An order fitting rule for optimal subspace averaging

I. Santamaria, L. L. Scharf, C. Peterson, M. Kirby, J. Francos

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

12 Scopus citations


The problem of estimating a low-dimensional subspace from a collection of experimentally measured subspaces arises in many applications of statistical signal processing. In this paper we address this problem, and give a solution for the average subspace that minimizes an extrinsic mean-squared error, defined by the squared Frobenius norm between projection matrices. The solution automatically returns the dimension of the optimal average subspace, which is the novel result of the paper. The proposed order fitting rule is based on thresholding the eigenvalues of the average projection matrix, and thus it is free of penalty terms or other tuning parameters commonly used by other rank estimation techniques. Several numerical examples demonstrate the usefulness and applicability of the proposed criterion, showing how the dimension of the average subspace captures the variability of the measured subspaces.

Original languageEnglish
Title of host publication2016 19th IEEE Statistical Signal Processing Workshop, SSP 2016
PublisherInstitute of Electrical and Electronics Engineers
ISBN (Electronic)9781467378024
StatePublished - 24 Aug 2016
Event19th IEEE Statistical Signal Processing Workshop, SSP 2016 - Palma de Mallorca, Spain
Duration: 25 Jun 201629 Jun 2016

Publication series

NameIEEE Workshop on Statistical Signal Processing Proceedings


Conference19th IEEE Statistical Signal Processing Workshop, SSP 2016
CityPalma de Mallorca


  • Grassmann manifold
  • Subspace signal processing
  • extrinsic mean
  • flag manifold
  • order-fitting
  • subspace averaging

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Applied Mathematics
  • Signal Processing
  • Computer Science Applications


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