Exploring the Spatial Association Between Spatial Categorical Data Using a Fuzzy Geographically Weighted Colocation Quotient Method
Abstract
1. Introduction
- (1)
- This study defines a fuzzy neighborhood between spatial categorical points and constructs a fuzzy geographically weighted matrix to measure spatial proximity.
- (2)
- This study proposes a new method, Fuzzy Geographically Weighted Colocation Quotient (FGWCLQ), to explore the association relationship between various categorical variables and visualize the spatial heterogeneity of these relationships.
- (3)
- This study proposes a multi-scale framework to explore the hidden spatial association rules among the different facility categories in Beijing using FGWCLQ.
2. Methodology
2.1. Fuzzy Neighbor Relationship Between Spatial Categorical Data
2.2. The Fuzzy Neighborhood Boundary Setting Approach
2.3. The Fuzzy Geographically Weighted Colocation Quotient
3. Study Area and Data
3.1. Study Area
3.2. Data Collection and Pre-Processing
4. Results
4.1. Experiment Setting
4.2. The Results of Global FGWCLQ
4.3. The Results of Local FGWCLQ
4.4. Comparison with Deterministic Methods
4.5. Sensitivity Analysis
5. Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Deng, Y.; Liu, J.; Liu, Y.; Luo, A. Detecting Urban Polycentric Structure from POI Data. ISPRS Int. J. Geo-Inf. 2019, 8, 283. [Google Scholar] [CrossRef]
- Gan, M.; Gao, L. Discovering Memory-Based Preferences for POI Recommendation in Location-Based Social Networks. ISPRS Int. J. Geo-Inf. 2019, 8, 279. [Google Scholar] [CrossRef]
- Cao, G.; Kyriakidis, P.C.; Goodchild, M.F. A multinomial logistic mixed model for the prediction of categorical spatial data. Int. J. Geogr. Inf. Sci. 2011, 25, 2071–2086. [Google Scholar] [CrossRef]
- Goodchild, M.F.; Yuan, M.; Cova, T.J. Towards a general theory of geographic representation in GIS. Int. J. Geogr. Inf. Sci. 2007, 21, 239–260. [Google Scholar] [CrossRef]
- Liu, J.; Liu, C.; Liu, Z.; Zhou, Y.; Li, X.; Yang, Y. Spatial analysis of air pollutant exposure and its association with metabolic diseases using machine learning. BMC Public Health 2025, 25, 831. [Google Scholar] [CrossRef]
- Wang, H.; Liang, G. Association Rules Between Urban Road Traffic Accidents and Violations Considering Temporal and Spatial Constraints: A Case Study of Beijing. Sustainability 2025, 17, 1680. [Google Scholar] [CrossRef]
- Li, L.; Cheng, J.; Bannister, J.; Mai, X. Geographically and temporally weighted co-location quotient: An analysis of spatiotemporal crime patterns in greater Manchester. Int. J. Geogr. Inf. Sci. 2022, 36, 918–942. [Google Scholar] [CrossRef]
- Zhou, M.; Yang, M.; Chen, Z. Flow colocation quotient: Measuring bivariate spatial association for flow data. Comput. Environ. Urban Syst. 2023, 99, 101916. [Google Scholar] [CrossRef]
- Andrzejewski, W.; Boinski, P. Co-location pattern mining using approximate Euclidean measure. Inf. Sci. 2025, 706, 122000. [Google Scholar] [CrossRef]
