# Probabilistic Modelling for Unsupervised Analysis of Human Behaviour in Smart Cities

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## Abstract

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## 1. Introduction

- We develop an extension of the ubiquitous Hidden Markov model, which can robustly segment different behaviours in monitoring applications while accounting for present contextual factors.
- We have derived a principled framework for inference in the developed AI-HMM approach.
- We have shown the particularly suitability of the nonparametric switching autoregressive model for analysis of GPS and traffic count data.

## 2. Related Work

## 3. Dynamic Time Series Modelling

#### 3.1. Vector Autoregressive Model (VAR)

#### 3.2. Autoregressive Infinite Hidden Markov Model (AR-iHMM)

## 4. Adaptive Input Infinite Hidden Markov Model (AI-iHMM)

#### 4.1. Model Specification

#### 4.2. Inference

## 5. Modelling With Fixed Inputs

#### 5.1. Dodgers Loop Sensor Dataset

#### 5.2. T-Drive Dataset

#### 5.2.1. Data Preprocessing

#### 5.2.2. AI-HMM Modelling with Predefined Input $\tau $

## 6. Adaptive Input

## 7. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AR | Autoregressive |

AI-HMM | Adaptive Input Hidden Markov Model |

AR-iHMM | Autoregressive infinite Hidden Markov Model |

CRHTI | Chicago Regional Household Travel Inventory |

DP | Dirichlet Process |

FF-BS | Forward Filtering Backward Sampling |

GEM | Griffiths, Engen and McCloskey |

GPS | Global Positioning System |

GRU | Gated Recurrent Unit |

HDP-HMM | Hierarchical Dirichlet Process Hidden Markov Model |

HMM | Hidden Markov Model |

iHMM | infinite Hidden Markov Model |

IQR | interquartile Range |

LSTM | Long-Short Term Memory |

MCMC | Markov Chain Monte Carlo |

MLP | Multi-Layer Perceptron |

MNIW | Matrix-Normal Inverse-Wishart |

PC | Principal Component |

PCA | Principal Component Analysis |

PGM | Probabilistic Graphical Model |

tSNE | t-distributed Stochastic Neighbour Embedding |

VAR | Vector Autoregressive |

VAR-HMM | Vector Autoregressive Hidden Markov Model |

## References

- Jang, S.; Jo, H.; Cho, S.; Mechitov, K.; Rice, J.A.; Sim, S.H.; Jung, H.J.; Yun, C.B.; Spencer, B.F., Jr.; Agha, G. Structural health monitoring of a cable-stayed bridge using smart sensor technology: Deployment and evaluation. Smart Struct. Syst.
**2010**, 6, 439–459. [Google Scholar] [CrossRef][Green Version] - Hong, I.; Park, S.; Lee, B.; Lee, J.; Jeong, D.; Park, S. IoT-based smart garbage system for efficient food waste management. Sci. World J.
**2014**, 2014, 646953. [Google Scholar] [CrossRef] [PubMed] - Castro, M.; Jara, A.J.; Skarmeta, A.F. Smart lighting solutions for smart cities. In Proceedings of the 2013 27th International Conference on Advanced Information Networking and Applications Workshops, Barcelona, Spain, 25–28 March 2013; pp. 1374–1379. [Google Scholar]
- Masse, R.A.C.; Ochoa-Zezzatti, A.; García, V.; Mejía, J.; Gonzalez, S. Application of IoT with haptics interface in the smart manufacturing industry. Int. J. Comb. Optim. Probl. Inform.
**2019**, 10, 57–70. [Google Scholar] - De Marsico, M.; Mecca, A.; Barra, S. Walking in a smart city: Investigating the gait stabilization effect for biometric recognition via wearable sensors. Comput. Electr. Eng.
**2019**, 80, 106501. [Google Scholar] [CrossRef] - Paul, A.; Ahmad, A.; Rathore, M.M.; Jabbar, S. Smartbuddy: Defining human behaviors using big data analytics in social internet of things. IEEE Wirel. Commun.
**2016**, 23, 68–74. [Google Scholar] [CrossRef] - Torre-Bastida, A.I.; Del Ser, J.; Laña, I.; Ilardia, M.; Bilbao, M.N.; Campos-Cordobés, S. Big Data for transportation and mobility: Recent advances, trends and challenges. IET Intell. Transp. Syst.
**2018**, 12, 742–755. [Google Scholar] [CrossRef] - Bhatti, F.; Shah, M.A.; Maple, C.; Islam, S.U. A novel internet of things-enabled accident detection and reporting system for smart city environments. Sensors
**2019**, 19, 2071. [Google Scholar] [CrossRef] [PubMed][Green Version] - Ahmad, A.; Paul, A.; Rathore, M.M.; Chang, H. Smart cyber society: Integration of capillary devices with high usability based on Cyber–Physical System. Future Gener. Comput. Syst.
**2016**, 56, 493–503. [Google Scholar] [CrossRef] - Kanungo, A.; Sharma, A.; Singla, C. Smart traffic lights switching and traffic density calculation using video processing. In Proceedings of the 2014 Recent Advances in Engineering and Computational Sciences (RAECS), Chandigarh, India, 6–8 March 2014; pp. 1–6. [Google Scholar]
- Ozkurt, C.; Camci, F. Automatic traffic density estimation and vehicle classification for traffic surveillance systems using neural networks. Math. Comput. Appl.
**2009**, 14, 187–196. [Google Scholar] [CrossRef][Green Version] - Ma, X.; He, Y.; Luo, X.; Li, J.; Zhao, M.; An, B.; Guan, X. Camera placement based on vehicle traffic for better city security surveillance. IEEE Intell. Syst.
**2018**, 33, 49–61. [Google Scholar] [CrossRef][Green Version] - Yuan, J.; Zheng, Y.; Xie, X.; Sun, G. Driving with knowledge from the physical world. In Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining, San Diego, CA, USA, 21–24 August 2011; pp. 316–324. [Google Scholar]
- Mehran, R.; Oyama, A.; Shah, M. Abnormal crowd behavior detection using social force model. In Proceedings of the 2009 IEEE Conference on Computer Vision and Pattern Recognition, Miami, FL, USA, 20–25 June 2009; pp. 935–942. [Google Scholar]
- Yao, D.; Zhang, C.; Zhu, Z.; Huang, J.; Bi, J. Trajectory clustering via deep representation learning. In Proceedings of the 2017 International Joint Conference on Neural Networks (IJCNN), Anchorage, AK, USA, 14–19 May 2017; pp. 3880–3887. [Google Scholar]
- Wang, Y.; Zhu, Y.; He, Z.; Yue, Y.; Li, Q. Challenges and Opportunities in Exploiting Large-Scale GPS Probe Data; Technical Report HPL-2011-109; HP Laboratories: Palo Alto, CA, USA, 21 July 2011. [Google Scholar]
- Ellam, L.; Girolami, M.; Pavliotis, G.; Wilson, A. Stochastic modelling of urban structure. Proc. R. Soc. A Math. Phys. Eng. Sci.
**2018**, 474, 20170700. [Google Scholar] [CrossRef] [PubMed][Green Version] - Witayangkurn, A.; Horanont, T.; Sekimoto, Y.; Shibasaki, R. Anomalous event detection on large-scale gps data from mobile phones using hidden markov model and cloud platform. In Proceedings of the 2013 ACM conference on Pervasive and ubiquitous computing adjunct publication, Zurich, Switzerland, 8–12 September 2013; pp. 1219–1228. [Google Scholar]
- Fox, E.; Sudderth, E.B.; Jordan, M.I.; Willsky, A.S. Nonparametric Bayesian learning of switching linear dynamical systems. In Proceedings of the Neural Information Processing Systems 2008, Vancouver, BC, Canada, 8–10 December 2008; pp. 457–464. [Google Scholar]
- Suzuki, N.; Hirasawa, K.; Tanaka, K.; Kobayashi, Y.; Sato, Y.; Fujino, Y. Learning motion patterns and anomaly detection by human trajectory analysis. In Proceedings of the 2007 IEEE International Conference on Systems, Man and Cybernetics, Montreal, QC, Canada, 7–10 October 2007; pp. 498–503. [Google Scholar]
- Jiang, S.; Ferreira, J.; González, M.C. Clustering daily patterns of human activities in the city. Data Min. Knowl. Discov.
