# Analyzing Urban Human Mobility Patterns through a Thematic Model at a Finer Scale

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## Abstract

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## 1. Introduction

## 2. Trip Extraction and Analysis

#### 2.1. Trip Extraction

**Definition 1:**

**Definition 2:**

#### 2.2. Distribution of Trips

## 3. Semantic Analysis

## 4. Trip Topic Modeling with LDA

#### 4.1. Latent Dirichlet Allocation

#### 4.2. Significance Definition

**Trip topic significance:**The topic is a concept or an aspect of a document, and it is characterized by a series of related words. The more correlated with the theme the words are, the more possible it is that they gather into a theme. The significance of a trip topic, F

_{t}, is defined as the total frequency of the trip destination (F) that supports the topic (t) in the hidden thematic knowledge, representing the topic importance. The greater the F

_{t}is, the more trip destinations the topic attracts. In Table 4, 10 topics are presented by the order of their topic significance (i.e., total frequency) from Topic00 to Topic09. The frequency of Topic08, which has the highest trip topic significance, F

_{t}, is 2460, while Topic05 saw the lowest F

_{t}, only having less than half of that at 1003. Therefore, among the 10 topics, Topic08 attracted more trip destinations attached to people’s trip behavior than any other topic.

**Trip destination significance:**Trip destination significance, denoted by ${F}_{w}\left(t\right)$, is the significance level of a trip destination (i.e., words) w in a given trip topic. A bigger value, ${F}_{w}\left(t\right)$, means that the word of a trip destination (w) offers more contributions to the production of trip topic t than other topics. The same trip destination may contribute to the production of several trip topics with different trip destination significance. For example, in Table 4, Link 22921, as a trip destination, contributes greatly to Topic01 and Topic06 with 25 percent and 44 percent support, respectively. At the same time, it plays a less important role in Topic00, Topic02, Topic04 and Topic09. However, it has no significance for Topic03, Topic05 and Topic07. In contrast, Link 10229 mainly contributes to two topics, amounting to 99% in total. One topic is Topic08 with 60% support, and another is Topic01 with 39%. Only one percent contributes to Topic00. All in all, this shows that the same link is more associated with some topics than other topics.

**Trip topic probability distribution:**Each trip topic is in fact a probability distribution of different trip destinations attached to various mobility patterns under the condition of this topic, namely ${\phi}_{t}<{p}_{{w}_{1}},\dots ,{p}_{{w}_{m}}>$, in which ${p}_{{w}_{i}}$ represents the probability of a trip destination, ${w}_{i}$, generating topic t. This is the ratio of trip destination significance over trip topic significance, $p\left({w}_{i}|t\right)={F}_{{w}_{i}}\left(t\right)/{F}_{t}$; a conditional probability of trip destination under the condition of topic t. Here, the conditional probability of all trip destinations over the topic sum to one, $\sum _{i}{p}_{{w}_{i}}=1$. The bigger the value $p\left({w}_{i}|t\right)$, the more representative the trip destination is expressed by topic t. Consequently, if a threshold δ is defined, then all trip destinations with a conditional probability higher than the threshold are considered as representative trip destinations for topic t, which will be used for the visual analysis of topics.

## 5. Trip Topic Analysis of Mobility Patterns in Wuhan

#### 5.1. Trip Topic Extraction and Visualization

#### 5.2. Trip Topic and Urban Dynamics

#### 5.3. Trip Topic Evolution

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Spatial distribution of pickups and drop offs of a taxicab on 2 June 2014; (

**b**) spatial distribution of pickups and drop offs of all taxicab on 2 June 2014. Yellow points and red points denote pick-up points and drop-off points, respectively.

**Figure 12.**(

**a**) Visualization of trip Topic09 during the morning rush hour; (

**b**) visualization of trip Topic01 during the evening rush hour.

Date | ID | Longitude | Latitude | Velocity | Heading | Status |
---|---|---|---|---|---|---|

2 June 2014 01:04:44 | 40416 | 114.27183 | 30.59821 | 6.284861 | 316.78 | 0 |

2 June 2014 01:04:49 | 40416 | 114.271583 | 30.598418 | 8.756667 | 329.19 | 0 |

2 June 2014 01:05:09 | 40416 | 114.27093 | 30.59895 | 5.190278 | 310.57 | 1 |

2 June 2014 01:05:41 | 40416 | 114.27055 | 30.600498 | 8.756667 | 51.46 | 1 |

2 June 2014 01:06:24 | 40416 | 114.273651 | 30.601985 | 12.759861 | 62.53 | 1 |

Date | Number of Records | Number of Taxies | Number of Trips | Number of Valid Trips |
---|---|---|---|---|

