# 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

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#### 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