- Krishnasamy, S.; Rajiah, M.; SenthilKumar, K.K.; Nagalingam Rajendiran, S. Association rule-based multilevel regression pricing and artificial neural networks based land selling price prediction based on market value. Concurr. Comput. Pract. Exp. 2023, 35, e7550. [Google Scholar] [CrossRef]
- Chakraborty, J. Revisiting Tobler’s first law of geography: Spatial regression models for assessing environmental justice and health risk disparities. Geospat. Anal. Environ. Health 2011, 4, 337–356. [Google Scholar]
- Yoo, J.S.; Park, S.J.; Raman, A. Micro-Level Incident Analysis using Spatial Association Rule Mining. In Proceedings of the 2019 IEEE International Conference on Big Knowledge (ICBK), Beijing, China, 10–11 November 2019; pp. 310–317. [Google Scholar]
- Petelin, B.; Kononenko, I.; Malačič, V.; Kukar, M. Multi-level association rules and directed graphs for spatial data analysis. Expert Syst. Appl. 2013, 40, 4957–4970. [Google Scholar] [CrossRef]
- Ge, Y.; Yao, Z.; Li, H. Computing Co-location Patterns in Spatial Data with Extended Objects: A Scalable Buffer-based Approach. IEEE Trans. Knowl. Data Eng. 2021, 33, 401–414. [Google Scholar] [CrossRef]
- Huang, Y.; Shekhar, S.; Xiong, H. Discovering colocation patterns from spatial data sets: A general approach. IEEE Trans. Knowl. Data Eng. 2004, 16, 1472–1485. [Google Scholar] [CrossRef]
- Chen, H.; Yang, M.; Tang, X. Association rule mining of aircraft event causes based on the Apriori algorithm. Sci. Rep. 2024, 14, 13440. [Google Scholar] [CrossRef]
- Smith, J.M. An Efficient Parallel FP-Growth Algorithm for Big Data Association Rule Mining. J. Comput. Sci. Softw. Appl. 2024, 4, 1–8. [Google Scholar] [CrossRef]
- Han, D.; Shi, Y.; Wang, W.; Dai, Y. Research on Multi-Level Association Rules Based on Geosciences Data. J. Softw. 2013, 8, 3269–3276. [Google Scholar] [CrossRef]
- Wang, F.; Hu, Y.; Wang, S.; Li, X. Local Indicator of Colocation Quotient with a Statistical Significance Test: Examining Spatial Association of Crime and Facilities. Prof. Geogr. 2016, 69, 22–31. [Google Scholar] [CrossRef]
- Shekhar, S.; Yan, H. Discovering Spatial Co-location Patterns: A Summary of Results. In Proceedings of the Advances in Spatial & Temporal Databases, International Symposium, SSTD, Redondo Beach, CA, USA, 12–15 July 2001. [Google Scholar]
- Yoo, J.S.; Bow, M. Mining spatial colocation patterns: A different framework. Data Min. Knowl. Discov. 2012, 24, 159–194. [Google Scholar] [CrossRef]
- Cressie, N.A.C. Statistics for Spatial Data; Wiley: New York, NY, USA, 1991. [Google Scholar]
- Leslie, T.F.; Kronenfeld, B.J. The Colocation Quotient: A New Measure of Spatial Association Between Categorical Subsets of Points. Geogr. Anal. 2011, 43, 306–326. [Google Scholar] [CrossRef]
- Cromley, R.G.; Hanink, D.M.; Bentley, G.C. Geographically Weighted Colocation Quotients: Specification and Application. Prof. Geogr. 2014, 66, 138–148. [Google Scholar] [CrossRef]
- Cai, J.; Kwan, M.-P. Discovering co-location patterns in multivariate spatial flow data. Int. J. Geogr. Inf. Sci. 2022, 36, 720–748. [Google Scholar] [CrossRef]
