# 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.$$Er{r}_{{O}_{i}}\left(r\right)=\left\{\begin{array}{cc}\hfill Er{r}_{{O}_{i}}^{poly}\left(r\right),& \phantom{\rule{4.pt}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}{O}_{i}\phantom{\rule{4.pt}{0ex}}\mathrm{is}\phantom{\rule{4.pt}{0ex}}\mathrm{Polygon}\phantom{\rule{4.pt}{0ex}}\hfill \\ \hfill Er{r}_{{O}_{i}}^{line}\left(r\right),& \phantom{\rule{4.pt}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}{O}_{i}\phantom{\rule{4.pt}{0ex}}\mathrm{is}\phantom{\rule{4.pt}{0ex}}\mathrm{Line}\phantom{\rule{4.pt}{0ex}}\mathrm{String}\phantom{\rule{4.pt}{0ex}}\hfill \\ \hfill 0,& \phantom{\rule{4.pt}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}{O}_{i}\phantom{\rule{4.pt}{0ex}}\mathrm{is}\phantom{\rule{4.pt}{0ex}}\mathrm{Point}\phantom{\rule{4.pt}{0ex}}\hfill \end{array}\right.$$$$Er{r}_{{O}_{i}}^{poly}\left(r\right)=\left|\frac{{S}_{orig}^{{O}_{i}}-{S}_{disc}^{{O}_{i}}\left(r\right)}{{S}_{orig}^{{O}_{i}}}\right|,\left({S}_{orig}\ne 0\right)$$$$Er{r}_{{O}_{i}}^{line}\left(r\right)=\left|\frac{{S}_{orig}^{{B}_{{b}_{l}}\left({O}_{i}\right)}-{S}_{disc}^{{O}_{i}}\left(r\right)}{{S}_{orig}^{{B}_{{b}_{l}}\left({O}_{i}\right)}}\right|,\left({S}_{orig}^{{B}_{{b}_{l}}\left({O}_{i}\right)}\ne 0\right)$$

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 |

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**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