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Original Articles

Bayesian Nonparametric Joint Mixture Model for Clustering Spatially Correlated Time Series

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Pages 313-329 | Received 08 Jun 2018, Accepted 08 Jun 2019, Published online: 22 Jul 2019

References

  • Akaike, H. (1974), “A New Look at the Statistical Model Identification,” IEEE Transactions on Automatic Control, 19, 716–723. DOI: 10.1109/TAC.1974.1100705.
  • Andrieu, C., De Freitas, N., Doucet, A., and Jordan, M. I. (2003), “An Introduction to MCMC for Machine Learning,” Machine Learning, 50, 5–43. DOI: 10.1023/A:1020281327116.
  • Assunção, R., and Krainski, E. (2009), “Neighborhood Dependence in Bayesian Spatial Models,” Biometrical Journal, 51, 851–869. DOI: 10.1002/bimj.200900056.
  • Au, T. S., Duan, R., Kim, H., and Ma, G.-Q. (2010), “Spatiotemporal Event Detection in Mobility Network,” in 2010 IEEE International Conference on Data Mining, IEEE, pp. 28–37.
  • Bach, F. R., and Jordan, M. I. (2002), “Kernel Independent Component Analysis,” Journal of Machine Learning Research, 3, 1–48.
  • Balcan, M.-F., Liang, Y., and Gupta, P. (2014), “Robust Hierarchical Clustering,” The Journal of Machine Learning Research, 15, 3831–3871.
  • Banfield, J. D., and Raftery, A. E. (1993), “Model-Based Gaussian and Non-Gaussian Clustering,” Biometrics, 49, 803–821. DOI: 10.2307/2532201.
  • Bernard, J. A., Seidler, R. D., Hassevoort, K. M., Benson, B. L., Welsh, R. C., Wiggins, J. L., Jaeggi, S. M., Buschkuehl, M., Monk, C. S., Jonides, J., and Peltier, S. J. (2012), “Resting State Cortico-Cerebellar Functional Connectivity Networks: A Comparison of Anatomical and Self-Organizing Map Approaches,” Frontiers in Neuroanatomy, 6, 31. DOI: 10.3389/fnana.2012.00031.
  • Berrocal, V. J., Gelfand, A. E., and Holland, D. M. (2012), “Space-Time Data Fusion Under Error in Computer Model Output: An Application to Modeling Air Quality,” Biometrics, 68, 837–848. DOI: 10.1111/j.1541-0420.2011.01725.x.
  • Blei, D. M., and Jordan, M. I. (2006), “Variational Inference for Dirichlet Process Mixtures,” Bayesian Analysis, 1, 121–143. DOI: 10.1214/06-BA104.
  • Blei, D. M., Kucukelbir, A., and McAuliffe, J. D. (2017), “Variational Inference: A Review for Statisticians,” Journal of the American Statistical Association, 112, 859–877. DOI: 10.1080/01621459.2017.1285773.
  • Blekas, K., Nikou, C., Galatsanos, N., and Tsekos, N. V. (2007), “Curve Clustering With Spatial Constraints for Analysis of Spatiotemporal Data,” in 19th IEEE International Conference on Tools With Artificial Intelligence, 2007. ICTAI 2007 (Vol. 1), IEEE, pp. 529–535.
  • Bouveyron, C., and Brunet-Saumard, C. (2014), “Model-Based Clustering of High-Dimensional Data: A Review,” Computational Statistics & Data Analysis, 71, 52–78. DOI: 10.1016/j.csda.2012.12.008.
  • Chavent, M., Kuentz-Simonet, V., Labenne, A., and Saracco, J. (2018), “ClustGeo: An R Package for Hierarchical Clustering With Spatial Constraints,” Computational Statistics, 33, 1799–1822. DOI: 10.1007/s00180-018-0791-1.
  • Chen, X., Jin, Y., Qiang, S., Hu, W., and Jiang, K. (2015), “Analyzing and Modeling Spatio-Temporal Dependence of Cellular Traffic at City Scale,” in 2015 IEEE International Conference on Communications (ICC), IEEE, pp. 3585–3591.
  • Cheung, Y.-m., and Xu, L. (2001), “Independent Component Ordering in ICA Time Series Analysis,” Neurocomputing, 41, 145–152. DOI: 10.1016/S0925-2312(00)00358-1.
  • Coppi, R., D’Urso, P., and Giordani, P. (2010), “A Fuzzy Clustering Model for Multivariate Spatial Time Series,” Journal of Classification, 27, 54–88. DOI: 10.1007/s00357-010-9043-y.