2 June | 2,446,961 | 2057 | 56,770 | 41,134 |

3 June | 2,468,565 | 2059 | 55,487 | 40,992 |

4 June | 2,449,164 | 2069 | 54,472 | 41,048 |

5 June | 2,483,043 | 2073 | 55,598 | 41,698 |

6 June | 2,510,001 | 2064 | 56,936 | 41,098 |

7 June | 2,539,803 | 2049 | 59,220 | 42,989 |

8 June | 2,498,303 | 2063 | 58,353 | 43,233 |

Total | 17,395,840 | 396,836 | 292,192 |

Taxi ID | Date | Latitude | Longitude | Link ID | Street Name | ODState |
---|---|---|---|---|---|---|

10319 | 2 June 2014 07:35:30 | 30.627251 | 114.381743 | 16373 | Gongye Road | origin |

10319 | 2 June 2014 07:40:02 | 30.63174 | 114.3775 | 16748 | Heping Road | destination |

16657 | 2 June 2014 18:24:44 | 30.515136 | 114.313965 | 9208 | Ping’an Road | origin |

16657 | 2 June 2014 18:44:42 | 30.548246 | 114.296945 | 10838 | Minzhu Road | destination |

**Table 4.**Latent Dirichlet Allocation (LDA) results: trip destination significance in topics. Freq and Prob stand for frequency and probability, respectively.

Topic | Total Frequency of Topic | Link 22921 | Link 10229 | Link 14346 | Link 10139 | ||||
---|---|---|---|---|---|---|---|---|---|

Freq | Prob | Freq | Prob | Freq | Prob | Freq | Prob | ||

Topic08 | 2460 | 11 | 0.08 | 39 | 0.60 | 1 | 0.02 | 109 | 0.53 |

Topic06 | 2173 | 60 | 0.44 | 0 | 0.00 | 18 | 0.28 | 0 | 0.00 |

Topic09 | 2066 | 9 | 0.06 | 0 | 0.00 | 0 | 0.00 | 30 | 0.15 |

Topic04 | 1728 | 5 | 0.04 | 0 | 0.00 | 14 | 0.22 | 28 | 0.14 |

Topic03 | 1641 | 0 | 0.00 | 0 | 0.00 | 10 | 0.16 | 0 | 0.00 |

Topic00 | 1543 | 4 | 0.03 | 0 | 0.01 | 0 | 0.00 | 2 | 0.01 |

Topic01 | 1449 | 33 | 0.25 | 26 | 0.39 | 21 | 0.32 | 21 | 0.10 |

Topic02 | 1381 | 13 | 0.10 | 0 | 0.00 | 0 | 0.00 | 0 | 0.00 |

Topic07 | 1244 | 0 | 0.00 | 0 | 0.00 | 0 | 0.00 | 16 | 0.08 |

Topic05 | 1003 | 0 | 0.00 | 0 | 0.00 | 0 | 0.00 | 0 | 0.00 |

Morning Rush Hour Topics | Topic Significance | Evening Rush Hour Topics | Topic Significance | Topic Similarity | Significance Change |
---|---|---|---|---|---|

Topic08 | 2460 | Topic05 | 2110 | 0.43 | −14.23% |

Topic06 | 2173 | Topic08 | 1805 | 0.40 | −16.94% |

Topic09 | 2066 | Topic01 | 2404 | 0.53 | +16.41% |

Topic04 | 1728 | Topic00 | 1426 | 0.29 | −17.49% |

Topic03 | 1641 | Topic03 | 1976 | 0.42 | +20.43% |

Topic00 | 1543 | Topic09 | 1489 | 0.47 | −3.45% |

Topic01 | 1449 | Topic00 | 1426 | 0.25 | −1.64% |

Topic02 | 1381 | Topic02 | 1672 | 0.13 | +21.10% |

Topic07 | 1244 | Topic00 | 1426 | 0.17 | +14.59% |

Topic05 | 1003 | Topic04 | 1073 | 0.22 | +7.02% |

Total topic significance | 16,687 | – | 17,681 | – | – |

© 2016 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/).

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**MDPI and ACS Style**

Zhang, F.; Zhu, X.; Guo, W.; Ye, X.; Hu, T.; Huang, L.
Analyzing Urban Human Mobility Patterns through a Thematic Model at a Finer Scale. *ISPRS Int. J. Geo-Inf.* **2016**, *5*, 78.
https://doi.org/10.3390/ijgi5060078

**AMA Style**

Zhang F, Zhu X, Guo W, Ye X, Hu T, Huang L.
Analyzing Urban Human Mobility Patterns through a Thematic Model at a Finer Scale. *ISPRS International Journal of Geo-Information*. 2016; 5(6):78.
https://doi.org/10.3390/ijgi5060078

**Chicago/Turabian Style**

Zhang, Faming, Xinyan Zhu, Wei Guo, Xinyue Ye, Tao Hu, and Liang Huang.
2016. "Analyzing Urban Human Mobility Patterns through a Thematic Model at a Finer Scale" *ISPRS International Journal of Geo-Information* 5, no. 6: 78.
https://doi.org/10.3390/ijgi5060078