Skip to main content
SpringerLink
Log in

Analysis of Multilinear Subspaces Based on Geodesic Distance

  • Conference paper
  • First Online:
Book cover Computer Analysis of Images and Patterns (CAIP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10424))

Included in the following conference series:

Abstract

Tensor principal component analysis enables the efficient analysis of spatial textures of volumetric images and spatio-temporal changes of volumetric video sequences. To extend the subspace methods for analysis of linear subspaces, we are required to quantitatively evaluate the differences between multilinear subspaces. This discrimination of multilinear subspaces is achieved by computing the geodesic distance between tensor subspaces.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Lu, H., Plataniotis, K.N., Venetsanopoulos, A.N.: MPCA: multilinear principal component analysis of tensor objects. IEEE Trans. Neural Netw. 19(1), 18–39 (2008)

    Article  Google Scholar 

  2. Itoh, H., Imiya, A., Sakai, T.: Approximation of N-way principal component analysis for organ data. In: Chen, C.-S., Lu, J., Ma, K.-K. (eds.) ACCV 2016. LNCS, vol. 10118, pp. 16–31. Springer, Cham (2017). doi:10.1007/978-3-319-54526-4_2

    Chapter  Google Scholar 

  3. Cock, K.D., Moor, B.D.: Subspace angles between ARMA models. Syst. Contr. Lett. 46, 265–270 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Knyazev, A.V., Argentati, M.E.: Principal angles between subspaces in an a-based scalar product: algorithms and perturbation estimates. SIAM J. Sci. Comput 23(6), 2009–2041 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Wong, Y.-C.: Differential geometry of Grassmann manifolds. Proc. Natl. Acad. Sci. 57, 589–594 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  6. Absil, P.-A., Mahony, R., Sepulchre, R.: Riemannian geometry of Grassmann manifolds with a view on algorithmic computation. Acta Applicandae Mathematicae 80(2), 199–220 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hamm, J., Lee, D.D.: Grassmann discriminant analysis: a unifying view on subspace-based learning. In Proceedings of International Conference on Machine Learning, pp. 376–383 (2008)

    Google Scholar 

  8. Edelman, A., Arias, T.A., Smith, S.T.: The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl. 20(2), 303–353 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  9. Turaga, P., Veeraraghavan, A., Chellappa, R.: Statistical analysis on Stiefel and Grassmann manifolds with applications in computer vision. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8, June 2008

    Google Scholar 

  10. Andreopoulos, A., Tsotsos, J.K.: Efficient and generalizable statistical models of shape and appearance for analysis of cardiac MRI. Med. Image Anal. 12, 335–357 (2008)

    Article  Google Scholar 

  11. Cichoki, A., Zdunek, R., Phan, A.H., Amari, S.: Nonnegative Matrix and Tensor Factorizations. Wiley, Chichester (2009)

    Book  Google Scholar 

  12. Lathauwer, L.D., Moor, B.D., Vandewalle, J.: On the best rank-1 and rank-(\(r_1, r_2, r_n\)) approximation of higher-order tensors. SIAM J. Matrix Anal. Appl. 21(4), 1324–1342 (2000)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Informatics, Nagoya University, Nagoya, Japan

    Hayato Itoh

  2. Graduate School of Advanced Integration Science, Chiba University, Chiba, Japan

    Hayato Itoh

  3. Institute of Management and Information Technologies, Chiba University, Chiba, Japan

    Atsushi Imiya

  4. Graduate School of Engineering, Nagasaki University, Nagasaki, Japan

    Tomoya Sakai

Authors
  1. Hayato Itoh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Atsushi Imiya
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tomoya Sakai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hayato Itoh .

Editor information

Editors and Affiliations

  1. Linköping University, Linköping, Sweden

    Michael Felsberg

  2. Lund University, Lund, Sweden

    Anders Heyden

  3. University of Southern Denmark, Odense, Denmark

    Norbert Krüger

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Itoh, H., Imiya, A., Sakai, T. (2017). Analysis of Multilinear Subspaces Based on Geodesic Distance. In: Felsberg, M., Heyden, A., Krüger, N. (eds) Computer Analysis of Images and Patterns. CAIP 2017. Lecture Notes in Computer Science(), vol 10424. Springer, Cham. https://doi.org/10.1007/978-3-319-64689-3_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-64689-3_31

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-64688-6

  • Online ISBN: 978-3-319-64689-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation