# Modeling Spatio-Temporal Evolution of Urban Crowd Flows

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Methodology

#### 3.1. Urban Lattice

#### 3.1.1. Spatial Partition

#### 3.1.2. Crowd Level

- Speed$$\begin{array}{c}\hfill {v}_{x,y}^{t}=\frac{{\sum}_{({x}^{{t}_{i}^{\prime}},{y}^{{t}_{i}^{\prime}})\in \overline{(x,y)}}{v}^{{t}_{i}^{\prime}}}{{\sum}_{({x}^{{t}_{i}^{\prime}},{y}^{{t}_{i}^{\prime}})\in \overline{(x,y)}}1}.\end{array}$$
- Volume (or density)$$\begin{array}{c}\hfill i{n}_{x,y}^{t}=|\{{\mathbb{P}}^{t}:({x}^{{t}_{1}^{\prime}},{y}^{{t}_{1}^{\prime}})\notin \overline{(x,y)},({x}^{{t}_{L}^{\prime}},{y}^{{t}_{L}^{\prime}})\in \overline{(x,y)}\}|,\end{array}$$$$\begin{array}{c}\hfill ou{t}_{x,y}^{t}=|\{{\mathbb{P}}^{t}:({x}^{{t}_{1}^{\prime}},{y}^{{t}_{1}^{\prime}})\in \overline{(x,y)},({x}^{{t}_{L}^{\prime}},{y}^{{t}_{L}^{\prime}})\notin \overline{(x,y)}\}|,\end{array}$$$$\begin{array}{c}\hfill pas{s}_{x,y}^{t}=|\{{\mathbb{P}}^{t}:({x}^{{t}_{1}^{\prime}},{y}^{{t}_{1}^{\prime}})\notin \overline{(x,y)},\exists ({x}^{{t}_{i}^{\prime}},{y}^{{t}_{i}^{\prime}})\in \overline{(x,y)},({x}^{{t}_{L}^{\prime}},{y}^{{t}_{L}^{\prime}})\notin \overline{(x,y)}\}|,\end{array}$$$$\begin{array}{c}\hfill sta{y}_{x,y}^{t}=|\{{\mathbb{P}}^{t}:({x}^{{t}_{1}^{\prime}},{y}^{{t}_{1}^{\prime}})\in \overline{(x,y)},({x}^{{t}_{L}^{\prime}},{y}^{{t}_{L}^{\prime}})\in \overline{(x,y)}\}|,\end{array}$$
- Flux$$\begin{array}{c}\hfill {f}_{x,y}^{t}=i{n}_{x,y}^{t}+ou{t}_{x,y}^{t}+pas{s}_{x,y}^{t}+sta{y}_{x,y}^{t}.\end{array}$$
- Crowd rate$$\begin{array}{c}\hfill {s}_{x,y}^{t}=\frac{i{n}_{x,y}^{t}+sta{y}_{x,y}^{t}}{i{n}_{x,y}^{t}+ou{t}_{x,y}^{t}+pas{s}_{x,y}^{t}+sta{y}_{x,y}^{t}}.\end{array}$$

- Free flow: ${I}_{x,y}^{t}=0$ for ${v}_{x,y}^{t}>\u03f5$;
- Slowed flow: ${I}_{x,y}^{t}=1$ for ${v}_{x,y}^{t}\le \u03f5$ and ${s}_{x,y}^{t}<\lambda $;
- Crowded flow: ${I}_{x,y}^{t}=2$ for ${v}_{x,y}^{t}\le \u03f5$ and ${s}_{x,y}^{t}\ge \lambda $;

