-6_7
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