# STO2Vec: A Multiscale Spatio-Temporal Object Representation Method for Association Analysis

^{*}

## Abstract

**:**

## 1. Introduction

- We propose an adaptive discretization method based on hexagons, which can decompose spatio-temporal objects of different scale sizes into a collection of grids with different resolutions, thereby conserving more of the original spatio-temporal features.
- We designed an associated heterogeneous graph model that can describe the geographic scope and frequency of co-occurrence between spatio-temporal objects based on scale differences. This model enables object embedding for association analysis.
- To improve the scalability of representation methods and the quality of representation results, we designed a biased sampling strategy that can provide richer, application-specific associative information for object representation.
- We constructed a multiscale spatio-temporal object representation method called STO2Vec, which is oriented towards association analysis. We performed accuracy tests on association analysis using the representation results of STO2Vec on real datasets.

## 2. Related Work

#### 2.1. Semantic Trajectory

#### 2.2. Location Embedding

## 3. Preliminary

#### 3.1. Spatio-Temporal Object

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

- (i)
- $\forall u\phantom{\rule{3.33333pt}{0ex}}s.t.\phantom{\rule{3.33333pt}{0ex}}1\le u\le m,\phantom{\rule{3.33333pt}{0ex}}{e}_{u}\phantom{\rule{3.33333pt}{0ex}}is\phantom{\rule{4.pt}{0ex}}a\phantom{\rule{4.pt}{0ex}}trajectory\phantom{\rule{4.pt}{0ex}}segment,\phantom{\rule{4.pt}{0ex}}which\phantom{\rule{4.pt}{0ex}}is\phantom{\rule{4.pt}{0ex}}a\phantom{\rule{4.pt}{0ex}}subsequence\phantom{\rule{4.pt}{0ex}}\{{a}_{l},{a}_{l+1},\dots ,{a}_{l+k}\}\phantom{\rule{3.33333pt}{0ex}}of\phantom{\rule{3.33333pt}{0ex}}Tr.$
- (ii)
- ${\bigcup}_{u=1}^{m}{e}_{u}=Tr\phantom{\rule{4.pt}{0ex}}and\phantom{\rule{4.pt}{0ex}}{e}_{u}\cap {e}_{v}=\varnothing ,(u\ne v)$.

#### 3.2. Space Discretization

**Definition**

**4.**

**Definition**

**5.**

#### 3.3. Heterogeneous Graph

**Definition**

**6.**

**Definition**

**7.**

**Definition**

**8.**

**Definition**

**9.**

## 4. Method

#### 4.1. Overall Framework

#### 4.2. Data Preprocessing

#### 4.3. Graph Construction

#### 4.3.1. Adaptive Discretization

- The number of grids ${N}_{{O}_{i}}\left(r\right)$: ${N}_{{O}_{i}}\left(r\right)$ is the total number of grids after discretization of the spatio-temporal object ${O}_{i}$ at level r. Obviously, the accuracy of the discretization ${O}_{i}$ increases as r increases, which also leads to an increase in ${N}_{{O}_{i}}\left(r\right)$ and the computational overhead.
- Discretization error $Er{r}_{{O}_{i}}\left(r\right)$: We use $Er{r}_{{O}_{i}}\left(r\right)$ to measure the information loss brought by discretization to the spatio-temporal object description, which is calculated as in Equation (4). For polygon elements, inspired by the error analysis method of rasterization of vector elements [43], we choose to use the area relative error $Er{r}_{{O}_{i}}^{poly}\left(r\right)$ to calculate (Equation (5)), where ${S}_{orig}^{{O}_{i}}$ is the area before discretization and ${S}_{disc}^{{O}_{i}}\left(r\right)$ is the area after discretization. For line elements, we generate the buffer ${B}_{{b}_{l}}\left({O}_{i}\right)$ of line elements with radius ${b}_{l}$ and then use the area relative error for calculation (Equation (6)). For point elements, a uniform grid resolution ${r}_{p}$ is used for discretization.$$Er{r}_{{O}_{i}}\left(r\right)=\left(\right)open="\{"\; close>\begin{array}{cc}\hfill Er{r}_{{O}_{i}}^{poly}\left(r\right),& \phantom{\rule{4.pt}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}{O}_{i}\phantom{\rule{4.pt}{0ex}}\mathrm{is}\phantom{\rule{4.pt}{0ex}}\mathrm{Polygon}\phantom{\rule{4.pt}{0ex}}\hfill \\ \hfill Er{r}_{{O}_{i}}^{line}\left(r\right),& \phantom{\rule{4.pt}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}{O}_{i}\phantom{\rule{4.pt}{0ex}}\mathrm{is}\phantom{\rule{4.pt}{0ex}}\mathrm{Line}\phantom{\rule{4.pt}{0ex}}\mathrm{String}\phantom{\rule{4.pt}{0ex}}\hfill \\ \hfill 0,& \phantom{\rule{4.pt}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}{O}_{i}\phantom{\rule{4.pt}{0ex}}\mathrm{is}\phantom{\rule{4.pt}{0ex}}\mathrm{Point}\phantom{\rule{4.pt}{0ex}}\hfill \end{array}$$$$Er{r}_{{O}_{i}}^{poly}\left(r\right)=\left(\right)open="|"\; close="|">\frac{{S}_{orig}^{{O}_{i}}-{S}_{disc}^{{O}_{i}}\left(r\right)}{{S}_{orig}^{{O}_{i}}}$$$$Er{r}_{{O}_{i}}^{line}\left(r\right)=\left(\right)open="|"\; close="|">\frac{{S}_{orig}^{{B}_{{b}_{l}}\left(\right)open="("\; close=")">{O}_{i}}}{-}{S}_{orig}^{{B}_{{b}_{l}}\left(\right)open="("\; close=")">{O}_{i}}$$