#### 3.2. Urban Crowd Hotspot

#### 3.2.1. Connectivity

#### 3.2.2. Connected Component

#### 3.2.3. Crowd Region

#### 3.3. Spatio-Temporal Evolution

#### 3.3.1. Mask Region

#### 3.3.2. Crowd Morphology

Algorithm 1: Morphological analysis. |

#### 3.3.3. Nested Crowd Evolution

Algorithm 2: Nested morphological analysis. |

## 4. Case Study

#### 4.1. Scenario I: Simulation

#### 4.1.1. Synthetic Data

#### 4.1.2. Pattern Assignments

#### 4.2. Scenario II: Real Observation

#### 4.2.1. Case Study Area

#### 4.2.2. Citywide Crowd Hotspots

#### 4.2.3. Morphological Evolutionary Patterns

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Barthelemy, M. A global take on congestion in urban areas. Environ. Plan. B Plan. Des.
**2016**, 43, 800–804. [Google Scholar] [CrossRef] [Green Version] - Batty, M. The New Science of Cities; MIT Press: Cambridge, MA, USA, 2013. [Google Scholar]
- Kerner, B.S. Breakdown in Traffic Networks: Fundamentals of Transportation Science; Springer: Berlin/Heidelberg, Germany, 2017. [Google Scholar]
- Liu, Y.; Liu, X.; Gao, S.; Gong, L.; Kang, C.; Zhi, Y.; Chi, G.; Shi, L. Social Sensing: A New Approach to Understanding Our Socioeconomic Environments. Ann. Assoc. Am. Geogr.
**2015**, 105, 512–530. [Google Scholar] [CrossRef] - Zheng, Y.; Capra, L.; Wolfson, O.; Yang, H. Urban Computing: Concepts, Methodologies, and Applications. ACM Trans. Intell. Syst. Technol.
**2014**, 5, 38. [Google Scholar] [CrossRef] - Kang, C.; Qin, K. Understanding Operation Behaviors of Taxicabs in Cities by Matrix Factorization. Comput. Environ. Urban Syst.
**2016**, 60, 79–88. [Google Scholar] [CrossRef] - Rao, A.M.; Rao, K.R. Measuring Urban Traffic Congestion-A Review. Int. J. Traffic Transp. Eng.
**2012**, 2, 286–305. [Google Scholar] - Stathopoulos, A.; Karlaftis, M.G. Modeling Duration of Urban Traffic Congestion. J. Transp. Eng.
**2002**, 128, 587–590. [Google Scholar] [CrossRef] - Sweet, M. Does Traffic Congestion Slow the Economy? J. Plan. Lit.
**2011**, 26, 391–404. [Google Scholar] [CrossRef] - Kan, Z.; Tang, L.; Kwan, M.P.; Ren, C.; Liu, D.; Li, Q. Traffic congestion analysis at the turn level using Taxis’ GPS trajectory data. Comput. Environ. Urban Syst.
**2019**, 74, 229–243. [Google Scholar] [CrossRef] - Zhang, J.; Zheng, Y.; Qi, D. Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction. In Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, San Francisco, CA, USA, 4–9 February 2017; pp. 1655–1661. [Google Scholar]
- Gidófalvi, G.; Yang, C. Scalable Detection of Traffic Congestion from Massive Floating Car Data Streams. In Proceedings of the 1st International ACM SIGSPATIAL Workshop on Smart Cities and Urban Analytics, Bellevue, WA, USA, 3–6 November 2015; ACM: New York, NY, USA, 2015; pp. 114–121. [Google Scholar] [CrossRef]
- Kaiser, M.S.; Lwin, K.T.; Mahmud, M.; Hajializadeh, D.; Chaipimonplin, T.; Sarhan, A.; Hossain, M.A. Advances in Crowd Analysis for Urban Applications Through Urban Event Detection. IEEE Trans. Intell. Transp. Syst.
**2017**, 19, 3092–3112. [Google Scholar] [CrossRef] [Green Version] - Maurin, B.; Masoud, O.; Papanikolopoulos, N.P. Tracking all traffic: Computer vision algorithms for monitoring vehicles, individuals, and crowds. IEEE Robot. Autom. Mag.
**2005**, 12, 29–36. [Google Scholar] [CrossRef] - Kang, C.; Liu, Y.; Ma, X.; Wu, L. Towards estimating urban population distributions from mobile call data. J. Urban Technol.
**2012**, 19, 3–21. [Google Scholar] [CrossRef] - Domínguez, D.R.; Redondo, R.P.D.; Vilas, A.F.; Khalifa, M.B. Sensing the city with Instagram: Clustering geolocated data for outlier detection. Expert Syst. Appl.
**2017**, 78, 319–333. [Google Scholar] [CrossRef] - Cheng, T.; Tanaksaranond, G.; Brunsdon, C.; Haworth, J. Exploratory visualisation of congestion evolutions on urban transport networks. Transp. Res. Part C Emerg. Technol.
**2013**, 36, 296–306. [Google Scholar] [CrossRef] [Green Version] - Ma, Y.; Lin, T.; Cao, Z.; Li, C.; Wang, F.; Chen, W. Mobility viewer: An Eulerian approach for studying urban crowd flow. IEEE Trans. Intell. Transp. Syst.
**2016**, 17, 2627–2636. [Google Scholar] [CrossRef] - Wu, F.; Zhu, M.; Wang, Q.; Zhao, X.; Chen, W.; Maciejewski, R. Spatial-temporal visualization of city-wide crowd movement. J. Vis.