- Xia, Z.; Li, H.; Chen, Y.; Yu, W. Detecting urban fire high-risk regions using colocation pattern measures. Sustain. Cities Soc. 2019, 49, 101607. [Google Scholar] [CrossRef]
- Liu, H.; Kwan, M.-P.; Hu, M.; Wang, H.; Zheng, J. Application of the local colocation quotient method in jobs-housing balance measurement based on mobile phone data: A case study of Nanjing City. Comput. Environ. Urban Syst. 2024, 109, 102079. [Google Scholar] [CrossRef]
- Zhou, L.; Wang, C. Detecting the Spatial Association between Commercial Sites and Residences in Beijing on the Basis of the Colocation Quotient. ISPRS Int. J. Geo-Inf. 2023, 13, 7. [Google Scholar] [CrossRef]
- Yu, W. Spatial co-location pattern mining for location-based services in road networks. Expert Syst. Appl. 2016, 46, 324–335. [Google Scholar] [CrossRef]
- Mennis, J.; Liu, J.W. Mining Association Rules in Spatio-Temporal Data: An Analysis of Urban Socioeconomic and Land Cover Change. Trans. GIS 2010, 9, 5–17. [Google Scholar] [CrossRef]
- Santos, M.Y.; Amaral, L.A. Geo-spatial data mining in the analysis of a demographic database. Soft Comput. 2005, 9, 374–384. [Google Scholar] [CrossRef]
- Bembenik, R.; Rybinski, H. FARICS: A method of mining spatial association rules and collocations using clustering and Delaunay diagrams. J. Intell. Inf. Syst. 2009, 33, 41–64. [Google Scholar] [CrossRef]
- Akbari, M.; Samadzadegan, F. Identification of air pollution patterns using a modified fuzzy co-occurrence pattern mining method. Int. J. Environ. Sci. Technol. 2015, 12, 3551–3562. [Google Scholar] [CrossRef]
- Zadeh, L.A. Fuzzy Sets. Inf. Control 1965, 8, 338–353. [Google Scholar] [CrossRef]
- Hu, Y.; Miller, H.J.; Li, X. Detecting and Analyzing Mobility Hotspots using Surface Networks. Trans. GIS 2014, 18, 911–935. [Google Scholar] [CrossRef]
- Jadidi, A.; Mostafavi, M.; Bédard, Y.; Shahriari, K. Spatial Representation of Coastal Risk: A Fuzzy Approach to Deal with Uncertainty. ISPRS Int. J. Geo-Inf. 2014, 3, 1077–1100. [Google Scholar] [CrossRef]
- Wang, M.; Chen, Y.; Wu, Y.; He, L. Spatial co-location pattern mining based on the improved density peak clustering and the fuzzy neighbor relationship. Math. Biosci. Eng. 2021, 18, 8223–8244. [Google Scholar] [CrossRef] [PubMed]
- Wang, M.J.; Wang, L.Z.; Zhao, L.H. Spatial Co-location Pattern Mining Based on Fuzzy Neighbor Relationship. J. Inf. Sci. Eng. 2019, 35, 1343–1363. [Google Scholar] [CrossRef]
- Cui, X.; Wang, J.; Wu, F.; Li, J.; Gong, X.; Zhao, Y.; Zhu, R. Extracting Main Center Pattern from Road Networks Using Density-Based Clustering with Fuzzy Neighborhood. ISPRS Int. J. Geo-Inf. 2019, 8, 238. [Google Scholar] [CrossRef]
- Zheng, K.; Huo, X.; Jasimuddin, S.; Zhang, J.Z.; Battaïa, O. Logistics distribution optimization: Fuzzy clustering analysis of e-commerce customers’ demands. Comput. Ind. 2023, 151, 103960. [Google Scholar] [CrossRef]
- Baser, F.; Koc, O.; Selcuk-Kestel, A.S. Credit risk evaluation using clustering based fuzzy classification method. Expert. Syst. Appl. 2023, 223, 119882. [Google Scholar] [CrossRef]
