{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:42:56Z","timestamp":1760236976158,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,1,31]],"date-time":"2020-01-31T00:00:00Z","timestamp":1580428800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The growth of urban areas in recent years has motivated a large amount of new sensor applications in smart cities. At the centre of many new applications stands the goal of gaining insights into human activity. Scalable monitoring of urban environments can facilitate better informed city planning, efficient security, regular transport and commerce. A large part of monitoring capabilities have already been deployed; however, most rely on expensive motion imagery and privacy invading video cameras. It is possible to use a low-cost sensor alternative, which enables deep understanding of population behaviour such as the Global Positioning System (GPS) data. However, the automated analysis of such low dimensional sensor data, requires new flexible and structured techniques that can describe the generative distribution and time dynamics of the observation data, while accounting for external contextual influences such as time of day or the difference between weekend\/weekday trends. In this paper, we propose a novel time series analysis technique that allows for multiple different transition matrices depending on the data\u2019s contextual realisations all following shared adaptive observational models that govern the global distribution of the data given a latent sequence. The proposed approach, which we name Adaptive Input Hidden Markov model (AI-HMM) is tested on two datasets from different sensor types: GPS trajectories of taxis and derived vehicle counts in populated areas. We demonstrate that our model can group different categories of behavioural trends and identify time specific anomalies.<\/jats:p>","DOI":"10.3390\/s20030784","type":"journal-article","created":{"date-parts":[[2020,1,31]],"date-time":"2020-01-31T11:55:56Z","timestamp":1580471756000},"page":"784","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Probabilistic Modelling for Unsupervised Analysis of Human Behaviour in Smart Cities"],"prefix":"10.3390","volume":"20","author":[{"given":"Yazan","family":"Qarout","sequence":"first","affiliation":[{"name":"Department of Mathematics, Aston University, Birmingham B4 7ET, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yordan P.","family":"Raykov","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aston University, Birmingham B4 7ET, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Max A.","family":"Little","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Birmingham, Birmingham B15 2TT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"439","DOI":"10.12989\/sss.2010.6.5_6.439","article-title":"Structural health monitoring of a cable-stayed bridge using smart sensor technology: Deployment and evaluation","volume":"6","author":"Jang","year":"2010","journal-title":"Smart Struct. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"646953","DOI":"10.1155\/2014\/646953","article-title":"IoT-based smart garbage system for efficient food waste management","volume":"2014","author":"Hong","year":"2014","journal-title":"Sci. World J."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Castro, M., Jara, A.J., and Skarmeta, A.F. (2013, January 25\u201328). Smart lighting solutions for smart cities. Proceedings of the 2013 27th International Conference on Advanced Information Networking and Applications Workshops, Barcelona, Spain.","DOI":"10.1109\/WAINA.2013.254"},{"key":"ref_4","first-page":"57","article-title":"Application of IoT with haptics interface in the smart manufacturing industry","volume":"10","author":"Masse","year":"2019","journal-title":"Int. J. Comb. Optim. Probl. Inform."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"106501","DOI":"10.1016\/j.compeleceng.2019.106501","article-title":"Walking in a smart city: Investigating the gait stabilization effect for biometric recognition via wearable sensors","volume":"80","author":"Mecca","year":"2019","journal-title":"Comput. Electr. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1109\/MWC.2016.7721744","article-title":"Smartbuddy: Defining human behaviors using big data analytics in social internet of things","volume":"23","author":"Paul","year":"2016","journal-title":"IEEE Wirel. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1049\/iet-its.2018.5188","article-title":"Big Data for transportation and mobility: Recent advances, trends and challenges","volume":"12","author":"Ilardia","year":"2018","journal-title":"IET Intell. Transp. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Bhatti, F., Shah, M.A., Maple, C., and Islam, S.U. (2019). A novel internet of things-enabled accident detection and reporting system for smart city environments. Sensors, 19.","DOI":"10.3390\/s19092071"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1016\/j.future.2015.08.004","article-title":"Smart cyber society: Integration of capillary devices with high usability based on Cyber\u2013Physical System","volume":"56","author":"Ahmad","year":"2016","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Kanungo, A., Sharma, A., and Singla, C. (2014, January 6\u20138). Smart traffic lights switching and traffic density calculation using video processing. Proceedings of the 2014 Recent Advances in Engineering and Computational Sciences (RAECS), Chandigarh, India.","DOI":"10.1109\/RAECS.2014.6799542"},{"key":"ref_11","first-page":"187","article-title":"Automatic traffic density estimation and vehicle classification for traffic surveillance systems using neural networks","volume":"14","author":"Ozkurt","year":"2009","journal-title":"Math. Comput. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1109\/MIS.2018.223110904","article-title":"Camera placement based on vehicle traffic for better city security surveillance","volume":"33","author":"Ma","year":"2018","journal-title":"IEEE Intell. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Yuan, J., Zheng, Y., Xie, X., and Sun, G. (2011, January 21\u201324). Driving with knowledge from the physical world. Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining, San Diego, CA, USA.","DOI":"10.1145\/2020408.2020462"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Mehran, R., Oyama, A., and Shah, M. (2009, January 20\u201325). Abnormal crowd behavior detection using social force model. Proceedings of the 2009 IEEE Conference on Computer Vision and Pattern Recognition, Miami, FL, USA.","DOI":"10.1109\/CVPR.2009.5206641"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Yao, D., Zhang, C., Zhu, Z., Huang, J., and Bi, J. (2017, January 14\u201319). Trajectory clustering via deep representation learning. Proceedings of the 2017 International Joint Conference on Neural Networks (IJCNN), Anchorage, AK, USA.","DOI":"10.1109\/IJCNN.2017.7966345"},{"key":"ref_16","unstructured":"Wang, Y., Zhu, Y., He, Z., Yue, Y., and Li, Q. (2011). Challenges and Opportunities in Exploiting Large-Scale GPS Probe Data, HP Laboratories. Technical Report HPL-2011-109."},{"key":"ref_17","first-page":"20170700","article-title":"Stochastic modelling of urban structure","volume":"474","author":"Ellam","year":"2018","journal-title":"Proc. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Witayangkurn, A., Horanont, T., Sekimoto, Y., and Shibasaki, R. (2013, January 8\u201312). Anomalous event detection on large-scale gps data from mobile phones using hidden markov model and cloud platform. Proceedings of the 2013 ACM conference on Pervasive and ubiquitous computing adjunct publication, Zurich, Switzerland.","DOI":"10.1145\/2494091.2497352"},{"key":"ref_19","unstructured":"Fox, E., Sudderth, E.B., Jordan, M.I., and Willsky, A.S. (2008, January 8\u201310). Nonparametric Bayesian learning of switching linear dynamical systems. Proceedings of the Neural Information Processing Systems 2008, Vancouver, BC, Canada."},{"key":"ref_20","unstructured":"Suzuki, N., Hirasawa, K., Tanaka, K., Kobayashi, Y., Sato, Y., and Fujino, Y. (2007, January 7\u201310). Learning motion patterns and anomaly detection by human trajectory analysis. Proceedings of the 2007 IEEE International Conference on Systems, Man and Cybernetics, Montreal, QC, Canada."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1007\/s10618-012-0264-z","article-title":"Clustering daily patterns of human activities in the city","volume":"25","author":"Jiang","year":"2012","journal-title":"Data Min. Knowl. Discov."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/15230406.2015.1010585","article-title":"Personal mobility pattern mining and anomaly detection in the GPS era","volume":"43","author":"Shih","year":"2016","journal-title":"Cartogr. Geogr. Inf. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Mahadevan, V., Li, W., Bhalodia, V., and Vasconcelos, N. (2010, January 13\u201318). Anomaly detection in crowded scenes. Proceedings of the 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Francisco, CA, USA.","DOI":"10.1109\/CVPR.2010.5539872"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Rodriguez, M., Sivic, J., Laptev, I., and Audibert, J.Y. (2011, January 6\u201313). Data-driven crowd analysis in videos. Proceedings of the 2011 International Conference on Computer Vision, Barcelona, Spain.","DOI":"10.1109\/ICCV.2011.6126374"},{"key":"ref_25","unstructured":"Fu, Z., Hu, W., and Tan, T. (2005, January 14). Similarity based vehicle trajectory clustering and anomaly detection. Proceedings of the IEEE International Conference on Image Processing 2005, Genova, Italy."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1544","DOI":"10.1109\/TCSVT.2008.2005599","article-title":"Trajectory-based anomalous event detection","volume":"18","author":"Piciarelli","year":"2008","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_27","unstructured":"Frank, P. (2020, January 28). Chicago Regional Household Travel Inventory, Available online: https:\/\/www.cmap.illinois.gov\/documents\/10180\/77659\/TravelTracker_ModeShareReport20100604.pdf\/a67bf419-c05a-45c2-a127-a18d7984cd7d."},{"key":"ref_28","first-page":"32","article-title":"Geolife: A collaborative social networking service among user, location and trajectory","volume":"33","author":"Zheng","year":"2010","journal-title":"IEEE Data Eng. Bull."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Raykov, Y.P., Ozer, E., Dasika, G., Boukouvalas, A., and Little, M.A. (2016, January 12\u201316). Predicting room occupancy with a single passive infrared (PIR) sensor through behavior extraction. Proceedings of the 2016 ACM International Joint Conference on Pervasive and Ubiquitous Computing, Heidelberg, Germany.","DOI":"10.1145\/2971648.2971746"},{"key":"ref_30","unstructured":"Kunst, R.M. (2020, January 28). Vector Autoregressions. Available online: https:\/\/homepage.univie.ac.at\/robert.kunst\/var.pdf."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Beal, M.J., Ghahramani, Z., and Rasmussen, C.E. (2002, January 9\u201314). The infinite hidden Markov model. Proceedings of the Advances in Neural Information Processing Systems 2002, Vancouver, BC, Canada.","DOI":"10.7551\/mitpress\/1120.003.0079"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1566","DOI":"10.1198\/016214506000000302","article-title":"Hierarchical Dirichlet Processes","volume":"101","author":"Teh","year":"2006","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_33","unstructured":"Fox, E.B. (2009). Bayesian Nonparametric Learning of Complex Dynamical Phenomena. [Ph.D. Thesis, Massachusetts Institute of Technology]."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1017\/S0963548302005163","article-title":"Poisson\u2013Dirichlet and GEM invariant distributions for split-and-merge transformations of an interval partition","volume":"11","author":"Pitman","year":"2002","journal-title":"Comb. Probab. Comput."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Ihler, A., Hutchins, J., and Smyth, P. (2006, January 20\u201323). Adaptive event detection with time-varying poisson processes. Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Philadelphia, PA, USA.","DOI":"10.1145\/1150402.1150428"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Yuan, J., Zheng, Y., Zhang, C., Xie, W., Xie, X., Sun, G., and Huang, Y. (2010, January 2\u20135). T-drive: Driving directions based on taxi trajectories. Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems, San Jose, CA, USA.","DOI":"10.1145\/1869790.1869807"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Van Brummelen, G. (2012). Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, Princeton University Press.","DOI":"10.1515\/9781400844807"},{"key":"ref_38","unstructured":"Zhang, H.H. (2019, March 07). Beijing Still Struggling Deal Traffic Congestion. Available online: https:\/\/www.scmp.com\/news\/china\/article\/1298559\/beijing-still-struggling-deal-traffic-congestion."},{"key":"ref_39","first-page":"2579","article-title":"Visualizing data using t-SNE","volume":"9","author":"Maaten","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Singleton, A.D., Spielman, S., and Folch, D. (2017). Urban Analytics, Sage Publishing.","DOI":"10.4135\/9781529793703"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/3\/784\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:53:31Z","timestamp":1760172811000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/3\/784"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,31]]},"references-count":40,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["s20030784"],"URL":"https:\/\/doi.org\/10.3390\/s20030784","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,1,31]]}}}