**2017**, 20, 183–194. [Google Scholar] [CrossRef] - Wirz, M.; Franke, T.; Roggen, D.; Mitleton-Kelly, E.; Lukowicz, P.; Tröster, G. Probing crowd density through smartphones in city-scale mass gatherings. EPJ Data Sci.
**2013**, 2, 5. [Google Scholar] [CrossRef] [Green Version] - Calabrese, F.; Colonna, M.; Lovisolo, P.; Parata, D.; Ratti, C. Real-time urban monitoring using cell phones: A case study in Rome. IEEE Trans. Intell. Transp. Syst.
**2011**, 12, 141–151. [Google Scholar] [CrossRef] - Ben Khalifa, M.; Redondo, R.P.D.; Vilas, A.F.; Rodríguez, S.S. Identifying urban crowds using geo-located Social media data: A Twitter experiment in New York City. J. Intell. Inf. Syst.
**2017**, 48, 287–308. [Google Scholar] [CrossRef] - Zhu, X.; Guo, D. Mapping large spatial flow data with hierarchical clustering. Trans. GIS
**2014**, 18, 421–435. [Google Scholar] [CrossRef] - Chen, W.; Guo, F.; Wang, F.Y. A survey of traffic data visualization. IEEE Trans. Intell. Transp. Syst.
**2015**, 16, 2970–2984. [Google Scholar] [CrossRef] - Helbing, D.; Johansson, A.; Al-Abideen, H.Z. Dynamics of crowd disasters: An empirical study. Phys. Rev. E
**2007**, 75, 046109. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Liu, S.; Liu, Y.; Ni, L.; Li, M.; Fan, J. Detecting crowdedness spot in city transportation. IEEE Trans. Veh. Technol.
**2013**, 62, 1527–1539. [Google Scholar] [CrossRef] - D’Andrea, E.; Marcelloni, F. Detection of traffic congestion and incidents from GPS trace analysis. Expert Syst. Appl.
**2017**, 73, 43–56. [Google Scholar] [CrossRef] - Fan, Z.; Pei, T.; Ma, T.; Du, Y.; Song, C.; Liu, Z.; Zhou, C. Estimation of urban crowd flux based on mobile phone location data: A case study of Beijing, China. Comput. Environ. Urban Syst.
**2018**, 69, 114–123. [Google Scholar] [CrossRef] - Hadjieleftheriou, M.; Kollios, G.; Gunopulos, D.; Tsotras, V.J. On-Line Discovery of Dense Areas in Spatio-temporal Databases. In Advances in Spatial and Temporal Databases; Hadzilacos, T., Manolopoulos, Y., Roddick, J., Theodoridis, Y., Eds.; Springer: Berlin/Heidelberg, Germany, 2003; pp. 306–324. [Google Scholar]
- Tao, Y.; Kollios, G.; Considine, J.; Li, F.; Papadias, D. Spatio-temporal aggregation using sketches. In Proceedings of the 20th International Conference on Data Engineering, Boston, MA, USA, 30 March–2 April 2004; pp. 214–225. [Google Scholar] [CrossRef] [Green Version]
- Jensen, C.S.; Lin, D.; Ooi, B.C.; Zhang, R. Effective Density Queries on Continuously Moving Objects. In Proceedings of the 22nd International Conference on Data Engineering, Atlanta, GA, USA, 3–7 April 2006; p. 71. [Google Scholar] [CrossRef]
- Ma, Y.; Xu, W.; Zhao, X.; Li, Y. Modeling the hourly distribution of population at a high spatiotemporal resolution using subway smart card data: A case study in the central area of Beijing. ISPRS Int. J. Geo-Inf.
**2017**, 6, 128. [Google Scholar] [CrossRef] [Green Version] - Fan, Z.; Song, X.; Shibasaki, R.; Adachi, R. CityMomentum: An online approach for crowd behavior prediction at a citywide level. In Proceedings of the 2015 ACM International Joint Conference on Pervasive and Ubiquitous Computing, Osaka, Japan, 7–11 September 2015; pp. 559–569. [Google Scholar]
- Khezerlou, A.V.; Zhou, X.; Li, L.; Shafiq, Z.; Liu, A.X.; Zhang, F. A Traffic Flow Approach to Early Detection of Gathering Events: Comprehensive Results. ACM Trans. Intell. Syst. Technol.
**2017**, 8, 74:1–74:24. [Google Scholar] [CrossRef] - Zhang, J.; Zheng, Y.; Qi, D.; Li, R.; Yi, X.; Li, T. Predicting Citywide Crowd Flows Using Deep Spatio-Temporal Residual Networks. Artif. Intell.
**2018**, 259, 147–166. [Google Scholar] [CrossRef] [Green Version] - Wang, Z.; Lu, M.; Yuan, X.; Zhang, J.; Van De Wetering, H. Visual traffic jam analysis based on trajectory data. IEEE Trans. Vis. Comput. Graph.
**2013**, 19, 2159–2168. [Google Scholar] [CrossRef] [Green Version] - Hoang, M.X.; Zheng, Y.; Singh, A.K. FCCF: Forecasting citywide crowd flows based on big data. In Proceedings of the 24th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, Burlingame, CA, USA, 31 October–3 November 2016; p. 6. [Google Scholar]
- Yang, D.; Guo, Z.; Rundensteiner, E.A.; Ward, M.O. CLUES: A Unified Framework Supporting Interactive Exploration of Density-Based Clusters in Streams. In Proceedings of the 20th ACM International Conference on Information and Knowledge Management, Glasgow, Scotland, UK, 24–28 October 2011; pp. 815–824. [Google Scholar]