**2012**, 25, 478–510. [Google Scholar] [CrossRef][Green Version] - Shih, D.H.; Shih, M.H.; Yen, D.C.; Hsu, J.H. Personal mobility pattern mining and anomaly detection in the GPS era. Cartogr. Geogr. Inf. Sci.
**2016**, 43, 55–67. [Google Scholar] [CrossRef] - Mahadevan, V.; Li, W.; Bhalodia, V.; Vasconcelos, N. Anomaly detection in crowded scenes. In Proceedings of the 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Francisco, CA, USA, 13–18 June 2010; pp. 1975–1981. [Google Scholar]
- Rodriguez, M.; Sivic, J.; Laptev, I.; Audibert, J.Y. Data-driven crowd analysis in videos. In Proceedings of the 2011 International Conference on Computer Vision, Barcelona, Spain, 6–13 November 2011; pp. 1235–1242. [Google Scholar]
- Fu, Z.; Hu, W.; Tan, T. Similarity based vehicle trajectory clustering and anomaly detection. In Proceedings of the IEEE International Conference on Image Processing 2005, Genova, Italy, 14 Septemer 2005. [Google Scholar]
- Piciarelli, C.; Micheloni, C.; Foresti, G.L. Trajectory-based anomalous event detection. IEEE Trans. Circuits Syst. Video Technol.
**2008**, 18, 1544–1554. [Google Scholar] [CrossRef] - Frank, P. Chicago Regional Household Travel Inventory. Available online: https://www.cmap.illinois.gov/documents/10180/77659/TravelTracker_ModeShareReport20100604.pdf/a67bf419-c05a-45c2-a127-a18d7984cd7d (accessed on 28 January 2020).
- Zheng, Y.; Xie, X.; Ma, W.Y. Geolife: A collaborative social networking service among user, location and trajectory. IEEE Data Eng. Bull.
**2010**, 33, 32–39. [Google Scholar] - Raykov, Y.P.; Ozer, E.; Dasika, G.; Boukouvalas, A.; Little, M.A. Predicting room occupancy with a single passive infrared (PIR) sensor through behavior extraction. In Proceedings of the 2016 ACM International Joint Conference on Pervasive and Ubiquitous Computing, Heidelberg, Germany, 12–16 September 2016; pp. 1016–1027. [Google Scholar]
- Kunst, R.M. Vector Autoregressions. Available online: https://homepage.univie.ac.at/robert.kunst/var.pdf (accessed on 28 January 2020).
- Beal, M.J.; Ghahramani, Z.; Rasmussen, C.E. The infinite hidden Markov model. In Proceedings of the Advances in Neural Information Processing Systems 2002, Vancouver, BC, Canada, 9–14 December 2002; pp. 577–584. [Google Scholar]
- Teh, Y.W.; Jordan, M.I.; Beal, M.J.; Blei, D.M. Hierarchical Dirichlet Processes. J. Am. Stat. Assoc.
**2006**, 101, 1566–1581. [Google Scholar] [CrossRef] - Fox, E.B. Bayesian Nonparametric Learning of Complex Dynamical Phenomena. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, USA, 2009. [Google Scholar]
- Pitman, J. Poisson–Dirichlet and GEM invariant distributions for split-and-merge transformations of an interval partition. Comb. Probab. Comput.
**2002**, 11, 501–514. [Google Scholar] [CrossRef][Green Version] - Ihler, A.; Hutchins, J.; Smyth, P. Adaptive event detection with time-varying poisson processes. In Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Philadelphia, PA, USA, 20–23 August 2006; pp. 207–216. [Google Scholar]
- Yuan, J.; Zheng, Y.; Zhang, C.; Xie, W.; Xie, X.; Sun, G.; Huang, Y. T-drive: Driving directions based on taxi trajectories. In Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems, San Jose, CA, USA, 2–5 November 2010; pp. 99–108. [Google Scholar]
- Van Brummelen, G. Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry; Princeton University Press: Princeton, NJ, USA, 2012; pp. 160–162. [Google Scholar]
- Zhang, H.H. Beijing Still Struggling Deal Traffic Congestion. Available online: https://www.scmp.com/news/china/article/1298559/beijing-still-struggling-deal-traffic-congestion (accessed on 7 March 2019).
- Maaten, L.; Hinton, G. Visualizing data using t-SNE. J. Mach. Learn. Res.
**2008**, 9, 2579–2605. [Google Scholar] - Singleton, A.D.; Spielman, S.; Folch, D. Urban Analytics; Sage Publishing: Thousand Oaks, CA, USA, 2017. [Google Scholar]