  • Earnest, A., Morgan, G., Mengersen, K., Ryan, L., Summerhayes, R., and Beard, J. (2007), “Evaluating the Effect of Neighbourhood Weight Matrices on Smoothing Properties of Conditional Autoregressive (CAR) Models,” International Journal of Health Geographics, 6, 54–58. DOI: 10.1186/1476-072X-6-54.
  • Ewens, W. J. (1990), “Population Genetics Theory—The Past and the Future,” in Mathematical and Statistical Developments of Evolutionary Theory, Dordrecht: Springer, pp. 177–227.
  • Ferguson, T. S. (1973), “A Bayesian Analysis of Some Nonparametric Problems,” The Annals of Statistics, 1, 209–230. DOI: 10.1214/aos/1176342360.
  • Finkenstadt, B., Held, L., and Isham, V. (2006), Statistical Methods for Spatio-Temporal Systems, Boca Raton, FL: Chapman and Hall/CRC.
  • Foti, N., Xu, J., Laird, D., and Fox, E. (2014), “Stochastic Variational Inference for Hidden Markov Models,” in Advances in Neural Information Processing Systems, pp. 3599–3607.
  • Friston, K. J., Jezzard, P., and Turner, R. (1994), “Analysis of Functional MRI Time-Series,” Human Brain Mapping, 1, 153–171. DOI: 10.1002/hbm.460010207.
  • Gelfand, A. E., Kottas, A., and MacEachern, S. N. (2005), “Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing,” Journal of the American Statistical Association, 100, 1021–1035. DOI: 10.1198/016214504000002078.
  • Giraldo, R., Delicado, P., and Mateu, J. (2012), “Hierarchical Clustering of Spatially Correlated Functional Data,” Statistica Neerlandica, 66, 403–421. DOI: 10.1111/j.1467-9574.2012.00522.x.
  • Görür, D., and Rasmussen, C. E. (2010), “Dirichlet Process Gaussian Mixture Models: Choice of the Base Distribution,” Journal of Computer Science and Technology, 25, 653–664. DOI: 10.1007/s11390-010-9355-8.
  • Haggarty, R. A., Miller, C. A., and Scott, E. M. (2015), “Spatially Weighted Functional Clustering of River Network Data,” Journal of the Royal Statistical Society, Series C, 64, 491–506. DOI: 10.1111/rssc.12082.
  • Huang, B., Wu, B., and Barry, M. (2010), “Geographically and Temporally Weighted Regression for Modeling Spatio-Temporal Variation in House Prices,” International Journal of Geographical Information Science, 24, 383–401. DOI: 10.1080/13658810802672469.
  • Jiang, H., and Serban, N. (2012), “Clustering Random Curves Under Spatial Interdependence With Application to Service Accessibility,” Technometrics, 54, 108–119. DOI: 10.1080/00401706.2012.657106.
  • Johnson, S. C. (1967), “Hierarchical Clustering Schemes,” Psychometrika, 32, 241–254.
  • Jordan, M. I., Ghahramani, Z., Jaakkola, T. S., and Saul, L. K. (1999), “An Introduction to Variational Methods for Graphical Models,” Machine Learning, 37, 183–233. DOI: 10.1023/A:1007665907178.
  • Kao, Y., Reich, B., Storlie, C., and Anderson, B. (2015), “Malware Detection Using Nonparametric Bayesian Clustering and Classification Techniques,” Technometrics, 57, 535–546. DOI: 10.1080/00401706.2014.958916.
  • Kim, H., Duan, R., Kim, S., Lee, J., and Ma, G.-Q. (2019), “Spatial Cluster Detection in Mobility Networks: A Copula Approach,” Journal of the Royal Statistical Society, Series C, 68, 99–120. DOI: 10.1111/rssc.12307.
  • Kim, J., Lee, Y., and Kim, H. (2018), “Detection and Clustering of Mixed-Type Defect Patterns in Wafer Bin Maps,” IISE Transactions, 50, 99–111. DOI: 10.1080/24725854.2017.1386337.
  • Lee, D., Zhou, S., Zhong, X., Niu, Z., Zhou, X., and Zhang, H. (2014), “Spatial Modeling of the Traffic Density in Cellular Networks,” IEEE Wireless Communications, 21, 80–88. DOI: 10.1109/MWC.2014.6757900.
  • Li, Y., and Guan, Y. (2014), “Functional Principal Component Analysis of Spatiotemporal Point Processes With Applications in Disease Surveillance,” Journal of the American Statistical Association, 109, 1205–1215. DOI: 10.1080/01621459.2014.885434.