Algorithm 1: Adaptive Discretization Algorithm |

#### 4.3.2. Heterogeneous Graph Model

#### 4.4. Embedding

#### 4.4.1. Objective Function

#### 4.4.2. Biased Sampling

## 5. Experiment

#### 5.1. Experiment Setup

#### 5.1.1. Data Preparation

#### 5.1.2. Parameter Setting

#### 5.1.3. Evaluation Metrics

#### 5.1.4. Baseline

- Mot2vec [28]: The algorithm is based on the Word2vec model, which uses the trajectories of pedestrians moving between geographic entities to construct a behavioral representation of locations. The algorithm does not use grid partitioning but rather generates IDs of geographic entities based on point clustering and then converts the trajectories into ID sequences for embedding. According to the data characteristics, we use a time window of $timestep=5$ $\mathrm{min}$ in the preprocessing stage to label the trajectories with geographic entities, with the minimum spatial resolution being 5 km.
- Hier [32]: This similar algorithm uses a multilevel embedding grid, which aggregates rectangular grid vectors of different levels into fine-grained grids during embedding. Due to the large study area in this paper, we used 100 km and 10 km grid cells in the first and second level, respectively. The fine-grained level uses 1 km grid cells. The embedding dimension is the same as STO2Vec, the first 48 dimensions correspond to 100 km grid, the last 80 dimensions correspond to a 10 km grid, the remaining 128 dimensions correspond to a 1 km grid.
- GCN-L2V [31]: To generate fine-grained grid embeddings, the GCN and Skip-gram models were used to construct spatial graphs and flow graphs to account for both spatial proximity and the movement patterns of moving objects. The algorithm uses a single-level Google S2 grid system. According to the scale of the study area, we mapped trajectories and geographic entities to the 11-level (the average area of each grid area is about 20.2682 km${}^{2}$) of Google S2 to generate edges between grids in spatial graphs with a distance threshold of 1 km.

#### 5.2. Homogeneous Association Analysis

#### 5.2.1. Trajectory Similarity Analysis

**Ground Truth Generation.**For moving objects, the similar association of their trajectories is a typical spatio-temporal association. By comparing the similarity analysis results of trajectories, we could verify the effect of the algorithm in association metrics and discovery between moving objects. There are many existing mature algorithms for trajectory similarity metrics based on geometric features, which accurately calculate the similarity between trajectories by matching point by point.Therefore, we used the dynamic time warping algorithm [52] to generate the similarity matrix between trajectories on the dataset A. We then created the experimental ground truth according to the order of similarity, ensuring that all trajectories had a similarity greater than $0.7$.

**Result for Trajectory Similarity Analysis.**We randomly selected 1000 trajectories from the dataset A, using different models to generate a list of similar trajectories for comparison with the ground truth. Since the results of the trajectory similarity metric are order sensitive, we used $NDCG@K$ to evaluate the experimental results. The results are shown in Table 4.