- Kalia, H.; Dehuri, S.; Ghosh, A.; Cho, S.-B. Surrogate-Assisted Multi-objective Genetic Algorithms for Fuzzy Rule-Based Classification. Int. J. Fuzzy Syst. 2018, 20, 1938–1955. [Google Scholar] [CrossRef]
- Anari, Z.; Hatamlou, A.; Anari, B. Finding Suitable Membership Functions for Mining Fuzzy Association Rules in Web Data Using Learning Automata. Int. J. Pattern Recognit. Artif. Intell. 2021, 35, 2159026. [Google Scholar] [CrossRef]
- Zhang, Z.; Huang, J.; Hao, J.; Gong, J.; Chen, H. Extracting relations of crime rates through fuzzy association rules mining. Appl. Intell. 2019, 50, 448–467. [Google Scholar] [CrossRef]
- McBratney, A.B.; Moore, A.W. Application of fuzzy sets to climatic classification. Agric. For. Meteorol. 1985, 35, 165–185. [Google Scholar] [CrossRef]
- Dubois, D.; Prade, H. The three semantics of fuzzy sets. Fuzzy Sets Syst. 1997, 90, 141–150. [Google Scholar] [CrossRef]
- Velmurugan, S.; Kumar, S.A.; Udhayakumar, R. Analysis of Fuzzy Membership Function on Greenhouse Gas Emission Estimation by Triangular and Trapezoidal Membership Functions in Indian Smart Cities. Contemp. Math. 2024, 5, 2508–2530. [Google Scholar] [CrossRef]
- Jain, A.; Sharma, A. Membership function formulation methods for fuzzy logic systems: A comprehensive review. J. Crit. Rev. 2020, 7, 8717–8733. [Google Scholar]
- Ali, O.A.M.; Ali, A.Y.; Sumait, B.S. Comparison between the effects of different types of membership functions on fuzzy logic controller performance. Int. J. Emerg. Eng. Res. Technol. 2015, 3, 76–83. [Google Scholar]
- Wang, X.; Lei, L.; Wang, L.; Yang, P.; Chen, H. Spatial Colocation Pattern Discovery Incorporating Fuzzy Theory. IEEE Trans. Fuzzy Syst. 2021, 30, 2055–2072. [Google Scholar] [CrossRef]
- Xu, Z.; Gautam, M.; Mehta, S. Cumulative frequency fit for particle size distribution. Appl. Occup. Environ. Hyg. 2002, 17, 538–542. [Google Scholar] [CrossRef] [PubMed]
- Baride, S. Algorithms for Spatial Colocation Pattern Mining. Ph.D. Thesis, The Department of Computer Science and Engineering Indraprastha Institute of Information Technology, New Delhi, India, 7 December 2023. [Google Scholar]
- Yang, Y.; Wong, K.K.F.; Wang, T. How do hotels choose their location? Evidence from hotels in Beijing. Int. J. Hosp. Manag. 2012, 31, 675–685. [Google Scholar] [CrossRef]
- Li, G.; Jin, F.; Chen, Y.; Jiao, J.; Liu, S. Location characteristics and differentiation mechanism of logistics nodes and logistics enterprises based on points of interest (POI): A case study of Beijing. J. Geogr. Sci. 2017, 27, 879–896. [Google Scholar] [CrossRef]
- Li, M.; Fang, L.; Huang, X.; Goh, C. A spatial–temporal analysis of hotels in urban tourism destination. Int. J. Hosp. Manag. 2015, 45, 34–43. [Google Scholar] [CrossRef] [PubMed]
- Di Marino, M.; Tomaz, E.; Henriques, C.; Chavoshi, S.H. The 15-minute city concept and new working spaces: A planning perspective from Oslo and Lisbon. Eur. Plan. Stud. 2023, 31, 598–620. [Google Scholar] [CrossRef]
