# A Correlation Analysis Method for Geographical Object Flows from a Geoeconomic Perspective

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Framework

#### 2.2. Method of Organizing Geographic Object Flow Data

#### 2.2.1. Time Series Segmentation of Data

#### 2.2.2. Determination of Attribute Data

_{ab}is the rate of change of the flow of geographical objects from$Ob{j}_{a}$ to $Ob{j}_{b}$ in the period from t − 1 to t.

_{ab}is a multivalued discrete dataset, when mining association rules, the continuous data are usually divided into intervals using mathematical and statistical methods. Then, the corresponding attributes for each interval are identified according to the statistical significance of the relations among the data. Next, the transformed attribute I is mined with the association rule algorithm. The attributes obtained through geographic object flow association rule mining can be divided into 5 categories, as shown in Table 1.

#### 2.2.3. Hierarchical Organization of Data

#### 2.3. Association Rule Mining Algorithm Based on Hierarchical Constraints

#### 2.3.1. Related Definitions Used in Association Rule Mining

#### 2.3.2. Hierarchical Constraints and Implementation Methods

- Same-level Constraints. A frequent termset ${C}_{k}$ that satisfies $\left\{{C}_{k}\right|{I}_{1},{I}_{2},\dots {I}_{i}\}$ or $\left\{{C}_{k}\right|{I}_{i-1},{I}_{i-2},\dots {I}_{i-j}\}$ when$\mathrm{k}\ge 2$ exists. ${I}_{i}$ is a parent attribute item for a geographic object flow, and ${I}_{i-j}$ is a child attribute item for a geographic object flow i.e., either or all the parent or child attribute items of geographic object flows are in the frequent item set.
- Cross-level constraints. There is a frequent termset ${C}_{k}$ that satisfies$\left\{{C}_{k}\right|{I}_{i},{I}_{i-j}\}$ when$k\ge 2$. ${I}_{i}$ is a parent attribute item for a geographic object flow, and ${I}_{i-j}$ is a child attribute item for a geographic object flow; i.e., there must be at least one parent attribute item and one child attribute for a geographic object flow in the frequent item set.
- The frequent item sets used for association analysis must be greater than or equal to the 2 items.
- A sublevel geographic object flow is a frequent item set if the corresponding parent geographic object flow is frequent.

#### 2.3.3. Hierarchical Constraint-Based Association Rule Mining Algorithm

- Read the data
- Obtain the set of 1-candidate item sets for the parent and child geographic object flows
- Calculate the support of all 1-candidate item sets, and filter the 1-frequent item sets that exceed the support threshold
- Construct the parent–child candidate matrix
- Generate a 2-frequent item set that satisfies the hierarchical constraints
- Loop: When the number of (k − 1)-frequent item sets is greater than 0
- k candidate item sets are generated from (k − 1)-frequent item sets
- Iterate over the support of k candidate item sets and filter out k frequent item sets that are greater than the support threshold
- Calculate the confidence level for each k-frequent item set and filter out the item sets that are greater than the confidence level threshold
- K = k + 1
- The loop ends, and all strongly associated rules that satisfy the support and confidence threshold conditions are obtained.

#### 2.3.4. Validation Method Based on Correlation Analysis

## 3. Experiment and Results

#### 3.1. Study Area and Data Sources

#### 3.2. Results and Analysis

#### 3.2.1. Analysis of the Basic Features of Trade Flow Associations

- Basic information on trade flows with strong linkages

- 2.
- Frequency characteristics of strongly correlated trade flows

- 3.
- Characteristics of the subject country distribution for strongly correlated trade flows