#### 5.2.2. Region Association Analysis

**Ground Truth Generation.**According to the first law of geography [3] and the semantic characteristics of geographic entities, it is known that geographic entities with spatial proximity and semantic similarity are more strongly associated [30]. Region association analysis is often used to discover the functional structure of cities to help in transportation and urban planning. Due to the large-scale of the study area, we consider geospatial entities within the same $region$ as clusters that have associations. We generate a ground truth by sorting these clusters according to their distance from each other. The $region$ range was generated by the Urban dataset.

**Results for Trajectory Similarity Analysis.**There are a total of 16,073 other geographic entities with containment relationship with the Urban dataset, from which we randomly selected 2000 for testing. Ideally, the K geographic entities with the greatest association strength with the sample still belong to the region where the sample is located. Moreover, the closer the entities are, the higher the association strength. For this reason, we chose $NDCG@K$ for evaluation. The experimental results are shown in Table 5.

#### 5.3. Heterogeneous Association Analysis

**Ground Truth Generation.**In our experiments, we used different models to output the K geographic entities most associated with moving objects, to test the effectiveness of the algorithm predictions by comparing the actual visit results. The actual access results, namely ground truth, are generated by extracting the geographic entities visited by each moving object from the dataset C.

**Result for Trajectory Similarity Analysis.**To obtain more information on historical visits, we construct a heterogeneous graph oriented to spatio-temporal association based on the B dataset and the geographic entity dataset, containing $\mathrm{1,676,516}$ nodes and $\mathrm{4,206,884}$ edges, setting the homogeneous parameter $k=1$, the heterogeneous parameter $m=2$ and the spatial parameter $l=0$. Since the real visited list is not order sensitive, we used the hit rate $HR@K$ as the evaluation metric for this experiment. The experimental results are shown in Table 6.

