# Prediction of Suspect Location Based on Spatiotemporal Semantics

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## Abstract

**:**

## 1. Introduction

- (1)
- A Bayes probability model that is able to uncover the moving preferences among a large numbers of locations instead of being confined to describe the relations of the address and crime locations is proposed to represent the complex location transition patterns for the individual suspect.
- (2)
- A ranking algorithm is developed to measure the similarities of social movement preferences between suspects relying on the spatiotemporal semantics to fuse the mobility data of similar suspects together to cope with the data sparsity problem.
- (3)
- The availability and robustness of the proposed model are enhanced by exploring KDE smoothing techniques on both spatial semantics and spatial proximity so that the transition frequencies between unobserved locations and other locations can be obtained.
- (4)
- Extensive experiments were conducted using suspect mobility data, crime events data and other urban data in Wuhan city to investigate the performance of the proposed model on metrics of top-k error, top-k precision and missing percentiles. The results validate that the proposed model significantly outperformed other baseline methods with greater robustness and effectiveness.

## 2. Related Work

#### 2.1. Criminal Geographic Profiling (CGP)

#### 2.1.1. Morphology

#### 2.1.2. Propinquity

#### 2.2. Location Prediction

#### 2.2.1. Multiple Data Integrated Models

#### 2.2.2. Location Recommendation

#### 2.2.3. Geographic Proximity Models

## 3. Methodology

#### 3.1. Overview

#### 3.2. Formal Statement of Problem

**Given:**

_{1}, g

_{2},…,g

_{|G|}}, g

_{i}denotes a location (region);

^{p}= {n

_{1}= g

_{k+1}, n

_{2}= g

_{k+2},…, n

_{j-1}= g

_{k+t}}, n

_{i}denotes a trajectory point, $k,\left(k+t\right)\in \left[1,\left|G\right|\right]$;

**Solve:**Obtaining the probability of the next point n

_{j}of T

^{p}being g

_{d}:

#### 3.3. Basic Concepts and Definitions

**Definition**

**1**

**Definition**

**2**

**Definition**

**3**

_{r}= <s

_{r1}, s

_{r2}, …>, where s

_{ri}is the ith social environment feature of the location r, including crime rate, population, house density, occupation, road density and POI categories, etc.

**Definition**

**4**

^{d}, points p

_{x}and p

_{y}∈ F

^{d}, the density function that represent the influence of p

_{y}to p

_{x}can be determined by the product of the attribute value c

_{y}in p

_{y}and the kernel function $K(\cdot )$:

**Definition**

**5**

_{i}and p

_{x}∈ F

^{d}, if {$\exists $p

_{i}| p

_{i}∈ D, d(p

_{x},p

_{i}) ≤ ε}, we call D the density attracting set of p

_{x}and call p

_{i}the density attracting point that is attracted by p

_{x}.

**Definition**

**6**

_{x}∈ F

^{d}, the density attracting set D = {p

_{1}, p

_{2}, …, p

_{N}} ∈ F

^{d}of p

_{x}, the density value of p

_{x}is the average of the aggregating density function values of all the density attracting points in D:

**Definition**

**7**

_{x}and p

_{y}∈ F

^{d}, p

_{x}is the start point and p

_{y}is the end point, we denote the movement from p

_{x}to p

_{y}as a transition.

#### 3.4. Suspects Mobility Data Fusion

- (1)
- Mobility Points Clustering: To make movement patterns of different suspects comparable according to the sparse individual mobility data, we cluster the mobility points of the entire dataset into multiple regions based on spatial semantics similarity and spatial proximity.
- (2)
- Top-n Similar Suspects: The similarity scores between suspects are measured by overlaps among the spatiotemporal distributions of the regions created in step (1). Therefore, we can easily find the top-n similar suspects of the target suspect by ranking the similarity scores.

#### 3.4.1. Mobility Points Clustering

_{i}and s

_{j}:

#### 3.4.2. Top-n Similar Suspects

- (1)
- Hour bins of day, HBOD ∈ {< 0–6>, < 7–12>, <12–19>, < 20–24>}, denoting before-dawn, morning, afternoon and night, respectively.
- (2)
- Day of week, DOW = {1 ,..., 7}, representing Monday to Sunday, respectively.
- (3)
- Rest of Day, ROD = {0, 1}, where 0 express the current day is a rest day, and 1 is a working day.