- 4.
- Cross-level trade flow correlation characteristics

#### 3.2.2. Country-Specific Trade Flow Correlation Analysis

- The strongly correlated trade flows observed for Japan mainly involve South Korea, the United States, Malaysia, Thailand, and the Philippines, indicating that trade transactions between Japan and these countries have the greatest impact on Japan’s trade relations with other countries to some extent. However, overall, the probability that each country in the region being strongly associated with Japan is relatively small. This indicates that Japan has a relatively balanced trade pattern in the study area, which is one of the important reasons why Japan is characterized by high economic influence in the region.
- The strongly correlated trade flows observed for the U.S. are relatively uniformly distributed among different countries, with only two countries, Japan and Malaysia, being slightly more prominent. The differences among the results for other countries are not significant. Although the number of trade flows strongly associated with the U.S. in the region is smaller than that for Japan, the distribution of the probability of trading with specific countries displays a more balanced degree of interconnectedness. As part of the strategic economic framework of the U.S., economic and trade relations have been established with most countries in the Indo-Pacific region in recent years through the establishment of alliances, organizations, and rules. Thus, the influence of the U.S. in the region has been continuously expanding, and relatively balanced geoeconomic relationships have been established.
- Strongly correlated trade flows between China and South Korea, Japan, Brunei, the United States, and Thailand appear most frequently, indicating that China’s trade with these countries is frequent and important, with a pronounced impact on China’s trading in the Indo-Pacific region. Notably, the merchandise trade between China and South Korea accounts for 6% of China’s trade in the region. Additionally, South Korea is an important trading partner for China and has influenced China’s trade with other countries. In addition, Brunei, as a strategic partner of China, became a founding member of the Asian Infrastructure Investment Bank (AIIB), initiated by China in 2014, and is one of the countries in the economic corridor. Thus, the trade between Brunei and China has displayed an increasing trend in recent years.
- The strongly correlated trade flows in Korea mainly involve Japan, the United States, China, and Thailand. The probability of the occurrence of trading with these countries is relatively high, while other countries only account for a very low percentage of trades. Thus, Korea’s geoeconomic relations in the study region are not evenly distributed, with a strategy that focuses on a few countries in the region that are active in trade. Thus, trade changes in Korea do not have a significant impact on most other countries. Korea’s economy is externally oriented, dependent on exports, and limited in volume, so Korea’s geoeconomic ties in the Indo-Pacific region are slightly laxer than those of other countries.
- As seen from the strongly correlated trade flow statistics for India, the countries that appear more frequently are the United States, China, and Thailand. The correlations between trade flows with other countries in the region are not significant. Thus, it appears that India is characterized by a geoeconomic imbalance in the study region and is more influenced by or dependent on specific countries. This pattern, to some extent, signals high trade risk for India.

#### 3.2.3. Evaluation of Analysis Results

- In the cross-level trade flow association feature analysis, the analysis results of the cross-level trade flow association rule are verified by the correlation coefficient between category trade flow and overall trade flow.
- In the analysis of the frequency characteristics of strongly correlated trade flows, the high degree of influence of the annual average trade flows between Japan and Korea in the regional economy is confirmed by the method of mathematical statistics.
- The validity of the method is demonstrated by the similarity of the findings in the analysis of the subject countries of strongly correlated trade flows by comparing them with the existing generally accepted research arguments.

## 4. Discussion

- Dynamic Relevance: A geographic object flow is a dynamic spatiotemporal process, and the direction, velocity, and rate of a geographic object flow can change dynamically with time. Dynamically changing geographic object flows are often correlated. Changes in one set of geographic object flows can result in changes in other related geographic object flows. The dynamic associations of geographic object flows can be used to map the development of and changes in geopolitical relations among countries in a region.
- Cross-Level Interactivity: The structure of a geographic object flow determines and influences the interactions among components at different levels. In different application scenarios, there are differences in the form and intensity of interactions between parent and child geographic object flows in a hierarchy. Through the mining of cross-level association rules, it is possible to discover the characteristics of the associations between parent–child levels, identify the elements that have a critical impact on geoeconomic relations in a region, and analyze geoeconomic relations at different scales.
- Restrictive Spatial and Temporal Scopes: The state and development trends of a geographical object flow occur in a certain time and space. Space is the domain of object existence and movement, and time is related to movement and feature transformation processes; thus, as an objectively existing process, the geographic object flow has distinct spatial and temporal characteristic. The correlations among geographic object flows are somewhat transitive, at least within a limited spatial context. Therefore, association rule mining for geographic object flows is limited to a certain spatial domain, which is a closed interval. In addition, changes in the relationships between the flows of geographical objects are continuous [36], and in a certain period of time, there are relatively obvious correlations between the flows of geographical objects; these obvious correlations are relevant for analyses of the geoeconomic relations between countries and their geoeconomic positions in the region. Therefore, a correlation analysis of geographic object flows has limited spatial and temporal scopes with defined sets of objects and flows rather than considering infinite migration and expansion.

- The concept of a geographic object flow is proposed, and the mechanism of geographic object flow in spatial interactions are used to determine the correlations among and changes in geospatial units. Compared with the direct use of mathematical models for quantitative analysis, the use of the proposed data mining method for geographic object flows reduces the one-sidedness and subjectivity of index selection to a certain extent and improves the objectivity of the analysis.
- An association rule mining method with hierarchical constraints is proposed. By constructing a matrix of parent–child attribute terms, the association relationships between flows of geographical objects with hierarchical characteristics can be identified. Key factors can be targeted among many related attributes at different levels to explore the association rules between geographical objects at different scales.

