A Dirichlet Process Gaussian State Machine Model for Change Detection in Transient Processes

References

• Alippi, C., and Roveri, M. (2008), “Just-in-Time Adaptive ClassifiersPart I: Detecting Nonstationary Changes,” IEEE Transactions on Neural Networks, 19, 1145–1153.
   Web of Science ®Google Scholar
• Bertuccelli, L. F., and How, J. P. (2008), “Estimation of Non-Stationary Markov Chain Transition Models,” in Proceedings of the 47th IEEE Conference on Decision and Control, IEEE, pp. 55–60.
   Google Scholar
• Bukkapatnam, S. T. S., and Cheng, C. (2010), “Forecasting the Evolution of Nonlinear and Nonstationary Systems Using Recurrence-Based Local Gaussian Process Models,” Physical Review E, 82, 056206.
   Web of Science ®Google Scholar
• Cheng, C., Sa-Ngasoongsong, A., Beyca, O., Le, T., Yang, H., Kong, Z., and Bukkapatnam, S. T. (2015), “Time Series Forecasting for Nonlinear and Non-Stationary Processes: A Review and Comparative Study,” IIE Transactions, 47, 1053–1071.
   Web of Science ®Google Scholar
• Choi, H., Ombao, H., and Ray, B. (2012), “Sequential Change-Point Detection Methods for Nonstationary Time Series,” Technometrics, 50, 40–52.
   Google Scholar
• Chordia, P., and Rae, A. (2008), “Real-Time Raag Recognition for Interactive Music,” in Proceedings of the 8th International Conference on New Interfaces for Musical Expression NIME08, Citeseer, pp. 331–334.
   Google Scholar
• Crommelin, D., and Vanden-Eijnden, E. (2006), “Fitting Timeseries by Continuous-Time Markov Chains: A Quadratic Programming Approach,” Journal of Computational Physics, 217, 782–805.
   Web of Science ®Google Scholar
• Cvitanovic, P., Artuso, R., Mainieri, R., Tanner, G., Vattay, G., and Whelan, N. (2005), Chaos: Classical and Quantum, Copenhagen, Denmark: Niels Bohr Institute.
   Google Scholar
• Dai, A. M., and Storkey, A. J. (2015), “The Supervised Hierarchical Dirichlet Process,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 37, 243–255.
   PubMed Web of Science ®Google Scholar
• Davis, R. A., Lee, T. C. M., and Rodriguez-Yam, G. A. (2006), “Structural Break Estimation for Nonstationary Time Series Models,” Journal of the American Statistical Association, 101, 223–239.
   Web of Science ®Google Scholar
• Érdi, P., and Lente, G. (2014), Stochastic Chemical Kinetics: Theory and (Mostly) Systems Biological Applications, New York: Springer.
   Google Scholar
• Fan, J., and Yao, Q. (2008), Nonlinear Time Series: Nonparametric and Parametric Methods, New York: Springer-Verlag.
   Google Scholar
• Genc, M. S., Karasu, I., Acikel, H. H., Akpolat, M. T., and Genc, M. (2012), “Low Reynolds Number Flows and Transition,” in Low Reynolds Number Aerodynamics and Transition, ed. MS Genc, Rijeka, Croatia: InTech, pp. 1–28.
   Google Scholar
• Genovese, C. R., and Wasserman, L. (2000), “Rates of Convergence for the Gaussian Mixture Sieve,” Annals of Statistics, 28, 1105–1127.
   Web of Science ®Google Scholar
• Ghazali, R., Hussain, A. J., Nawi, N. M., and Mohamad, B. (2009), “Non-Stationary and Stationary Prediction of Financial Time Series Using Dynamic Ridge Polynomial Neural Network,” Neurocomputing, 72, 2359–2367.
   Web of Science ®Google Scholar
• Ghosal, S., Ghosh, J. K., and Van Der Vaart, A. W. (2000), “Convergence Rates of Posterior Distributions,” Annals of Statistics, 28, 500–531.
   Web of Science ®Google Scholar
• Ghosal, S., and Van Der Vaart, A. W. (2001), “Entropies and Rates of Convergence for Maximum Likelihood and Bayes Estimation for Mixtures of Normal Densities,” Annals of Statistics, 29, 1233–1263.
   Web of Science ®Google Scholar
• Ghosal, S., Van Der Vaart, A. W. et al., (2007), “Convergence Rates of Posterior Distributions for Noniid Observations,” The Annals of Statistics, 35, 192–223.
   Web of Science ®Google Scholar
• Guo, H., Paynabar, K., and Jin, J. (2012), “Multiscale Monitoring of Autocorrelated Processes Using Wavelets Analysis,” IIE Transactions, 44, 312–326.
   Web of Science ®Google Scholar
• Hinrichs, N. S., and Pande, V. S. (2007), “Calculation of the Distribution of Eigenvalues and Eigenvectors in Markovian State Models for Molecular Dynamics,” The Journal of Chemical Physics, 126, 244101.
   PubMed Web of Science ®Google Scholar
• Hogg, R. V., and Craig, A. T. (1994), Introduction to Mathematical Statistics (5th ed.), Upper Saddle River, NJ: Prentice Hall.
   Google Scholar
• Isola, S. (1999), “Renewal Sequences and Intermittency,” Journal of Statistical Physics, 97, 263–280.
   Web of Science ®Google Scholar
• Katok, A., and Hasselblatt, B. (1997), Introduction to the Modern Theory of Dynamical Systems, Cambridge: Cambridge University Press.