_{u}= ≤ q

_{t,u,1},q

_{t,u,2},…, q

_{t,u,s}…, >

_{t,u,s}is the visiting intensity of region s for suspect u in a semantic time t as,

_{t,u}is the total visiting number of all the regions at semantic time t for suspect u, b

_{t,u,s}stands for the visiting number of region s at semantic time t for suspect u, and I

_{t}{s} represents the number of suspects that visit the region s at semantic time t.

#### 3.5. First-Order Transition Probabilities Estimation

- (1)
- A significant characteristic of human activity is that the transition probability from one location to another one is inversely proportional to the distance between them [46]. Therefore, we can exploit such a geographical characteristic to build the transition patterns for an unobserved location from its spatially adjacent observed locations.
- (2)
- The similarity in social environment between locations that are nearby each other may lead to similar crime spatial activity patterns and transition patterns for them [56,57]. Thus, it can be leveraged such spatial semantic similarity to help us estimate the transition probabilities for unobserved locations.

#### 3.5.1. Transition Frequencies from Trajectory Location to Peripheral Location

_{x}is the peripheral location, that the trajectory location p

_{0}is the starting point of N transitions Ʈ = {${\U0001d4c9}_{1},\dots ,{\U0001d4c9}_{N}$}, and that D = { p

_{1}, p

_{2}, …, p

_{N}} is the density attracting set of p

_{x}. The trajectory locations p

_{1}, p

_{2}, …, p

_{N}are the end points of transitions in Ʈ. Given the transition frequency ${c}_{i}^{0}$ from p

_{0}to every p

_{i}∈ D, the transition frequency from p

_{0}to p

_{x}can be obtained by aggregating ${c}_{i}^{0}$ and dividing it by N according to Formula (3) when only considering the spatial proximity:

_{x},p

_{i}) indicates the spatial distance between p

_{x}and p

_{y}, and h

_{d}is the bandwidth for spatial distance in the kernel function.

_{s}is the bandwidth for spatial semantics closeness in the kernel function.

_{1}$\in \left[0,1\right]$ is a weight controlling the influences of spatial proximity and spatial semantics on the transition frequency.

_{x}is a peripheral location (red grid), and its density attracting set D is composed of the trajectory locations p

_{5}, p

_{6}and p

_{7}(green grids located in the green eclipse). Meanwhile, c

_{5}, c

_{6}and c

_{7}(blue arrows) denote the known transition frequencies from p

_{0}to p

_{5}, p

_{6}and p

_{7}, respectively. Then, we can estimate the unknown transition frequency (red dotted arrow) from p

_{0}to p

_{x}by importing c

_{5}, c

_{6}and c

_{7}into Formulas (11)–(13).

#### 3.5.2. Transition Frequencies from Peripheral Location to Trajectory Location

_{0}is the end point of N transitions Ʈ = {${\U0001d4c9}_{1},\dots ,{\U0001d4c9}_{N}$}, D = { p

_{1}, p

_{2}, …, p

_{N}} is the density attracting set of the peripheral location p

_{x}, and the trajectory locations in D are the starting points of the transitions in Ʈ. Given the transition frequency ${c}_{0}^{i}$ from p

_{i}∈ D to p

_{0}in each transition of Ʈ, the transition frequencies from p

_{x}to p

_{0}can be obtained by Formulas (11) and (12) as ${\stackrel{\xb4}{c}}_{0}^{x}$ and ${\stackrel{`}{c}}_{0}^{x}$, respectively. Therefore, the final transition frequencies from p

_{x}to p

_{0}are

_{2}$\text{}\in \left[0,1\right]$ is a weight.

