Visualizing State of Time-Series Data by Supervised Gaussian Process Dynamical Models

Nobuhiko Yamaguchi

doi:10.20965/jaciii.2015.p0688

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JACIII Vol.19 No.5 pp. 688-696

doi: 10.20965/jaciii.2015.p0688

(2015)

Paper:

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Visualizing State of Time-Series Data by Supervised Gaussian Process Dynamical Models

Nobuhiko Yamaguchi

Faculty of Science and Engineering, Saga University
1 Honjo, Saga 840-8502, Japan

Received:

April 28, 2015

Accepted:

July 24, 2015

Published:

September 20, 2015

Keywords:

gaussian process dynamical models, time-series data, visualization, supervised learning

Abstract

Gaussian Process Dynamical Models (GPDMs) constitute a nonlinear dimensionality reduction technique that provides a probabilistic representation of time series data in terms of Gaussian process priors. In this paper, we report a method based on GPDMs to visualize the states of time-series data. Conventional GPDMs are unsupervised, and therefore, even when the labels of data are available, it is not possible to use this information. To overcome the problem, we propose a supervised GPDM (S-GPDM) that utilizes both the data and their corresponding labels. We demonstrate experimentally that the S-GPDM can locate related motion data closer together than conventional GPDMs.

Cite this article as:

N. Yamaguchi, “Visualizing State of Time-Series Data by Supervised Gaussian Process Dynamical Models,” J. Adv. Comput. Intell. Intell. Inform., Vol.19 No.5, pp. 688-696, 2015.

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References

[1] G. Box and G. Jenkins, “Time Series Analysis: Forecasting and Control,” Wiley, 2008.
[2] J. Hamilton, “Time Series Analysis,” Princeton University Press, 1994.
[3] T. Kohonen, M. Schroeder, and T. Huang, “Self-Organizing Maps,” Springer-Verlag, 2001.
[4] N. Lawrence, “Gaussian process latent variable models for visualisation of high dimensional data,” Advances in Neural Information Processing Systems, Vol.16, pp. 329-336, 2004.
[5] J. Wang, D. Fleet, and A. Hertzmann, “Gaussian process dynamical models,” Advances in Neural Information Processing Systems, Vol.18, pp. 1441-1448, 2005.
[6] W. Fan and N. Bouguila, “Generating Video Textures by PPCA and Gaussian Process Dynamical Model,” Proc. of the 14th Iberoamerican Conf. on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications, pp. 801-808, 2009.
[7] N. Gamage, Y. Kuang, R. Akmeliawati, and S. Demidenko, “Gaussian Process Dynamical Models for hand gesture interpretation in Sign Language,” Pattern Recognition Letters, Vol.32, No.15, pp. 2009-2014, 2011.
[8] J. Wang, D. Fleet, and A. Hertzmann, “Gaussian Process Dynamical Models for Human Motion,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol.30, No.2, pp. 283-298, 2008.
[9] J. Wang, Y. Yin, and H. Man, “Multiple Human Tracking Using Particle Filter with Gaussian Process Dynamical Model,” EURASIP J. on Image and Video Processing, 2008.
[10] X. Gao, X. Wang, D. Tao, and X. Li, “Supervised Gaussian Process Latent Variable Model for Dimensionality Reduction,” IEEE Trans. on Systems, Man, and Cybernetics, Part B (Cybernetic), Vol.41, No.2, pp. 425-434, 2010.
[11] “CMU Graphics Lab Motion Capture Database,”
http://mocap.cs.cmu.edu/.
[12] C. Rasmussen and C. Williams, “Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning),” MIT Press, 2005.
[13] M. Moller, “A Scaled Conjugate Gradient Algorithm for Fast Supervised Learning,” Neural Networks, Vol.6, No.4, pp. 525-533, 1993.
[14] R. Urtasun, D. Fleet, and P. Fua, “3D People Tracking with Gaussian Process Dynamical Models,” IEEE Computer Society Conf. on Computer Vision and Pattern Recognition, pp. 238-245, 2006.
[15] N. Lawrence, M. Seeger, and R. Herbrich, “Fast Sparse Gaussian Process Methods: The Informative Vector Machine,” Advances in Neural Information Processing Systems, Vol.15, pp. 625-632, 2003.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] G. Box and G. Jenkins, “Time Series Analysis: Forecasting and Control,” Wiley, 2008.

[2] [2] J. Hamilton, “Time Series Analysis,” Princeton University Press, 1994.

[3] [3] T. Kohonen, M. Schroeder, and T. Huang, “Self-Organizing Maps,” Springer-Verlag, 2001.

[4] [4] N. Lawrence, “Gaussian process latent variable models for visualisation of high dimensional data,” Advances in Neural Information Processing Systems, Vol.16, pp. 329-336, 2004.

[5] [5] J. Wang, D. Fleet, and A. Hertzmann, “Gaussian process dynamical models,” Advances in Neural Information Processing Systems, Vol.18, pp. 1441-1448, 2005.

[6] [6] W. Fan and N. Bouguila, “Generating Video Textures by PPCA and Gaussian Process Dynamical Model,” Proc. of the 14th Iberoamerican Conf. on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications, pp. 801-808, 2009.

[7] [7] N. Gamage, Y. Kuang, R. Akmeliawati, and S. Demidenko, “Gaussian Process Dynamical Models for hand gesture interpretation in Sign Language,” Pattern Recognition Letters, Vol.32, No.15, pp. 2009-2014, 2011.

[8] [8] J. Wang, D. Fleet, and A. Hertzmann, “Gaussian Process Dynamical Models for Human Motion,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol.30, No.2, pp. 283-298, 2008.

[9] [9] J. Wang, Y. Yin, and H. Man, “Multiple Human Tracking Using Particle Filter with Gaussian Process Dynamical Model,” EURASIP J. on Image and Video Processing, 2008.

[10] [10] X. Gao, X. Wang, D. Tao, and X. Li, “Supervised Gaussian Process Latent Variable Model for Dimensionality Reduction,” IEEE Trans. on Systems, Man, and Cybernetics, Part B (Cybernetic), Vol.41, No.2, pp. 425-434, 2010.

[11] [11] “CMU Graphics Lab Motion Capture Database,”
http://mocap.cs.cmu.edu/.

[12] [12] C. Rasmussen and C. Williams, “Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning),” MIT Press, 2005.

[13] [13] M. Moller, “A Scaled Conjugate Gradient Algorithm for Fast Supervised Learning,” Neural Networks, Vol.6, No.4, pp. 525-533, 1993.

[14] [14] R. Urtasun, D. Fleet, and P. Fua, “3D People Tracking with Gaussian Process Dynamical Models,” IEEE Computer Society Conf. on Computer Vision and Pattern Recognition, pp. 238-245, 2006.

[15] [15] N. Lawrence, M. Seeger, and R. Herbrich, “Fast Sparse Gaussian Process Methods: The Informative Vector Machine,” Advances in Neural Information Processing Systems, Vol.15, pp. 625-632, 2003.