Visualizing States of Time-Series Data by Autoregressive Gaussian Process Dynamical Models
Faculty of Science and Engineering, Saga University
1 Honjo, Saga 840-8502, Japan
Gaussian process dynamical models (GPDMs) are used for nonlinear dimensionality reduction in time series by means of Gaussian process priors. An extension of GPDMs is proposed for visualizing the states of time series. The conventional GPDM approach associates a state with an observation value. Therefore, observations changing over time cannot be represented by a single state. Consequently, the resulting visualization of state transition is difficult to understand, as states change when the observation values change. To overcome this issue, autoregressive GPDMs, called ARGPDMs, are proposed. They associate a state with a vector autoregressive (VAR) model. Therefore, observations changing over time can be represented by a single state. The resulting visualization is easier to understand, as states change only when the VAR model changes. We demonstrate experimentally that the ARGPDM approach provides better visualization compared with conventional GPDMs.
-  G. Box and G. Jenkins, “Time Series Analysis: Forecasting and Control,” Wiley, 2008.
-  J. Hamilton, “Time Series Analysis,” Princeton University Press, 1994.
-  T. Kohonen, M. Schroeder, and T. Huang, eds., “Self-Organizing Maps,” Springer-Verlag, 2001.
-  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.
-  J. Wang, D. Fleet, and A. Hertzmann, “Gaussian process dynamical models,” Advances in Neural Information Processing Systems, Vol.18, pp. 1441-1448, 2005.
-  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.
-  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.
-  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.
-  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.
-  C. Kim and C. Nelson, “State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications,” MIT Press, 1999.
-  C. Rasmussen and C. Williams, “Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning),” MIT Press, 2005.
-  M. Møller, “A Scaled Conjugate Gradient Algorithm for Fast Supervised Learning,” Neural Networks, Vol.6, No.4, pp. 525-533, 1993.
-  R. Urtasun, D. Fleet, and P. Fua, “3D People Tracking with Gaussian Process Dynamical Models,” 2006 IEEE Computer Society Conf. on Computer Vision and Pattern Recognition, pp. 238-245, 2006.
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