- Zacharov, P.; Rezacova, D.; Brozkova, R. Evaluation of the QPF of convective flash flood rainfalls over the Czech territory in 2009. Atmos. Res. 2013, 131, 95–107. [Google Scholar] [CrossRef]
- Wei, M. Spatial distribution and the agglomeration performance of high-star hotels. Tour. Anal. 2017, 22, 31–43. [Google Scholar] [CrossRef]
- Lee, K.H.; Kang, S.; Terry, W.C.; Schuett, M.A. A spatial relationship between the distribution patterns of hotels and amenities in the United States. Cogent Soc. Sci. 2018, 4, 1444918. [Google Scholar] [CrossRef]
- Chen, L.; Chen, S.; Li, S.; Shen, Z. Temporal and spatial scaling effects of parameter sensitivity in relation to non-point source pollution simulation. J. Hydrol. 2019, 571, 36–49. [Google Scholar] [CrossRef]
- Lilburne, L.; Tarantola, S. Sensitivity analysis of spatial models. Int. J. Geogr. Inf. Sci. 2009, 23, 151–168. [Google Scholar] [CrossRef]
- Grekousis, G. Local fuzzy geographically weighted clustering: A new method for geodemographic segmentation. Int. J. Geogr. Inf. Sci. 2021, 35, 152–174. [Google Scholar] [CrossRef]
- Zhang, J.X.; Stuart, N. Fuzzy methods for categorical mapping with image-based land cover data. Int. J. Geogr. Inf. Sci. 2001, 15, 175–195. [Google Scholar] [CrossRef]
- Guo, J.F.; Mao, J.; Cui, T.J.; Li, C.W. A Multi-Scale Fuzzy Spatial Analysis Framework for Large Data Based on IT2 FS. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 2015, 23, 73–104. [Google Scholar] [CrossRef]
- Zhang, X.; Han, D.; Zhang, C.; Feng, W.; Wu, J.; Xie, Y.; He, Y. Spatial Pattern Evolution and Influencing Factors of Foreign Star-Rated Hotels in Chinese Cities. Reg. Sci. Environ. Econ. 2024, 2, 1. [Google Scholar] [CrossRef]
- Qin, Y.; Qin, J.; Liu, C. Spatial-temporal evolution patterns of hotels in China: 1978–2018. Int. J. Contemp. Hosp. Manag. 2021, 33, 2194–2218. [Google Scholar] [CrossRef]
Notation | Definition |
---|---|
F | The categories of spatial objects |
O | A set of spatial objects within the study area |
fi, fj | Two different categories from the set F |
oi, oj | Two different objects from dataset O |
d(oi, oj) | Distance between two objects oi and oj |
A set of category fi objects | |
The number of category fi | |
N | The total number of O |
Categories | Explicate | Count | Portion |
---|---|---|---|
2-STR | Two Star Hotel and Economy Hotel | 4051 | 59.49% |
3-STR | Three Star Hotel | 647 | 9.50% |
4-STR | Four Star Hotel | 525 | 7.71% |
5-STR | Five Star Hotel | 232 | 3.41% |
Transportation (TP) | Subway Stations, Railway stations, Bus stations, and Airports | 432 | 6.34% |
Tourism (TS) | Urban squares, National scenic spots, and Famous scenic spots | 923 | 13.55% |
Total | 6810 | 100.00% |
Spatial Scale[d1, d2] | Fuzzy Neighborhood | Exploration |
---|---|---|
500–1000 m | nearby | 5–10 min neighborhood: the walking distance at an average walking speed of around 1 m/s [57] |
1000–2000 m | medium | 15–20 min neighborhood: people’s daily needs can be satisfied within walkable or cyclable distances [58] |
2000–5000 m | faraway | The service radius of the hotel that can be reached by car [55] |
