On Efficient Computation of Tensor Subspace Kernels for Multi-dimensional Data

Bogusław Cyganek, Michał Woźniak

Abstract

In pattern classification problems kernel based methods and multi-dimensional methods have shown many advantages. However, since the well-known kernel functions are defined over one-dimensional vector spaces, it is not straightforward to join these two domains. Nevertheless, there are attempts to develop kernel functions which can directly operate with multi-dimensional patterns, such as the recently proposed kernels operating on Grassmannian manifolds. These are based on the concept of the principal angles between the orthogonal spaces rather than simple distances between vectors. An example is the chordal kernel operating on the subspaces obtained after tensor unfolding. However, a real problem with these methods are their high computational demands. In this paper we address the problem of efficient implementation of the chordal kernel for operation with tensors in classification tasks of real computer vision problems. The paper extends our previous works in this field. The proposed method was tested in the problems of object recognition in computer vision. The experiments show good accuracy and accelerated performance.

References

  1. 46, Part A, pp. 10-22 (2015) Demmel J.W.: Applied Numerical Linear Algebra. Siam (1997) Georgia Tech Face Database, 2013.
  2. Cambridge Universisty Press (2014) Lathauwer, de L.: Signal Processing Based on Multilinear Algebra. PhD dissertation, Katholieke Universiteit Leuven (1997) Lathauwer, de L., Moor de, B., Vandewalle, J.: A Multilinear Singular Value Decomposition. SIAM Journal of Matrix Analysis and Applications, Vol. 21, No. 4, 1253-1278 (2000) Liu C., Wei-sheng X., Qi-di W.: Tensorial Kernel Principal Component Analysis for Action Recognition.
  3. Mathematical Problems in Engineering, Vol. 2013, Article ID 816836, 16 pages, 2013.
  4. doi:10.1155/2013/816836.
  5. Marot J., Fossati C., Bourennane S.: About Advances in Tensor Data Denoising Methods. EURASIP Journal on Advances in Signal Processing, (2008) Meyer C.D.: Matrix Analysis and Applied Linear Algebra Book and Solutions Manual. SIAM (2001) Signoretto M., De Lathauwer L., Suykens J.A.K. : A kernel-based framework to tensorial data analysis.
Download


Paper Citation


in Harvard Style

Cyganek B. and Woźniak M. (2017). On Efficient Computation of Tensor Subspace Kernels for Multi-dimensional Data . In Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 5: VISAPP, (VISIGRAPP 2017) ISBN 978-989-758-226-4, pages 378-383. DOI: 10.5220/0006229003780383


in Bibtex Style

@conference{visapp17,
author={Bogusław Cyganek and Michał Woźniak},
title={On Efficient Computation of Tensor Subspace Kernels for Multi-dimensional Data},
booktitle={Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 5: VISAPP, (VISIGRAPP 2017)},
year={2017},
pages={378-383},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006229003780383},
isbn={978-989-758-226-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 5: VISAPP, (VISIGRAPP 2017)
TI - On Efficient Computation of Tensor Subspace Kernels for Multi-dimensional Data
SN - 978-989-758-226-4
AU - Cyganek B.
AU - Woźniak M.
PY - 2017
SP - 378
EP - 383
DO - 10.5220/0006229003780383