#### 3.5.3. Transition Frequencies from Peripheral Location to Peripheral Location

_{x}to another peripheral location p

_{y}through two aspects: (1) deeming p

_{y}as the trajectory location as in Section 3.5.2 and (2) regarding p

_{x}as the trajectory location as in Section 3.5.3. Then, we combined the two estimated visiting frequencies, denoted as c

_{xy}and c

_{yx}, respectively, to produce the final result ${c}_{y}^{x}$:

_{3}$\text{}\in \left[0,1\right]$ is a weight.

#### 3.5.4. Markov Location Transition Matrix

**M**:

#### 3.6. Total Transition Probability Estimation

_{i→j}that expresses the transition probability between a pair of locations through all possible paths, each of which is made up of a number of bypass locations. Luckily, this total transition probability can be generated from

**M**by multiplying itself. In general,

**M**

^{1+r}(r ∈ [0, ∞)) holds the probabilities of transition from one location to another one in exactly r steps (bypass locations). The following example demonstrates the concept of the total transition probability. By referring to Figure 5 and Figure 6a, the probability of travelling from g

_{0}to g

_{3}is found to be zero (${\mathrm{M}}_{03}^{1}$ = 0) because

**M**only stores the probability of movement from one location to another through exactly zero steps (bypass locations). Nevertheless, when

**M**is multiplied by itself 2 times to form

**M**

_{3}, each entry in it indicates the transition probability from one location to another in two steps. Hence, the transition probability from g

_{0}to g

_{3}through 2 steps is 0.729 (${\mathrm{M}}_{03}^{3}=0.729$), as shown in Figure 6c.

**M**, we can obtain the total transition probability p

_{i→j}by the sum of r-step transition probabilities of all possible paths between p

_{i}and p

_{j}. Formally [34]:

- (1)
- The paths with different numbers of steps do not necessarily have the same influences on the total transition probability. For instance, the pair of locations with short spatial distance prefers a small number of steps rather than many bypass locations. Therefore, how are we to capture various influences of different
**M**^{r}on the total transition probability? - (2)
- How do we define the maximum value of r since the number of paths from one location to another is infinitely large without restrictions?

_{ij}is the spatial distance between locations i and j. When d

_{ij}is fixed, a large r will cause a small w

_{r}, reflecting the fact that a path with too many bypass locations is seldom chosen by suspects.

_{max}is usually 1.2 times the shortest steps between the start and end locations. However, this idea only fits specific trajectory datasets. Furthermore, it may yield an irrelevant r

_{max}when focusing on a different individual suspect. It is suggested that r

_{max}should account for the shortest steps of the target suspect as well as the spatial distance between the two locations. The procedure to compute the r

_{max}for an individual suspect is shown as below.

- (1)
- Give a constant value q > 1, assuming it equals to 2.
- (2)
- Build a transition weight matrix
**H**. If there is no transition between locations g_{i}and g_{j}, the entry H_{ij}= ∞; if the target suspect is involved in this transition, H_{ij}= 1; else, H_{ij}= q. - (3)
- Obtain the top-k shortest paths [56] based on
**H**in which the entries are considered to be the distances among locations; - (4)
- Computer the conformity t
_{m}for every path m in the top-k shortest paths by

_{4}is a fixed coefficient larger than zero, l

_{m}denotes the distance of path m, r

_{m}denotes the number of bypass locations in path m, and e

_{m}denotes the number of locations visited by the target suspect in path m. Therefore, a path with more locations that the target suspect has visited and fewer bypass locations has more power to describe the r that the target suspect prefers.

_{max}in the path with the largest conformity t

_{max}is what we need.

_{r}and r

_{max}are obtained, we can efficiently compute the total transition probability matrix for all pairs of locations by a dynamic programming method [34].

#### 3.7. Bayes-Based Location Prediction

_{j}contains the destination location ${g}_{d}$ conditioning on the query trajectory T

^{p}. This probability was previously given in Formula (1) and is extended using Bayer’s inference here as:

^{p}) is the path probability of the query trajectory T

^{p}; p

_{(j-1)→j}is the total transition probability of moving from n

_{(j-1)}, the end location of T

^{p}, to the predicted destination n

_{j}= ${g}_{d}$; and p

_{1→j}is the total transition probability of travelling from n

_{1}, the starting location of T

^{p}, to n

_{j}= ${g}_{d}$.