   Google Scholar
• Kawabata, T., and Nishikawa, K. (2000), “Protein Structure Comparison Using the Markov Transition Model of Evolution,” Proteins: Structure, Function, and Bioinformatics, 41, 108–122.
   PubMed Web of Science ®Google Scholar
• Killick, R., Eckley, I., and Jonathan, P. (2013), “A Wavelet-Based Approach for Detecting Changes in Second Order Structure Within Nonstationary Time Series,” Electronic Journal of Statistics, 7, 1167–1183.
   Web of Science ®Google Scholar
• Kristan, M., Leonardis, A., and Skočaj, D. (2011), “Multivariate Online Kernel Density Estimation With Gaussian Kernels,” Pattern Recognition, 44, 2630–2642.
   Web of Science ®Google Scholar
• Lai, Y.-C. (1996), “Distinct Small-Distance Scaling Behavior of On-Off Intermittency in Chaotic Dynamical Systems,” Physical Review E, 54, 321.
   Web of Science ®Google Scholar
• Last, M., and Shumway, R. (2008), “Detecting Abrupt Changes in a Piecewise Locally Stationary Time Series,” Journal of Multivariate Analysis, 99, 191–214.
   PubMed Web of Science ®Google Scholar
• Liu, C.-S. (2007), “A Study of Type I Intermittency of a Circular Differential Equation Under a Discontinuous Right-Hand Side,” Journal of Mathematical Analysis and Applications, 331, 547–566.
   Web of Science ®Google Scholar
• Ma, J., Xu, L., and Jordan, M. I. (2000), “Asymptotic Convergence Rate of the EM Algorithm for Gaussian Mixtures,” Neural Computation, 12, 2881–2907.
   PubMed Web of Science ®Google Scholar
• MacEachern, S. N., and Müller, P. (1998), “Estimating Mixture of Dirichlet Process Models,” Journal of Computational and Graphical Statistics, 7, 223–238.
   Web of Science ®Google Scholar
• Montes De Oca, V., Jeske, D. R., Zhang, Q., Rendon, C., and Marvasti, M. (2010), “A Cusum Change-Point Detection Algorithm for Non-Stationary Sequences With Application to Data Network Surveillance,” Journal of Systems and Software, 83, 1288–1297.
   Web of Science ®Google Scholar
• Nakano, M., Le Roux, J., Kameoka, H., Ono, N., and Sagayama, S. (2011), “Infinite-State Spectrum Model for Music Signal Analysis,” in Proceedings of the 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, pp. 1972–1975.
   Google Scholar
• Neal, R. M. (2000), “Markov Chain Sampling Methods for Dirichlet Process Mixture Models,” Journal of Computational and Graphical Statistics, 9, 249–265.
   Web of Science ®Google Scholar
• Noé, F., and Fischer, S. (2008), “Transition Networks for Modeling the Kinetics of Conformational Change in Macromolecules,” Current Opinion in Structural Biology, 18, 154–162.
   PubMed Web of Science ®Google Scholar
• Purple, D. (2012), Machine Head, London, UK: EMI Records, Limited.
   Google Scholar
• Raghavan, V., and Veeravalli, V. V. (2010), “Quickest Change Detection of a Markov Process across a Sensor Array,” IEEE Transactions on Information Theory, 56, 1961–1981.
   Web of Science ®Google Scholar
• Rao, P. K., Bhushan, M. B., Bukkapatnam, S. T., Kong, Z., Byalal, S., Beyca, O. F., Fields, A., and Komanduri, R. (2014), “Process-Machine Interaction (PMI) Modeling and Monitoring of Chemical Mechanical Planarization (CMP) Process Using Wireless Vibration Sensors,” IEEE Transactions on Semiconductor Manufacturing, 27, 1–15.
   Web of Science ®Google Scholar
• Shen, W., Tokdar, S. T., and Ghosal, S. (2013), “Adaptive Bayesian Multivariate Density Estimation with Dirichlet Mixtures,” Biometrika, 100, 623–640.
   Web of Science ®Google Scholar
• Sturman, R., and Ashwin, P. (2004), “Internal Dynamics of Intermittency,” in Dynamics And Bifurcation of Patterns in Dissipative Systems, Singapore: World Scientific, pp. 357–372.
   Google Scholar
• Wang, X.-J. (1989), “Statistical Physics of Temporal Intermittency,” Physical Review A, 40, 6647.
   Web of Science ®Google Scholar
• Wang, Z., Bukkapatnam, S. T., Kumara, S. R., Kong, Z., and Katz, Z. (2014), “Change Detection in Precision Manufacturing Processes Under Transient Conditions,” CIRP Annals-Manufacturing Technology, 63, 449–452.
   Web of Science ®Google Scholar
• Webber Jr, C. L., and Marwan, N. (2007), Recurrence Quantification Analysis, London: Springer.
   Google Scholar
• Zbilut, J. P., Thomasson, N., and Webber, C. L. (2002), “Recurrence Quantification Analysis As a Tool for Nonlinear Exploration of Nonstationary Cardiac Signals,” Medical Engineering & Physics, 24, 53–60.
   PubMed Web of Science ®Google Scholar
• Zhang, M., Xu, S., and Fulcher, J. (2002), “Neuron-Adaptive Higher Order Neural-Network Models for Automated Financial Data Modeling,” IEEE Transactions on Neural Networks, 13, 188–204.
   PubMed Web of Science ®Google Scholar