#### 5.4. Case Study

#### 5.4.1. Urban Association Analysis

#### 5.4.2. Coastline Association Analysis

## 6. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

POI | point of interest |

OD | origin destination |

UTM | Universal Transverse Mercator |

GPS | global positioning system |

ICAO | International Civil Aviation Organization |

HR | hitting ratio |

NDCG | normalized discounted cumulative gain |

## References

- Hamdi, A.; Shaban, K.; Erradi, A.; Mohamed, A.; Rumi, S.K.; Salim, F.D. Spatiotemporal Data Mining: A Survey on Challenges and Open Problems. Artif. Intell. Rev.
**2022**, 55, 1441–1488. [Google Scholar] [CrossRef] [PubMed] - Sharma, A.; Jiang, Z.; Shekhar, S. Spatiotemporal Data Mining: A Survey. arXiv
**2022**, arXiv:2206.12753. [Google Scholar] [CrossRef] - Tobler, W.R. A Computer Movie Simulating Urban Growth in the Detroit Region. Econ. Geogr.
**1970**, 46, 234. [Google Scholar] [CrossRef] - Wu, C.; Zhu, Q.; Zhang, Y.T.; Du, Z.Q.; Zhou, Y.; Xie, X.; He, F. An Adaptive Organization Method of Geovideo Data for Spatio-Temporal Association Analysis. ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci.
**2015**, II-4/W2, 29–34. [Google Scholar] [CrossRef] - Crivellari, A.; Ristea, A. CrimeVec—Exploring Spatial-Temporal Based Vector Representations of Urban Crime Types and Crime-Related Urban Regions. ISPRS Int. J. Geo-Inf.
**2021**, 10, 210. [Google Scholar] [CrossRef] - Riyadh, M.; Mustapha, N.; Riyadh, D. Review of Trajectories Similarity Measures in Mining Algorithms. In Proceedings of the 2018 Al-Mansour International Conference on New Trends in Computing, Communication, and Information Technology (NTCCIT), Baghdad, Iraq, 14–15 November 2018; pp. 36–40. [Google Scholar] [CrossRef]
- Cai, J.; Deng, M.; Guo, Y.; Xie, Y.; Shekhar, S. Discovering Regions of Anomalous Spatial Co-Locations. Int. J. Geogr. Inf. Sci.
**2021**, 35, 974–998. [Google Scholar] [CrossRef] - Noureddine, H.; Ray, C.; Claramunt, C. A Hierarchical Indoor and Outdoor Model for Semantic Trajectories. Trans. GIS
**2022**, 26, 214–235. [Google Scholar] [CrossRef] - Sakouhi, T.; Akaichi, J. Dynamic and Multi-Source Semantic Annotation of Raw Mobility Data Using Geographic and Social Media Data. Pervasive Mob. Comput.
**2021**, 71, 101310. [Google Scholar] [CrossRef] - Kontarinis, A.; Zeitouni, K.; Marinica, C.; Vodislav, D.; Kotzinos, D. Towards a Semantic Indoor Trajectory Model: Application to Museum Visits. Geoinformatica
**2021**, 25, 311–352. [Google Scholar] [CrossRef] - Alvares, L.O.; Bogorny, V.; Kuijpers, B.; de Macedo, J.A.F.; Moelans, B.; Vaisman, A. A Model for Enriching Trajectories with Semantic Geographical Information. In Proceedings of the 15th Annual ACM International Symposium on Advances in Geographic Information Systems—GIS’07, Seattle, WA, USA, 7–9 November 2007; p. 1. [Google Scholar] [CrossRef]
- Zhao, B.; Liu, M.; Han, J.; Ji, G.; Liu, X. Efficient Semantic Enrichment Process for Spatiotemporal Trajectories. Wirel. Commun. Mob. Commun.
**2021**, 2021, 4488781. [Google Scholar] [CrossRef] - Vidal-Filho, J.N.; Times, V.C.; Lisboa-Filho, J.; Renso, C. Towards the Semantic Enrichment of Trajectories Using Spatial Data Infrastructures. ISPRS Int. J. Geo-Inf.
**2021**, 10, 825. [Google Scholar] [CrossRef] - Ibrahim, A.; Zhang, H.; Clinch, S.; Harper, S. From GPS to Semantic Data: How and Why—A Framework for Enriching Smartphone Trajectories. Computing
**2021**, 103, 2763–2787. [Google Scholar] [CrossRef] - Ying, J.J.C.; Lee, W.C.; Tseng, V.S. Mining Geographic-Temporal-Semantic Patterns in Trajectories for Location Prediction. ACM Trans. Intell. Syst. Technol.
**2013**, 5, 1–33. [Google Scholar] [CrossRef] - Noureddine, H.; Ray, C.; Claramunt, C. Semantic Trajectory Modelling in Indoor and Outdoor Spaces. In Proceedings of the 2020 21st IEEE International Conference on Mobile Data Management (MDM), Versailles, France, 30 June–3 July 2020; pp. 131–136. [Google Scholar] [CrossRef]
- Choi, D.W.; Pei, J.; Heinis, T. Efficient Mining of Regional Movement Patterns in Semantic Trajectories. Proc. VLDB Endow.