^{p}) can be obtained by:

_{k(k+1)}is the first-order transition probability between locations n

_{k}and n

_{(k+1)}.

Algorithm 1. Location Prediction Algorithm. |

Input: query trajectory T^{p} = {n_{1},…,n_{(j−1)}} |

Output: top-k predicted locations. |

1 list = ∅; |

2 construct path probability P(T^{p}) from M; |

3 Foreach n_{j} in G do |

4 Retrieve p_{1→j} and p_{(j-1)→j} from M^{r}; |

5 Compute $P\left({n}_{j}={g}_{d}\right)$; |

6 Compute P(T^{p} | n_{j} = ${g}_{d}$); |

7 Compute P(n_{j} = ${g}_{d}$ | T^{p}); |

8 Store P(n_{j} = ${g}_{d}$ | T^{p}) in list; |

9 sort list; |

10 return: top-k elements in list. |

## 4. Experimental Section

#### 4.1. Data Preparation

#### 4.1.1. Study Area

^{2}urban areas of Wuhan City as shown in Figure 7, and each of grid (256 m × 224 m) denotes a location as the basic spatial unit.

#### 4.1.2. Data Sources

- The mobility data for each suspect is extremely sparse. For example, there are 70% of suspects with fewer than 50 records, 83% of suspects with fewer than 50 trajectories, and 80% of them with fewer than 8 different venues. It can also be inferred that each suspect was frequently detected in several limited areas.
- The distances between continuous trajectory points varied from 0 km to 10 km.
- The visiting distribution of venue types is shown in Figure 9, where the suspects accessed banks (mostly ATM machines) up to 9207 times. The second highest accessing place is cybercafés, followed by hotels, rental housing, recreation, traffic sites (airports and bus stations, etc.) and other types (such as shopping malls, etc.).

#### 4.2. Evaluation Metrics

- (1)
- Top-k Precision [54] (TP): If the correct destination falls within the top-k predicted locations, this time is considered to be the correct time. Thus, the ratio of correct times to the total times is called top-k precision. The higher this metric value is, the better performance the model has.
- (2)
- Top-k Error (TE): The shortest distance between the top-k predicted locations and the correct destination. If k = 1, it is called Accuracy Measures [27]. This metric is used to indicate how far the prediction results deviate from the true destinations. A better algorithm has a lower distance deviation.
- (3)
- Missing Percentiles (MP): The percentage of occurrences for which a model cannot give any result. This metric is used to evaluate the impact of the data sparsity on the robustness of the models. A better algorithm has a lower missing percentile.

#### 4.3. Baselines

^{p}; (ii) it terminates at a location in n

_{j}. The count is then divided by the number of trajectories that terminate at a location in n

_{j}to serve as the posterior probability. Formally,

_{j}. Afterwards, Formula (24) is substituted into Formula (20), thus yielding the probability of n

_{j}as the destination. Compared with Markov, ZMDB holds the advantage of modeling multi-order location transitions.

_{d}= 300 m, h

_{s}= 0.1, a

_{1}= 0.5, a

_{2}= 0.5, a

_{3}= 0.5 and a

_{4}= 0.7.