- An, S.; Yang, H.; Wang, J.; Cui, N.; Cui, J. Mining urban recurrent congestion evolution patterns from GPS-equipped vehicle mobility data. Inf. Sci.
**2016**, 373, 515–526. [Google Scholar] [CrossRef] - Rudomín, I.; Solar, G.V.; Oviedo, J.E.; Pérez, H.; Martini, J.L.Z. Modelling Crowds in Urban Spaces. Comput. Y Sist.
**2017**, 21, 57–66. [Google Scholar] [CrossRef] - An, S.; Yang, H.; Wang, J. Revealing Recurrent Urban Congestion Evolution Patterns with Taxi Trajectories. ISPRS Int. J. Geo-Inf.
**2018**, 7, 128. [Google Scholar] - Wang, Y.; Cao, J.; Li, W.; Gu, T.; Shi, W. Exploring traffic congestion correlation from multiple data sources. Pervasive Mob. Comput.
**2017**, 41, 470–483. [Google Scholar] [CrossRef] - Fang, Z.; Yang, X.; Xu, Y.; Shaw, S.L.; Yin, L. Spatiotemporal model for assessing the stability of urban human convergence and divergence patterns. Int. J. Geogr. Inf. Sci.
**2017**, 31, 2119–2141. [Google Scholar] [CrossRef] - Ji, Y.; Luo, J.; Geroliminis, N. Empirical observations of congestion propagation and dynamic partitioning with probe data for large-scale systems. Transp. Res. Rec. J. Transp. Res. Board
**2014**, 2422, 1–11. [Google Scholar] [CrossRef] [Green Version] - Chen, Z.; Yang, Y.; Huang, L.; Wang, E.; Li, D. Discovering Urban Traffic Congestion Propagation Patterns With Taxi Trajectory Data. IEEE Access
**2018**, 6, 69481–69491. [Google Scholar] [CrossRef] - Yuan, M. Modeling semantic, spatial and temporal information in GIS. In Geographic Information Research: Bridging the Atlantic; CRC Press: Boca Raton, FL, USA, 1996; pp. 334–347. [Google Scholar]
- Nadi, S.; Reza Delavar, M. Spatio-Temporal Modeling of Dynamic Phenomena in GIS. In Proceedings of the 9th Scandinavian Research Conference on Geographical Information Science, Espoo, Finland, 4–6 June 2003; pp. 215–225. [Google Scholar]
- Claramunt, C.; Thériault, M. Managing Time in GIS An Event-Oriented Approach. In Recent Advances in Temporal Databases; Clifford, J., Tuzhilin, A., Eds.; Springer: London, UK, 1995; pp. 23–42. [Google Scholar]
- Yuan, M. Temporal GIS and spatio-temporal modeling. In Proceedings of the Third International Conference Workshop on Integrating GIS and Environment Modeling, Sante Fe, NM, USA, 21–25 January 1996; Volume 33, pp. 1–13. [Google Scholar]
- Yuan, M. Representing complex geographic phenomena in GIS. Cartogr. Geogr. Inf. Sci.
**2001**, 28, 83–96. [Google Scholar] [CrossRef] - Hornsby, K.; Egenhofer, M. Identify-based change: A foundation for spatio- temporal knowledge representation. Int. J. Geogr. Inf. Sci.
**2000**, 14, 207–224. [Google Scholar] [CrossRef] - Grenon, P.; Smith, B. SNAP and SPAN: Towards dynamic spatial ontology. Spat. Cogn. Comput.
**2004**, 4, 69–104. [Google Scholar] [CrossRef] [Green Version] - Worboys, M. Event-oriented approaches to geographic phenomena. J. Geogr. Inf. Sci.
**2005**, 19, 1–28. [Google Scholar] [CrossRef] - Benenson, I.; Torrens, P.M.; Torrens, P. Geosimulation: Automata-Based Modeling of Urban Phenomena; John Wiley & Sons: Hoboken, NJ, USA, 2004. [Google Scholar]
- Ester, M.; Ester, M.; Kriegel, H.P.; Sander, J.; Xu, X. A density-based algorithm for discovering clusters in large spatial databases with noise. In Proceedings of the Second International Conference on Knowledge Discovery and Data Mining, Portland, Oregon, USA, 2–4 August 1996; pp. 226–231. [Google Scholar]
- Horn, R.A. The Hadamard product. In Proceedings of Symposia in Applied Mathematics; Johnson, C.R., Ed.; American Mathematical Society: Providence, RI, USA, 1990; Volume 40, pp. 87–169. [Google Scholar]
- Scherf, N.; Herberg, M.; Thierbach, K.; Zerjatke, T.; Kalkan, T.; Humphreys, P.; Smith, A.; Glauche, I.; Roeder, I. Imaging, quantification and visualization of spatio-temporal patterning in mESC colonies under different culture conditions. Bioinformatics
**2012**, 28, i556–i561. [Google Scholar] [CrossRef] [Green Version] - Hu, M.K. Visual pattern recognition by moment invariants. IRE Trans. Inf. Theory
**1962**, 8, 179–187. [Google Scholar] - Lenormand, M.; Louail, T.; Barthelemy, M.; Ramasco, J.J. Is spatial information in ICT data reliable? arXiv
**2016**, arXiv:1609.03375. [Google Scholar]