**2017**, 10, 2073–2084. [Google Scholar] [CrossRef] - Wan, C.; Zhu, Y.; Yu, J.; Shen, Y. SMOPAT: Mining Semantic Mobility Patterns from Trajectories of Private Vehicles. Inf. Sci.
**2018**, 429, 12–25. [Google Scholar] [CrossRef] - Fang, Z.; Du, Y.; Zhu, X.; Chen, L.; Gao, Y.; Jensen, C.S. Deep Spatially and Temporally Aware Similarity Computation for Road Network Constrained Trajectories. arXiv
**2022**, arXiv:2112.09339. [Google Scholar] [CrossRef] - Karami, F.; Malek, M.R. Trajectory Similarity Measurement: An Enhanced Maximal Travel Match Method. Trans. GIS
**2021**, 25, 1485–1503. [Google Scholar] [CrossRef] - Lehmann, A.L.; Alvares, L.O.; Bogorny, V. SMSM: A Similarity Measure for Trajectory Stops and Moves. Int. J. Geogr. Inf. Sci.
**2019**, 33, 1847–1872. [Google Scholar] [CrossRef] - Xiang, L.; Wu, T.; Ettema, D. An Intersection-Based Trajectory-Region Movement Study. Trans. GIS
**2017**, 21, 701–721. [Google Scholar] [CrossRef] - Sun, Z.; Jiao, H.; Wu, H.; Peng, Z.; Liu, L. Block2vec: An Approach for Identifying Urban Functional Regions by Integrating Sentence Embedding Model and Points of Interest. ISPRS Int. J. Geo-Inf.
**2021**, 10, 339. [Google Scholar] [CrossRef] - Zhang, C.; Xu, L.; Yan, Z.; Wu, S. A GloVe-Based POI Type Embedding Model for Extracting and Identifying Urban Functional Regions. ISPRS Int. J. Geo-Inf.
**2021**, 10, 372. [Google Scholar] [CrossRef] - Zhang, J.; Li, X.; Yao, Y.; Hong, Y.; He, J.; Jiang, Z.; Sun, J. The Traj2Vec Model to Quantify Residents’ Spatial Trajectories and Estimate the Proportions of Urban Land-Use Types. Int. J. Geogr. Inf. Sci.
**2021**, 35, 193–211. [Google Scholar] [CrossRef] - Zhu, M.; Chen, W.; Xia, J.; Ma, Y.; Zhang, Y.; Luo, Y.; Huang, Z.; Liu, L. Location2vec: A Situation-Aware Representation for Visual Exploration of Urban Locations. IEEE Trans. Intell. Transport. Syst.
**2019**, 20, 3981–3990. [Google Scholar] [CrossRef] - Du, J.; Chen, Y.; Wang, Y.; Pu, J. Zone2Vec: Distributed Representation Learning of Urban Zones. In Proceedings of the 2018 24th International Conference on Pattern Recognition (ICPR), Beijing, China, 20–24 August 2018; pp. 880–885. [Google Scholar] [CrossRef]
- Crivellari, A.; Beinat, E. From Motion Activity to Geo-Embeddings: Generating and Exploring Vector Representations of Locations, Traces and Visitors through Large-Scale Mobility Data. ISPRS Int. J. Geo-Inf.
**2019**, 8, 134. [Google Scholar] [CrossRef] - Jenkins, P.; Farag, A.; Wang, S.; Li, Z. Unsupervised Representation Learning of Spatial Data via Multimodal Embedding. In Proceedings of the 28th ACM International Conference on Information and Knowledge Management, Beijing, China, 3–7 November 2019; pp. 1993–2002. [Google Scholar] [CrossRef]
- Woźniak, S.; Szymański, P. Hex2vec: Context-Aware Embedding H3 Hexagons with OpenStreetMap Tags. In Proceedings of the 4th ACM SIGSPATIAL International Workshop on AI for Geographic Knowledge Discovery, Beijing, China, 2–5 November 2021; pp. 61–71. [Google Scholar] [CrossRef]
- Tian, C.; Zhang, Y.; Weng, Z.; Gu, X.; Chan, W.K. Learning Fine-grained Location Embedding from Human Mobility with Graph Neural Networks. In Proceedings of the 2022 International Joint Conference on Neural Networks (IJCNN), Padua, Italy, 18–23 July 2022; pp. 1–8. [Google Scholar] [CrossRef]
- Shimizu, T.; Yabe, T.; Tsubouchi, K. Enabling Finer Grained Place Embeddings Using Spatial Hierarchy from Human Mobility Trajectories. In Proceedings of the 28th International Conference on Advances in Geographic Information Systems, Seattle, WA, USA, 3–6 November 2020; pp. 187–190. [Google Scholar] [CrossRef]
- Yin, Y.; Liu, Z.; Zhang, Y.; Wang, S.; Shah, R.R.; Zimmermann, R. GPS2Vec: Towards Generating Worldwide GPS Embeddings. In Proceedings of the 27th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, Chicago, IL, USA, 5–8 November 2019; pp. 416–419. [Google Scholar] [CrossRef]