**Figure 1.**iHMM (top) and AR-iHMM (bottom) probabilistic graphical models. Mixing Parameters $\mathit{\beta}$ are used to sample the transition distribution ${\mathit{\pi}}_{k}$, which the state indicators $\mathbf{z}$ are sampled from. The observations ${\mathbf{y}}_{t}$ are generated from functions with parameters ${\mathsf{\Theta}}_{{z}_{t}}$ which are in turn sampled from base distribution H. The AR-iHMM differs such that there are autoregressive dependence between observations.

**Figure 2.**PGM of the AI-HMM structure. Observation ${\mathbf{y}}_{t}$ being dependent on the indicator variable ${z}_{t}$ and p previous observations, whereas ${z}_{t}$ is dependent on ${z}_{t-1}$ in addition to the semi-Markov feature ${\tau}_{t}$. Parameters $\mathit{\beta}$ are used to sample the transition distribution ${\mathit{\pi}}_{k}$ which the state indicators $\mathbf{z}$ are sampled from. The observations ${\mathbf{y}}_{t}$ are generated from functions with parameters ${\mathsf{\Theta}}_{{z}_{t}}$ which are in turn sampled from base distribution H.

**Figure 3.**Scatter plots for vehicular density counts on an average game day on a weekday (

**left**) and weekend (

**right**). The first two distinct peaks on the weekday represent the morning and afternoon traffic peaks respectively, whereas the sharp peaks around 23:00 on the weekday and on 16:30 on the weekend represent traffic caused by fans leaving the stadium after a baseball game.

**Figure 4.**Scatter plots for vehicular density counts. Each colour represents a specific state that the respective observations was clustered into. Morning and evening traffic peaks on weekdays are clustered into state 1 (blue) and state 3 (green), respectively. Traffic caused by evening baseball games near 23:00 (Wednesday, Friday and Saturday) have been clustered into state 6 (brown), whereas traffic peaks caused by afternoon games at about 16:30 (Sunday) were clustered into state 7 (pink).

**Figure 5.**Figure depicting the first four (PCs with the largest eigen values in the PCA analysis of the Dodgers loop sensor dataset). PC 2 capture the dynamics of the morning peak; PC 3 represents the sharp traffic rise due to the evening baseball game, which commonly occurs on weekdays and Saturdays; and PC 4 captures the dynamics of the weekend light midday traffic.

**Figure 6.**Results obtained from analysing 10 taxi trajectories using the novel AI-HMM framework (

**left**) and the GRU technique (

**right**). Each data point corresponds to a GPS observation where its colour represents the state to which it was assigned. The plots depict the longitude $\lambda $ against latitude l reconstructions of the movements of the taxi locations on a map.

**Figure 7.**Prediction of the value of ${\tau}_{t}$ corresponding to the taxi identity on the test. The top plot shows the sample labels, whereas the bottom plot shows the predicted ${\tau}_{t}$ values using the AI-HMM with an accuracy of 93%.

State | AI-HMM | GRU | ||||
---|---|---|---|---|---|---|

${\mathit{v}}_{\mathit{median}}$ | ${\mathit{v}}_{\mathit{IQR}}$ | ${\mathit{h}}_{\mathit{prominent}}$ | ${\mathit{v}}_{\mathit{median}}$ | ${\mathit{v}}_{\mathit{IQR}}$ | ${\mathit{h}}_{\mathit{prominent}}$ | |

1 | 26 | 35 | 00:00–23:00 | 18 | 24 | 12:00–18:00 |

2 | 18 | 19 | 17:00–23:00 | 18 | 34 | 00:00–06:00 |

3 | 0 | 0 | 00:00–23:00 | 2147 | 7697 | 00:00–23:00 |

4 | 23 | 27 | 00:00–06:00 | 16 | 29 | 06:00–13:00 |

5 | 19 | 19 | 10:00–18:00 | 16 | 22 | 18:00–23:00 |

6 | 497 | 1336 | 00:00–23:00 | 186 | 176 | 00:00–23:00 |

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**MDPI and ACS Style**

Qarout, Y.; Raykov, Y.P.; Little, M.A. Probabilistic Modelling for Unsupervised Analysis of Human Behaviour in Smart Cities. *Sensors* **2020**, *20*, 784.
https://doi.org/10.3390/s20030784

**AMA Style**

Qarout Y, Raykov YP, Little MA. Probabilistic Modelling for Unsupervised Analysis of Human Behaviour in Smart Cities. *Sensors*. 2020; 20(3):784.
https://doi.org/10.3390/s20030784

**Chicago/Turabian Style**

Qarout, Yazan, Yordan P. Raykov, and Max A. Little. 2020. "Probabilistic Modelling for Unsupervised Analysis of Human Behaviour in Smart Cities" *Sensors* 20, no. 3: 784.
https://doi.org/10.3390/s20030784