**Figure 1.**Overview of the proposed methodology for analyzing the morphological evolutionary patterns of urban crowd flows.

**Figure 2.**The temporal series of synthetic urban crowd distributions and the exemplary associated mask regions between the given consecutive time frames.

**Figure 3.**Assignment paths along the decision tree for the simulated crowd regions. Note that A, B, C, D, E, E’, F on the vertical axis are condition labels as defined in Algorithm 1.

**Figure 5.**Citywide crowd hotspots for the slowed flows (

**left**) and the crowded flows (

**right**). The color indicates the crowd rate of each cell. The subplot on the right demonstrates the derived crowded regions for slow flows, while the subplot on the left demonstrates the derived regions that were severely crowded.

**Figure 6.**Statistics of the morphological evolutionary patterns for the slowed flows (

**left**) and between the slowed and the crowded flows (

**right**).

**Figure 7.**Temporal transitions between the morphological evolutionary patterns for the slowed flows (

**top**) and the crowded flows (

**bottom**) at distinct time scales—that is, middle of the night, morning rush hours, afternoon rush hours, and evening rush hours. Note that the node size denotes the relative frequency of each pattern, the link width denotes the transmission probability between two nodes, and the link color denotes the originating node.

**Figure 8.**Temporal transitions between the morphological evolutionary patterns of the slowed flows (

**left**) and the crowded flows (

**right**) at five typical locations.

Morphology (t → t+1) | ||
---|---|---|

Centroid (x, y) | Area (Number of Cells) | |

Newly Occurring | None → Exist | Zero → Non-Zero |

Disappearing | Exist → None | Non-Zero → Zero |

Splitting and Merging | Multiple → Multiple | — |

Splitting | Single → Multiple | — |

Merging | Multiple → Single | — |

Stable | No Change | No Change |

Stable and Moving | Cell A → Cell B | No Change |

Shrinking | No Change | Large → Small |

Shrinking and Moving | Cell A → Cell B | Large → Small |

Growing | No Change | Small → Large |

Growing and Moving | Cell A → Cell B | Small → Large |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Qin, K.; Xu, Y.; Kang, C.; Sobolevsky, S.; Kwan, M.-P.
Modeling Spatio-Temporal Evolution of Urban Crowd Flows. *ISPRS Int. J. Geo-Inf.* **2019**, *8*, 570.
https://doi.org/10.3390/ijgi8120570

**AMA Style**

Qin K, Xu Y, Kang C, Sobolevsky S, Kwan M-P.
Modeling Spatio-Temporal Evolution of Urban Crowd Flows. *ISPRS International Journal of Geo-Information*. 2019; 8(12):570.
https://doi.org/10.3390/ijgi8120570

**Chicago/Turabian Style**

Qin, Kun, Yuanquan Xu, Chaogui Kang, Stanislav Sobolevsky, and Mei-Po Kwan.
2019. "Modeling Spatio-Temporal Evolution of Urban Crowd Flows" *ISPRS International Journal of Geo-Information* 8, no. 12: 570.
https://doi.org/10.3390/ijgi8120570