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Hierarchical Visualization of Time-Series Data Using Switching Linear Dynamical Systems
October 2003 (vol. 25 no. 10)
pp. 1202-1214

Abstract—We propose a novel visualization algorithm for high-dimensional time-series data. In contrast to most visualization techniques, we do not assume consecutive data points to be independent. The basic model is a linear dynamical system which can be seen as a dynamic extension of a probabilistic principal component model. A further extension to a particular switching linear dynamical system allows a representation of complex data onto multiple and even a hierarchy of plots. Using sensible approximations based on expectation propagation, the projections can be performed in essentially the same order of complexity as their static counterpart. We apply our method on a real-world data set with sensor readings from a paper machine.

[1] M.E. Tipping and C.M. Bishop, Probabilistic Principal Component Analysis J. Royal Statistical Soci., Series B, vol. 61, no. 3, 1999.
[2] S. Roweis, EM Algorithms for PCA and SPCA Proc. Neural Information Processing Systems 10, 1997.
[3] C.M. Bishop and M.E. Tipping, “A Hierarchical Latent Variable Model for Data Visualization,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 3, pp. 281-293, Mar. 1998.
[4] U. Lerner and R. Parr, Inference in Hybrid Networks: Theoretical Limits and Practical Algorithms Proc. 17th Ann. Conf. Uncertainty in Artificial Intelligence (UAI 2001), 2001.
[5] T. Minka, Expectation Propagation for Approximate Bayesian Inference Proc. 17th Ann. Conf. Uncertainty in Artificial Intelligence (UAI 2001), 2001.
[6] P.J. Harrison and C.F. Stevens, Bayesian Forecasting J. Royal Statistical Soc., Series B, vol. 38, pp. 205-247, 1976.
[7] Y. Bar-Shalom and X.-R. Li, Estimation and Tracking: Principles, Techniques, and Software. Artech House, 1993.
[8] J. Whittaker, Graphical Models in Applied Multivariate Statistics. John Wiley&Sons, 1989.
[9] F. Kschischang, B. Frey, and H. Loeliger, Factor Graphs and the Sum-Product Algorithm IEEE Trans. Information Theory, vol. 47, no. 2, pp. 498-519, 2001.
[10] T. Minka, The EP Energy Function and Minimization Schemes technical report, MIT Media Lab, 2001.
[11] J. Yedidia, W. Freeman, and Y. Weiss, Generalized Belief Propagation Neural Information Processing Systems (NIPS 13), pp. 689-695, 2001.
[12] T. Heskes and O. Zoeter, Expectation Propagation for Approximate Inference in Dynamic Bayesian Networks Proc. 18th Ann. Conf. Uncertainty in Artificial Intelligence (UAI 2002), 2002.
[13] Y. Teh and M. Welling, The Unified Propagation and Scaling Algorithm Proc. Advances in Neural Information Processing Systems 14, 2002.
[14] E. Alhoniemi, J. Hollmén, O. Simula, and J. Vesanto, Process Monitoring and Modeling Using the Self-Organizing Map Integrated Computer Aided Eng., vol. 6, no. 1, 1999.
[15] C.M. Bishop, G.E. Hinton, and I.G.D. Strachan, GTM through Time Proc. IEE Int'l Conf. Artificial Neural Networks, pp. 111-116, 1997.
[16] P. Tino and I. Nabney, Hierarchical GTM: Constructing Localized Non-Linear Projection Manifolds in a Principled Way IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 5, pp. 639-656, May 2002.
[17] R.H. Shumway and D.S. Stoffer, Dynamic Linear Models with Switching J. Am. Statistical Assoc., vol. 86, pp. 763-769, 1991.
[18] C.J. Kim and C.R. Nelson, State-Space Models with Regime Switching. MIT Press, 1999.
[19] C. Carter and R. Kohn, Markov Chain Monte Carlo in Conditionally Gaussian State Space Models Biometrika, vol. 83, no. 3, pp. 589-601, 1996.
[20] A. Doucet, N. de Freitas, K. Murphy, and S. Russell, Rao-Blackwellized Particle Filtering for Dynamic Bayesian Networks Proc. 16th Ann. Conf. Uncertainty in Artificial Intelligence (UAI 2000), 2000.
[21] S. Roweis, L. Saul, and G. Hinton, Global Coordination of Local Linear Models Proc. Neural Information Processing Systems 14, 2001.
[22] M. Beal and Z. Ghahramani, Propagation Algorithms for Variational Bayesian Learning Proc. Advances in Neural Information Processing Systems 13, 2001.
[23] S. Frühwirth-Schnatter, Fully Bayesian Analysis of Switching Gaussian State Space Models Annals Inst. of Statistical Math., vol. 53, no. 1, pp. 31-49, 2001.
[24] T. Heskes and O. Zoeter, Generalized Belief Propagation for Approximate Inference in Hybrid Bayesian Networks Proc. Ninth Int'l Workshop Artificial Intelligence and Statistics, 2003.
[25] J. Durbin and S.J. Koopman, Time Series Analysis by State Space Methods. Oxford Univ. Press, 2001.

Index Terms:
Data visualization, time-series, latent variables, principal component analysis, switching linear dynamical systems, approximate inference.
Citation:
Onno Zoeter, Tom Heskes, "Hierarchical Visualization of Time-Series Data Using Switching Linear Dynamical Systems," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 10, pp. 1202-1214, Oct. 2003, doi:10.1109/TPAMI.2003.1233895
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