- The efficiency of the association rule mining algorithms needs to be improved, especially in cases that require large-scale data analysis.
- The conclusions of association rule mining still lack practical meaning. It is difficult to directly evaluate the degree of matching between the association rules mined based on geographical object flows and the association relationships among countries in the real geoeconomy.
- The method of association rule mining requires a high level of data completeness, and it is difficult to supplement data by interpolation. For example, the experimental analysis in this paper did not include all countries in the Indo-Pacific region due to the lack of completeness of the data available for some countries. Association rule mining does not consider features other than geographic object flow parameters.

- For the algorithm efficiency problem, new strategies and technologies need to be introduced to improve the low efficiency and high complexity of traditional methods in future research.
- In response to questions about the accuracy of the study results, they must be verified from multiple perspectives by combining knowledge from multiple fields and mathematical models in subsequent studies.
- In response to the data limitation problem, subsequent research is needed on data interpolation and equivalent substitution methods, as well as adding multiclass attribute terms to reflect the rules of variation among multiple economic characteristics in the region.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Scope of the study area. Note: Made based on the standard map of GS(2021)5450 from the standard map service website of the Ministry of Natural Resources of China, with no modification to the base map.

**Figure 6.**Frequency of countries with strongly correlated trade flows. (Note: Made based on the standard map of GS(2021)5450 from the standard map service website of the Ministry of Natural Resources of China, with no modification to the base map.)

Geographic Object Flow Attribute Data Partitioning | Description of the Geographic Object Flow Properties | The Definition of Attributes for Term I |
---|---|---|

P_{ab} ≥ v1 | Significant increase | I = SIin − ObjFlow_{ab} |

v2 < P_{ab} < v1 | Increase | I = In − ObjFlow_{ab} |

P_{ab} = v2 | No change | I = St − ObjFlow_{ab} |

v3 < P_{ab} < v2 | Decrease | I = De − ObjFlow_{ab} |

P_{ab} ≤ v3 | Significant decrease | I = SIDe − ObjFlow_{ab} |

ID of Child_obj | Correlation Coefficient |
---|---|

HS_Code 84 | 0.81 |

HS_Code 93 | 0.56 |

HS_Code 27 | 0.54 |

HS_Code 10 | 0.24 |

HS_Code 88 | 0.10 |

Quantitative Methods Commonly Used in Geoeconomic Research | Advantages | Limitations | Applicability |
---|---|---|---|

Gravitational modeling method | More mature models | The spatial distance decay mechanism in relational strength cannot be reasonably quantified well | Applied to determine the relationship between two spatial units in a specific domain. |

Hierarchical Analysis | Simple and easy to use | Significant dependence on metrics | Applied to relationship evaluation supported by sufficient data. |

Event Analysis | High objectivity | Special events tend to create interference | Applied to relationship characterization in events. |

Network Analysis | Multilateral relationship judgment, easy to expand | The algorithm is relatively complex | Applied to the analysis of the network of relationships and network characteristics among multiple subjects. |

Association rule mining method | Direct, dynamic, cross-level relational analysis | High temporal requirements for data and algorithms affect efficiency | Used to discover the dynamic characteristics of relationships from phenomena and data. |

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## Share and Cite

**MDPI and ACS Style**

Zhao, W.; Jiang, N.; Yu, X.; Chen, Y.; Zhao, X.
A Correlation Analysis Method for Geographical Object Flows from a Geoeconomic Perspective. *Sustainability* **2022**, *14*, 9085.
https://doi.org/10.3390/su14159085

**AMA Style**

Zhao W, Jiang N, Yu X, Chen Y, Zhao X.
A Correlation Analysis Method for Geographical Object Flows from a Geoeconomic Perspective. *Sustainability*. 2022; 14(15):9085.
https://doi.org/10.3390/su14159085

**Chicago/Turabian Style**

Zhao, Wenshuang, Nan Jiang, Xinkai Yu, Yunhai Chen, and Xinke Zhao.
2022. "A Correlation Analysis Method for Geographical Object Flows from a Geoeconomic Perspective" *Sustainability* 14, no. 15: 9085.
https://doi.org/10.3390/su14159085