#### 4.4. Results Evaluation of Top-k Error

#### 4.5. Evaluation of Top-k Precision

#### 4.6. Evaluation of Missing Percentiles

#### 4.7. Evaluation of k

#### 4.8. Visualizations of Prediction Results

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Sun, N. Design and implementation of multi-source data track analysis system based on PGIS. Sci. Surv. Mapp.
**2013**, 38, 51–53. [Google Scholar] - Office of the Privacy Commissioner of Canada. Available online: https://www.priv.gc.ca/en/ (accessed on 10 March 2016).
- Shiode, S.; Shiode, N.; Block, R.; Block, C.R. Space-time characteristics of micro-scale crime occurrences: An application of a network-based space-time search window technique for crime incidents in Chicago. Int. J. Geogr. Inf. Sci.
**2015**, 29, 697–719. [Google Scholar] [CrossRef] - Hammond, L. Geographical profiling in a novel context: prioritizing the search for New Zealand sex offenders. Psychol. Crime Law
**2014**, 20, 358–371. [Google Scholar] [CrossRef] - Chen, N.C.; Shi, W.; Song, D.W. Prediction of series criminals: An Approach based on modeling. In Proceedings of the 2010 International Conference on Computational and Information Sciences, Chengdu, China, 17–19 December 2010; pp. 72–75. [Google Scholar]
- Qian, C.; Wang, Y.B.; Cao, J.D.; Lu, J.Q.; Kurths, J. Weighted-traffic-network–based geographic profiling for serial crime location prediction. EPL
**2011**, 93, 68006. [Google Scholar] [CrossRef] - Kent, J.D.; Leitner, M. Incorporating Land cover within bayesian journey-to-crime estimation models. Int. J. Psychol. Stud.
**2012**, 4, 120–140. [Google Scholar] [CrossRef] - Martineau, M.; Beauregard, E. Journey to murder: Examining the correlates of criminal mobility in sexual homicide. Police Pract. Res.
**2016**, 17, 68–83. [Google Scholar] [CrossRef] - Mohler, G.O.; Short, M.B. Geographic profiling from kinetic models of criminal behavior. SIAM J. Appl. Math.
**2012**, 72, 163–180. [Google Scholar] [CrossRef] - Rossmo, D.K. Geographic Profiling; CRC Press: Boca Raton, FL, USA, 2000. [Google Scholar]
- Song, C.; Koren, T.; Wang, P.; Barabási, A.L. Modelling the scaling properties of human mobility. Nat. Phys.
**2010**, 6, 818–823. [Google Scholar] [CrossRef] - Yang, A.; Wu, R.; Wu, H.M.; Liu, X. The research of tree topology model for growth of natural selection and application in geographical profile for criminal. Inf. Comput. Appl.
**2010**, 106, 383–390. [Google Scholar] - Van, K.M.V.; Elffers, H.; Ruiter, S. When to refrain from using likelihood surface methods for geographical offender profiling: An ex ante test of assumptions. J. Investig. Psychol. Offender Profiling
**2011**, 8, 242–256. [Google Scholar] - Song, C.; Qu, Z.; Blumm, N.; Barabási, A.L. Limits of predictability in human mobility. Science
**2010**, 327, 1018–1021. [Google Scholar] [CrossRef] [PubMed] - Xiao, X.Y.; Zheng, Y.; Luo, Q.; Xie, X. Inferring social ties between users with human location history. ACM Trans. Intell. Syst. Technol.
**2012**, 6, 2–27. [Google Scholar] [CrossRef] - Yuan, N.J.; Zheng, Y.; Xie, X.; Wang, Y.Z.; Zheng, K.; Xiong, H. Discovering urban functional zones using latent activity trajectories. IEEE Trans. Knowl. Data Eng.
**2015**, 27, 712–725. [Google Scholar] [CrossRef] - Mburu, L.; Helbich, M. Evaluating the accuracy and effectiveness of criminal geographic profiling methods: The case of Dandora, Kenya. Prof. Geogr.
**2015**, 67, 110–120. [Google Scholar] [CrossRef] - Bernasco, W.; Block, R. Robberies in Chicago: A block-level analysis of the influence of crime generators, crime attractors and offender anchor points. J. Res. Crime Delinq.
**2011**, 48, 33–57. [Google Scholar] [CrossRef] - Iwanski, N.; Frank, R.; Reid, A.; Dabbaghian, V. A Computational Model for Predicting the Location of Crime Attractors on a Road. In Proceedings of the European Intelligence and Security Informatics Conference, Odense, Denmark, 22–24 August 2012; pp. 60–67. [Google Scholar]
- Canter, D.; Youngs, D. Investigative Psychology: Offender Profiling and the Analysis of Criminal Action; Wiley: Chichester, UK, 2009. [Google Scholar]
- Canter, D.; Larkin, P. The Environmental Range of Serial Rapists. J. Environ. Psychol.
