Mean Polynomial Kernel and Its Application to Vector Sequence Recognition

Raissa RELATOR; Yoshihiro HIROHASHI; Eisuke ITO; Tsuyoshi KATO

doi:10.1587/transinf.E97.D.1855

Mean Polynomial Kernel and Its Application to Vector Sequence Recognition

Raissa RELATOR, Yoshihiro HIROHASHI, Eisuke ITO, Tsuyoshi KATO

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Classification tasks in computer vision and brain-computer interface research have presented several applications such as biometrics and cognitive training. However, like in any other discipline, determining suitable representation of data has been challenging, and recent approaches have deviated from the familiar form of one vector for each data sample. This paper considers a kernel between vector sets, the mean polynomial kernel, motivated by recent studies where data are approximated by linear subspaces, in particular, methods that were formulated on Grassmann manifolds. This kernel takes a more general approach given that it can also support input data that can be modeled as a vector sequence, and not necessarily requiring it to be a linear subspace. We discuss how the kernel can be associated with the Projection kernel, a Grassmann kernel. Experimental results using face image sequences and physiological signal data show that the mean polynomial kernel surpasses existing subspace-based methods on Grassmann manifolds in terms of predictive performance and efficiency.

Publication: IEICE TRANSACTIONS on Information Vol.E97-D No.7 pp.1855-1863

Publication Date: 2014/07/01

Publicized

Online ISSN: 1745-1361

DOI: 10.1587/transinf.E97.D.1855

Type of Manuscript: PAPER

Category: Pattern Recognition

Authors

Raissa RELATOR
  Gunma University
Yoshihiro HIROHASHI
  Gunma University
Eisuke ITO
  Gunma University
Tsuyoshi KATO
  Gunma University

Keyword

kernel methods, support vector machines, Grassmann distance and kernels, face recognition, brain-computer interface, vector sequence, binary classification

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Raissa RELATOR, Yoshihiro HIROHASHI, Eisuke ITO, Tsuyoshi KATO, "Mean Polynomial Kernel and Its Application to Vector Sequence Recognition" in IEICE TRANSACTIONS on Information, vol. E97-D, no. 7, pp. 1855-1863, July 2014, doi: 10.1587/transinf.E97.D.1855.
Abstract: Classification tasks in computer vision and brain-computer interface research have presented several applications such as biometrics and cognitive training. However, like in any other discipline, determining suitable representation of data has been challenging, and recent approaches have deviated from the familiar form of one vector for each data sample. This paper considers a kernel between vector sets, the mean polynomial kernel, motivated by recent studies where data are approximated by linear subspaces, in particular, methods that were formulated on Grassmann manifolds. This kernel takes a more general approach given that it can also support input data that can be modeled as a vector sequence, and not necessarily requiring it to be a linear subspace. We discuss how the kernel can be associated with the Projection kernel, a Grassmann kernel. Experimental results using face image sequences and physiological signal data show that the mean polynomial kernel surpasses existing subspace-based methods on Grassmann manifolds in terms of predictive performance and efficiency.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E97.D.1855/_p

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@ARTICLE{e97-d_7_1855,
author={Raissa RELATOR, Yoshihiro HIROHASHI, Eisuke ITO, Tsuyoshi KATO, },
journal={IEICE TRANSACTIONS on Information},
title={Mean Polynomial Kernel and Its Application to Vector Sequence Recognition},
year={2014},
volume={E97-D},
number={7},
pages={1855-1863},
abstract={Classification tasks in computer vision and brain-computer interface research have presented several applications such as biometrics and cognitive training. However, like in any other discipline, determining suitable representation of data has been challenging, and recent approaches have deviated from the familiar form of one vector for each data sample. This paper considers a kernel between vector sets, the mean polynomial kernel, motivated by recent studies where data are approximated by linear subspaces, in particular, methods that were formulated on Grassmann manifolds. This kernel takes a more general approach given that it can also support input data that can be modeled as a vector sequence, and not necessarily requiring it to be a linear subspace. We discuss how the kernel can be associated with the Projection kernel, a Grassmann kernel. Experimental results using face image sequences and physiological signal data show that the mean polynomial kernel surpasses existing subspace-based methods on Grassmann manifolds in terms of predictive performance and efficiency.},
keywords={},
doi={10.1587/transinf.E97.D.1855},
ISSN={1745-1361},
month={July},}

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TY - JOUR
TI - Mean Polynomial Kernel and Its Application to Vector Sequence Recognition
T2 - IEICE TRANSACTIONS on Information
SP - 1855
EP - 1863
AU - Raissa RELATOR
AU - Yoshihiro HIROHASHI
AU - Eisuke ITO
AU - Tsuyoshi KATO
PY - 2014
DO - 10.1587/transinf.E97.D.1855
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E97-D
IS - 7
JA - IEICE TRANSACTIONS on Information
Y1 - July 2014
AB - Classification tasks in computer vision and brain-computer interface research have presented several applications such as biometrics and cognitive training. However, like in any other discipline, determining suitable representation of data has been challenging, and recent approaches have deviated from the familiar form of one vector for each data sample. This paper considers a kernel between vector sets, the mean polynomial kernel, motivated by recent studies where data are approximated by linear subspaces, in particular, methods that were formulated on Grassmann manifolds. This kernel takes a more general approach given that it can also support input data that can be modeled as a vector sequence, and not necessarily requiring it to be a linear subspace. We discuss how the kernel can be associated with the Projection kernel, a Grassmann kernel. Experimental results using face image sequences and physiological signal data show that the mean polynomial kernel surpasses existing subspace-based methods on Grassmann manifolds in terms of predictive performance and efficiency.
ER -