  • Liao, W., Chen, H., Yang, Q., and Lei, X. (2008), “Analysis of fMRI Data Using Improved Self-Organizing Mapping and Spatio-Temporal Metric Hierarchical Clustering,” IEEE Transactions on Medical Imaging, 27, 1472–1483.
  • MacKay, D. J. (1998), “Introduction to Gaussian Processes,” NATO ASI Series F Computer and Systems Sciences, 168, 133–166.
  • MacKay, D. J. (2003), Information Theory, Inference and Learning Algorithms, Cambridge: Cambridge University Press.
  • Paisley, J., Wang, C., and Blei, D. (2011), “The Discrete Infinite Logistic Normal Distribution for Mixed-Membership Modeling,” in Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, pp. 74–82.
  • Park, S., Kim, Y.-D., and Choi, S. (2013), “Hierarchical Bayesian Matrix Factorization With Side Information,” in IJCAI, pp. 1593–1599.
  • Paul, U., Subramanian, A. P., Buddhikot, M. M., and Das, S. R. (2011), “Understanding Traffic Dynamics in Cellular Data Networks,” in 2011 Proceedings IEEE INFOCOM, IEEE, pp. 882–890.
  • Rand, W. M. (1971), “Objective Criteria for the Evaluation of Clustering Methods,” Journal of the American Statistical Association, 66, 846–850. DOI: 10.1080/01621459.1971.10482356.
  • Rees, G. (1999), “Single Subject Epoch (Block) Auditory fMRI Activation Data,” available at http://www.fil.ion.ucl.ac.uk/spm/data/auditory/.
  • Rodríguez, A., and Dunson, D. B. (2011), “Nonparametric Bayesian Models Through Probit Stick-Breaking Processes,” Bayesian Analysis, 6, 145–177. DOI: 10.1214/11-BA605.
  • Sahu, S. K., Gelfand, A. E., and Holland, D. M. (2007), “High-Resolution Space-Time Ozone Modeling for Assessing Trends,” Journal of the American Statistical Association, 102, 1221–1234. DOI: 10.1198/016214507000000031.
  • Schwarz, G. (1978), “Estimating the Dimension of a Model,” The Annals of Statistics, 6, 461–464. DOI: 10.1214/aos/1176344136.
  • Simmonds, D. J., Pekar, J. J., and Mostofsky, S. H. (2008), “Meta-Analysis of Go/No-Go Tasks Demonstrating That fMRI Activation Associated With Response Inhibition Is Task-Dependent,” Neuropsychologia, 46, 224–232. DOI: 10.1016/j.neuropsychologia.2007.07.015.
  • Strehl, A., and Ghosh, J. (2002), “Cluster Ensembles—A Knowledge Reuse Framework for Combining Multiple Partitions,” Journal of Machine Learning Research, 3, 583–617.
  • Titsias, M. K. (2009), “Variational Learning of Inducing Variables in Sparse Gaussian Processes,” in AISTATS (Vol. 12), pp. 567–574.
  • Woolrich, M. W., Ripley, B. D., Brady, M., and Smith, S. M. (2001), “Temporal Autocorrelation in Univariate Linear Modeling of FMRI Data,” Neuroimage, 14, 1370–1386. DOI: 10.1006/nimg.2001.0931.
  • Wu, X., Zurita-Milla, R., and Kraak, M.-J. (2015), “Co-Clustering Geo-Referenced Time Series: Exploring Spatio-Temporal Patterns in Dutch Temperature Data,” International Journal of Geographical Information Science, 29, 624–642. DOI: 10.1080/13658816.2014.994520.
  • Zhang, L., Guindani, M., Versace, F., Engelmann, J. M., and Vannucci, M. (2016), “A Spatiotemporal Nonparametric Bayesian Model of Multi-Subject fMRI Data,” The Annals of Applied Statistics, 10, 638–666. DOI: 10.1214/16-AOAS926.
  • Zhang, L., Guindani, M., Versace, F., and Vannucci, M. (2014), “A Spatio-Temporal Nonparametric Bayesian Variable Selection Model of fMRI Data for Clustering Correlated Time Courses,” NeuroImage, 95, 162–175. DOI: 10.1016/j.neuroimage.2014.03.024.
  • Zhou, Z., Matteson, D. S., Woodard, D. B., Henderson, S. G., and Micheas, A. C. (2015), “A Spatio-Temporal Point Process Model for Ambulance Demand,” Journal of the American Statistical Association, 110, 6–15. DOI: 10.1080/01621459.2014.941466.

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