**1993**, 13, 63–69. [Google Scholar] [CrossRef] - Snook, B.; Zito, M.; Bennell, C.; Taylor, P.J. On the complexity and accuracy of geographic profiling strategies. J. Quant. Criminol.
**2005**, 21, 1–26. [Google Scholar] [CrossRef] - Luini, L.P.; Scorzelli, M.; Mastroberardino, S.; Marucci, F.S. Spatial cognition and crime: The study of mental models of spatial relations in crime analysis. Cogn. Process.
**2012**, 13 (Suppl. 1), S253–S255. [Google Scholar] [CrossRef] [PubMed] - Levine, N. Introduction to the special issue on Bayesian journey-to-crime modelling. J. Investig. Psychol. Offender Profiling
**2009**, 6, 167–185. [Google Scholar] [CrossRef] - Taylor, P.J.; Bennell, C.; Snook, B. The bounds of cognitive heuristic performance on the geographic profiling task. Appl. Cogn. Psychol.
**2009**, 23, 410–430. [Google Scholar] [CrossRef] - Hammond, L.; Youngs, D. Decay functions and criminal spatial processes: Geographical offender profiling of volume crime. J. Investig. Psychol. Offender Prof.
**2011**, 9, 90–102. [Google Scholar] [CrossRef] - David, C.; Laura, H.; Donna, Y.; Juszczak, P. The Efficacy of ideographic models for geographical offender profiling. J. Quant. Criminol.
**2013**, 29, 423–446. [Google Scholar] - Bache, R. A Generative Model of Offenders’ Spatial Behaviour. Int. J. Uncertain. Fuzziness Knowl.Based Syst.
**2011**, 19, 825–842. [Google Scholar] [CrossRef] - Canter, D.; Hammond, L. A comparison of the efficacy of different decay functions in geographical profiling for a sample of US serial killers. J. Investig. Psychol. Offender Prof.
**2006**, 3, 91–103. [Google Scholar] [CrossRef] - Smith, W.; Bond, J.W.; Townsley, M. Determining how journeys-to-crime vary measuring inter- and intra-offender crime trip distributions. In Putting Crime in Its Place; Weisburd, D., Bernasco, W., Gerben, J., Bruinsma, N., Eds.; Filiquarian: London, UK, 2009. [Google Scholar]
- Levine, N. CrimeStat: A Spatial Statistics Program for the Analysis of Crime Incident Locations (V 3.3); Ned Levine & Associates: Houston, TX, USA; The National Institute of Justice: Washington, DC, USA, 2010.
- Kent, J.; Leitner, M. Utilizing land cover characteristics to enhance journey-to-crime estimation models. Crime Mapp. J. Res. Pract.
**2009**, 1, 33–54. [Google Scholar] - Paulsen, D. Human versus machine: A comparison of the accuracy of geographic profiling methods. J. Investig. Psychol. Offender Prof.
**2006**, 3, 77–89. [Google Scholar] [CrossRef] - Xue, A.Y.; Zhang, R.; Zheng, Y.; Xie, X.; Huang, J.; Xu, Z.H. Destination Prediction by Sub-Trajectory Synthesis and Privacy Protection Against Such Prediction. In Proceedings of the IEEE International Conference on Data Engineering, Brisbane, Australia, 8–12 April 2013; pp. 254–265. [Google Scholar]
- Cho, E.; Myers, S.A.; Leskovec, J. Friendship and Mobility: User Movement in Location-Based Social Networks. In Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining, San Diego, CA, USA, 21–24 August 2011; pp. 1082–1090. [Google Scholar]
- Sadilek, A.; Kautz, H.; Bigham, J.P. Finding Your Friends and Following Them to Where You Are. In Proceedings of the Fifth ACM International Conference on Web Search and Data Mining, Seattle, WA, USA, 8–12 February 2012; pp. 723–732. [Google Scholar]
- Noulas, A.; Scellato, S.; Lathia, N.; Mascolo, C. Mining User Mobility Features for Next Place Prediction in Location-Based Services. In Proceedings of the 2012 IEEE 12th International Conference on Data Mining, Brussels, Belgium, 10–13 December 2012; pp. 1038–1043. [Google Scholar]
- Chang, J.; Sun, E. Location3: How Users Share and Respond to Location-Based Data on Social. In Proceedings of the Fifth International AAAI Conference on Weblogs and Social Media, Barcelona, Spain, 17–21 July 2011; pp. 74–80. [Google Scholar]
- Gao, H.; Tang, J.; Liu, H. Exploring Social-Historical Ties on Location-Based Social Networks. In Proceedings of the Sixth International AAAI Conference on Weblogs and Social Media, Toronto, ON, Canada, 22–26 July 2012; pp. 114–121. [Google Scholar]
- Cheng, Z.; Caverlee, J.; Lee, K.; Sui, D.Z. Exploring Millions of Footprints in Location Sharing Services. In Proceedings of the Fifth International AAAI Conference on Weblogs and Social Media, Barcelona, Spain, 17–21 July 2011; pp. 81–88. [Google Scholar]
- Xiao, X.Y.; Zheng, Y.; Luo, Q.; Xie, X. Finding Similar Users Using Category-Based Location History. In Proceedings of the 18th ACM SIGSPATIAL Conference on Advances in Geographical Information Systems, San Jose, CA, USA, 2–5 November 2010; pp. 442–445. [Google Scholar]
- Horvitz, E.; Krumm, J. Some Help on the Way: Opportunistic Routing Under Uncertainty. In Proceedings of the ACM Conference on Ubiquitous Computing, Pittsburgh, PA, USA, 5–8 September 2012; pp. 371–380. [Google Scholar]