- Souza, A.P.R.; Renso, C.; Perego, R.; Bogorny, V. MAT-Index: An Index for Fast Multiple Aspect Trajectory Similarity Measuring. Trans. GIS
**2022**, 26, 691–716. [Google Scholar] [CrossRef] - Gao, C.; Zhang, Z.; Huang, C.; Yin, H.; Yang, Q.; Shao, J. Semantic Trajectory Representation and Retrieval via Hierarchical Embedding. Inf. Sci.
**2020**, 538, 176–192. [Google Scholar] [CrossRef] - Chu, C.; Zhang, H.; Lu, F. Inferring Consumption Behavior of Customers in Shopping Malls from Indoor Trajectories. J. Geo-Inf. Sci.
**2022**, 24, 1034–1046. [Google Scholar] - Niemeyer, G. Geohash. Available online: http://geohash.org/ (accessed on 16 October 2022).
- GitHub Inc. S2 Geometry. Available online: https://s2geometry.io (accessed on 21 October 2022).
- Uber Technologies Inc. H3: Uber’s Hexagonal Hierarchical Spatial Index. Available online: https://eng.uber.com/h3 (accessed on 17 December 2022).
- Pelekis, N.; Theodoulidis, B.; Kopanakis, I.; Theodoridis, Y. Literature Review of Spatio-Temporal Database Models. Knowl. Eng. Rev.
**2004**, 19, 235–274. [Google Scholar] [CrossRef] - Tao, Y.; Both, A.; Silveira, R.I.; Buchin, K.; Sijben, S.; Purves, R.S.; Laube, P.; Peng, D.; Toohey, K.; Duckham, M. A Comparative Analysis of Trajectory Similarity Measures. GIsci. Remote Sens.
**2021**, 58, 643–669. [Google Scholar] [CrossRef] - Mai, G.; Janowicz, K.; Hu, Y.; Gao, S.; Yan, B.; Zhu, R.; Cai, L.; Lao, N. A Review of Location Encoding for GeoAI: Methods and Applications. Int. J. Geogr. Inf. Sci.
**2022**, 36, 639–673. [Google Scholar] [CrossRef] - Chen, J.; Zhou, C.; Cheng, W. Area Error Analysis of Vector to Raster Conversion of Areal Feature in GIS. Acta Geod. Cartogr. Sin.
**2007**, 36, 344–350. [Google Scholar] - Mikolov, T.; Sutskever, I.; Chen, K.; Corrado, G.S.; Dean, J. Distributed Representations of Words and Phrases and Their Compositionality. In Proceedings of the Advances in Neural Information Processing Systems, Lake Tahoe, NV, USA, 5–10 December 2013; Burges, C.J., Bottou, L., Welling, M., Ghahramani, Z., Weinberger, K.Q., Eds.; Curran Associates, Inc.: Red Hook, NY, USA, 2013; Volume 26. [Google Scholar]
- Dong, Y.; Chawla, N.V.; Swami, A. Metapath2vec: Scalable Representation Learning for Heterogeneous Networks. In Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Halifax, NS, Canada, 13–17 August 2017; pp. 135–144. [Google Scholar] [CrossRef]
- Sun, Y.; Han, J.; Yan, X.; Yu, P.S.; Wu, T. PathSim: Meta Path-Based Top-K Similarity Search in Heterogeneous Information Networks. Proc. VLDB Endow.
**2011**, 4, 992–1003. [Google Scholar] [CrossRef] - Grover, A.; Leskovec, J. Node2vec: Scalable Feature Learning for Networks. arXiv
**2016**, arXiv:1607.00653. [Google Scholar] [CrossRef] - Kelso, N.V.; Patterson, T. Natural Earth. 2022. Available online: https://www.naturalearthdata.com/ (accessed on 10 November 2022).
- Megginson, D. Ourairports. 2022. Available online: https://ourairports.com (accessed on 23 December 2022).
- Schafer, M.; Strohmeier, M.; Lenders, V.; Martinovic, I.; Wilhelm, M. Bringing up OpenSky: A Large-Scale ADS-B Sensor Network for Research. In Proceedings of the IPSN-14 Proceedings of the 13th International Symposium on Information Processing in Sensor Networks, Berlin, Germany, 15–17 April 2014; pp. 83–94. [Google Scholar] [CrossRef]
- Han, P.; Wang, J.; Yao, D.; Shang, S.; Zhang, X. A Graph-based Approach for Trajectory Similarity Computation in Spatial Networks. In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, Singapore, 14–18 August 2021; pp. 556–564. [Google Scholar] [CrossRef]
- Keogh, E.J.; Pazzani, M.J. Scaling up Dynamic Time Warping for Datamining Applications. In Proceedings of the Sixth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Boston, MA, USA, 20–23 August 2000; pp. 285–289. [Google Scholar] [CrossRef]

**Figure 1.**Illustration of Spatio-Temporal Association. Aircraft A takes off from airport Q to farmland M on a pesticide-spraying mission and then lands at airport P. There is an association between A and B due to similar local trajectories; aircraft A hovers repeatedly over farmland M, so there is a strong association between A and M. There is also an association between A and L as creek C passes through farmland M to deliver pesticides to lake L.

**Figure 6.**Example of Association Heterogeneous Graph. The moving object ${M}_{a}$ has trajectory segments ${S}_{{a}_{1}}$ and ${S}_{{a}_{2}}$, where ${S}_{{a}_{1}}$ is discretized with grids ${H}_{1}$, ${H}_{2}$, ${H}_{3}$. The geographic entity ${G}_{a}$ has subgeographic entities ${P}_{{a}_{1}}$ and ${P}_{{a}_{2}}$, where ${P}_{{a}_{1}}$ is discretized with grids are ${H}_{7}$, ${H}_{8}$.

Grid Systems | Projection | Isotropy | Hierarchical Coverage |
---|---|---|---|

Google S2 | Regular hexahedron | Copoint, Colinear | Accurate |

Geohash | Orthoaxial equiangular cylindrical | Copoint, Colinear | Accurate |

Uber H3 | Regular icosahedron | Colinear | Approximate |

Geographic Entity | Count |
---|---|

Airport | 27,675 |

Coastline | 192 |

Lakes | 418 |

Parks and protected lands | 148 |

Railroad | 873 |

Rivers | 1391 |

River and lake center lines | 314 |

Roads | 39,918 |

State | 254 |

Urban | 1120 |

Dataset | A | B | C |
---|---|---|---|

Date | 20-06 | 06-06, 13-06, 20-06 | 27-06 |

Num.Aircraft | 5661 | 900 | 900 |

Num.Traces | 5661 | 2753 | 919 |

Num.Traces Seg | 50,321 | 41,846 | 13,166 |

Avg Num.Points | 330.757 | 519 | 522.534 |

Avg Trace Length ^{1} | 276.504 | 464.043 | 482.19 |

^{1}Data in minutes.

Method | NDCG@10 | NDCG@20 | NDCG@30 | NDCG@40 | NDCG@50 |
---|---|---|---|---|---|

Mot2Vec | 0.3325 | 0.3741 | 0.4021 | 0.4416 | 0.4592 |

Hier | 0.265 | 0.3327 | 0.3987 | 0.4122 | 0.4157 |

GCN-L2V | 0.3755 | 0.4312 | 0.498 | 0.5152 | 0.516 |

STO2Vec | 0.5468 | 0.6205 | 0.6562 | 0.671 | 0.6752 |

**bold**and the second best results are underlined.

Method | NDCG@10 | NDCG@20 | NDCG@30 | NDCG@40 | NDCG@50 |
---|---|---|---|---|---|

Mot2Vec | 0.3125 | 0.3853 | 0.4152 | 0.428 | 0.4394 |

Hier | 0.3875 | 0.4521 | 0.4817 | 0.4946 | 0.5084 |

GCN-L2V | 0.4133 | 0.497 | 0.5156 | 0.5227 | 0.5291 |

STO2Vec | 0.4096 | 0.4918 | 0.5262 | 0.5356 | 0.5434 |

**bold**and the second best results are underlined.

Method | HR@10 | HR@30 | HR@40 | HR@50 |
---|---|---|---|---|

Mot2Vec | 12.63% | 28.7% | 33.57% | 39.68% |

Hier | 16.76% | 35.66% | 42.57% | 46.9% |

GCN-L2V | 17.15% | 34.93% | 41.39% | 47.23% |

STO2Vec | 18.08% | 40.71% | 47.06% | 51.42% |

**bold**and the second best results are underlined.

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## Share and Cite

**MDPI and ACS Style**

Chen, N.; Yang, A.; Chen, L.; Xiong, W.; Jing, N.
STO2Vec: A Multiscale Spatio-Temporal Object Representation Method for Association Analysis. *ISPRS Int. J. Geo-Inf.* **2023**, *12*, 207.
https://doi.org/10.3390/ijgi12050207

**AMA Style**

Chen N, Yang A, Chen L, Xiong W, Jing N.
STO2Vec: A Multiscale Spatio-Temporal Object Representation Method for Association Analysis. *ISPRS International Journal of Geo-Information*. 2023; 12(5):207.
https://doi.org/10.3390/ijgi12050207

**Chicago/Turabian Style**

Chen, Nanyu, Anran Yang, Luo Chen, Wei Xiong, and Ning Jing.
2023. "STO2Vec: A Multiscale Spatio-Temporal Object Representation Method for Association Analysis" *ISPRS International Journal of Geo-Information* 12, no. 5: 207.
https://doi.org/10.3390/ijgi12050207