- Krumm, J.; Horvitz, E. Predestination: Where do you want to go today? IEEE Comput.
**2007**, 40, 105–107. [Google Scholar] [CrossRef] - Ziebart, B.D.; Maas, A.L.; Dey, A.K.; Bagnell, J.A. Navigate Like A Cabbie: Probabilistic Reasoning From Observed Context-Aware Behavior. In Proceedings of the 10th International Conference on Ubiquitous Computing, Seoul, Korea, 21–24 September 2008; pp. 322–331. [Google Scholar]
- Gogate, V.; Dechter, R.; Bidyuk, B. Modeling Transportation Routines Using Hybrid Dynamic Mixed Networks. In Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence, Edinburgh, UK, 26–29 July 2005; pp. 217–224. [Google Scholar]
- Cheng, C.; Yang, H.; King, I.; Lyu, M.R. Fused Matrix Factorization with Geographical and Social Influence in Location-Based Social Networks. In Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence, Toronto, ON, Canada, 22–26 July 2012; pp. 17–23. [Google Scholar]
- Liu, Y.; Wei, W.; Sun, A.; Miao, C. Exploiting Geographical Neighborhood Characteristics for Location Recommendation. In Proceedings of the 23rd ACM International Conference on Information and Knowledge Management, Shanghai, China, 3–7 November 2014; pp. 739–748. [Google Scholar]
- Ye, M.; Yin, P.; Lee, W.C.; Lee, D.L. Exploiting Geographical Influence for Collaborative Point of Interest Recommendation. In Proceedings of the 34th International ACM SIGIR Conference on Research and Development in Information Retrieval, Beijing, China, 24–28 July 2011; pp. 325–334. [Google Scholar]
- Gao, H.; Tang, J.; Liu, H. gSCorr: Modeling Geo-Social Correlations for New Check-Ins on Location based Social Networks. In Proceedings of the 21st ACM International Conference on Information and Knowledge Management, Maui, HI, USA, 29 November–2 October 2012; pp. 1582–1586. [Google Scholar]
- Liu, B.; Xiong, H. Point-of-Interest Recommendation in Location Based Social Networks with Topic and Location Awareness. In Proceedings of the 2013 SIAM International Conference on Data Mining, Austin, TX, USA, 2013; pp. 396–404. [Google Scholar]
- Lian, D.; Zhao, C.; Xie, X.; Sun, G.; Chen, E.; Rui, Y. Geomf: Joint Geographical Modeling and Matrix Factorization for Point-of-Interest Recommendation. In Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, New York, NY, USA, 24–27 August 2014; pp. 831–840. [Google Scholar]
- Wang, Y.; Yuan, N.J.; Lian, D.; Xu, L.; Xie, X.; Chen, E.; Rui, Y. Regularity and conformity: Location prediction using heterogeneous mobility data. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Sydney, Australia, 10–13 August 2015; pp. 1275–1284. [Google Scholar]
- Lian, D.; Xie, X.; Zheng, V.W.; Yuan, N.J.; Zhang, F.; Chen, E. CEPR: A collaborative exploration and periodically returning model for location prediction. ACM Trans. Intell. Syst. Technol.
**2015**, 6, 8. [Google Scholar] [CrossRef] - Tayebi, M.A.; Glasser, U.; Ester, M.; Brantingham, P.L. Personalized crime location prediction. Eur. J. Appl. Math.
**2016**, 27, 422–450. [Google Scholar] [CrossRef] - Ester, M.; Kriegel, H.P.; Sander, J.; Xu, X.W. A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise. In Proceedings of the 2nd International Conference on Knowledge Discovery and Data Mining, Portland, OR, USA, 2–4 August 1996; pp. 226–231. [Google Scholar]
- Aljazzar, H.; Leue, S. K: A heuristic search algorithm for finding the k shortest paths. Artif. Intell.
**2011**, 175, 2129–2154. [Google Scholar] [CrossRef] - Baidu Geocoding API. Available online: http://lbsyun.baidu.com/index.php?title=webapi/guide/webservice-geocoding (accessed on 10 June 2015).
- Geopy. Available online: https://github.com/geopy/geopy (accessed on 10 June 2015).
- Wikipedia. Hyperparameter Optimization. Available online: https://en.wikipedia.org/wiki/Hyperparameter_optimization (accessed on 15 June 2015).
- Wells, W.; Wu, L.; Ye, X. Patterns of near-repeat gun assaults in Houston. J. Res. Crime Delinq.
**2012**, 49, 186–212. [Google Scholar] [CrossRef] - Chen, N.; Chen, Y.; Song, S.; Huang, C.T.; Ye, X. Smart Urban Surveillance Using Fog Computing. IEEE/ACM Symp. Edge Comput. (SEC)
**2016**, 95–96. [Google Scholar] - Ye, X.; Huang, Q.; Li, W. Integrating big social data, computing and modeling for spatial social science. Cartogr. Geogr. Inf. Sci.
**2016**, 43, 377–378. [Google Scholar] [CrossRef] - Ye, X.; Liu, L. Spatial Crime Analysis and Modeling. Ann. GIS
**2012**, 18, 157. [Google Scholar] [CrossRef]

**Figure 3.**(

**a**) No transition information for unobserved location (

**b**) Transition information for unobserved location.

**Figure 4.**(

**a**) trajectory location to peripheral location (

**b**) peripheral location to trajectory location.

Parameter | Parameter Space |
---|---|

ε | {300, 350, …, 800} |

h_{d} | {100, 200, …, 500} |

h_{s} | {0.1, 0.2, …, 0.5} |

a_{1} | {0, 0.1, …, 1} |

a_{2,} | {0, 0.1, …, 1} |

a_{3} | {0, 0.1, …, 1} |

a_{4} | {0, 0.1, …, 1} |

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## Share and Cite

**MDPI and ACS Style**

Duan, L.; Ye, X.; Hu, T.; Zhu, X.
Prediction of Suspect Location Based on Spatiotemporal Semantics. *ISPRS Int. J. Geo-Inf.* **2017**, *6*, 185.
https://doi.org/10.3390/ijgi6070185

**AMA Style**

Duan L, Ye X, Hu T, Zhu X.
Prediction of Suspect Location Based on Spatiotemporal Semantics. *ISPRS International Journal of Geo-Information*. 2017; 6(7):185.
https://doi.org/10.3390/ijgi6070185

**Chicago/Turabian Style**

Duan, Lian, Xinyue Ye, Tao Hu, and Xinyan Zhu.
2017. "Prediction of Suspect Location Based on Spatiotemporal Semantics" *ISPRS International Journal of Geo-Information* 6, no. 7: 185.
https://doi.org/10.3390/ijgi6070185