Fuzzy Neighborhood | Categories | 2-STR | 3-STR | 4-STR | 5-STR | TP | TS |
---|---|---|---|---|---|---|---|
500–1000 m | 2-STR | 0.943 | 0.938 | 0.935 | 0.946 | 0.907 | |
3-STR | 1.084 | 1.130 | 1.247 | 1.010 | 0.926 | ||
4-STR | 1.070 | 1.411 | 1.555 | 0.996 | |||
5-STR | 0.858 | 1.111 | 1.463 | 2.611 | 0.881 | 0.934 | |
TP | 0.859 | 0.872 | |||||
TS | 0.798 | 0.898 | 0.895 | ||||
1000–2000 m | 2-STR | 1.010 | 0.971 | 1.008 | 1.039 | 0.908 | |
3-STR | 0.963 | 1.066 | 1.126 | 1.265 | 0.898 | 1.027 | |
4-STR | 0.948 | 1.068 | 1.232 | 0.850 | 1.017 | ||
5-STR | 0.911 | 1.119 | 1.917 | 0.851 | 0.969 | ||
TP | 0.969 | 0.964 | 1.034 | 1.852 | 0.773 | ||
TS | 0.869 | 0.895 | 0.935 | 0.955 | 0.627 | 1.871 | |
2000–5000 m | 2-STR | 0.992 | 1.020 | 1.049 | 1.100 | 1.036 | |
3-STR | 0.965 | 1.061 | 1.089 | 1.238 | 0.882 | 1.056 | |
4-STR | 0.958 | 1.051 | 1.130 | 1.264 | 1.072 | ||
5-STR | 0.936 | 1.112 | 1.517 | 0.792 | |||
TP | 1.024 | 1.024 | 1.132 | 0.933 | |||
TS | 0.906 | 0.976 | 1.027 | 1.099 | 0.743 | 1.513 |
Method | Category | 2-STR | 3-STR | 4-STR | 5-STR | TP | TS |
---|---|---|---|---|---|---|---|
FGWCLQ (1000–2000 m) | 2-STR | 1.010 | 0.971 | 1.008 | 1.039 | 0.908 | |
3-STR | 0.963 | 1.066 | 1.126 | 1.265 | 0.898 | 1.027 | |
4-STR | 0.948 | 1.068 | 1.232 | 0.850 | 1.017 | ||
5-STR | 0.911 | 1.119 | 1.917 | 0.851 | 0.969 | ||
TP | 0.969 | 0.964 | 1.034 | 1.852 | 0.773 | ||
TS | 0.869 | 0.895 | 0.935 | 0.955 | 0.627 | 1.871 | |
GWCLQ (1500 m) | 2-STR | 1.003 | 0.981 | 1.018 | 1.060 | 0.915 | 1.015 |
3-STR | 0.962 | 1.068 | 1.114 | 1.263 | 1.043 | ||
4-STR | 1.065 | 1.202 | 0.836 | 1.024 | |||
5-STR | 0.925 | 1.125 | 1.284 | 1.737 | 0.829 | ||
TP | 0.983 | 0.970 | 1.032 | 1.522 | 0.803 | ||
TS | 0.880 | 0.947 | 0.968 | 1.789 |
Method | 5-STR → TP | 5-STR → TS | Bandwidth | ||
---|---|---|---|---|---|
Number | Proportion | Number | Proportion | ||
FGWCLQ | 84 | 36.21% | 73 | 31.46% | [1000 m, 2000 m] |
GWCLQ | 71 | 30.6% | 62 | 26.72% | 1500 m |
Category | 2-STR | 3-STR | 4-STR | 5-STR | TP | TS |
---|---|---|---|---|---|---|
2-STR | 0.025 | 0.031 | 0.042 | 0.066 | 0.024 | 0.063 |
3-STR | 0.004 | 0.034 | 0.019 | 0.025 | 0.084 | 0.057 |
4-STR | 0.023 | 0.012 | 0.110 | 0.097 | 0.043 | 0.040 |
5-STR | 0.039 | 0.005 | 0.105 | 0.262 | 0.059 | 0.068 |
TP | 0.064 | 0.050 | 0.076 | 0.067 | 0.564 | 0.157 |
TS | 0.054 | 0.075 | 0.058 | 0.090 | 0.095 | 0.200 |
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Share and Cite
Li, L.; Duan, L.; Li, M.; Mai, X. Exploring the Spatial Association Between Spatial Categorical Data Using a Fuzzy Geographically Weighted Colocation Quotient Method. ISPRS Int. J. Geo-Inf. 2025, 14, 296. https://doi.org/10.3390/ijgi14080296
Li L, Duan L, Li M, Mai X. Exploring the Spatial Association Between Spatial Categorical Data Using a Fuzzy Geographically Weighted Colocation Quotient Method. ISPRS International Journal of Geo-Information. 2025; 14(8):296. https://doi.org/10.3390/ijgi14080296
Chicago/Turabian StyleLi, Ling, Lian Duan, Meiyi Li, and Xiongfa Mai. 2025. "Exploring the Spatial Association Between Spatial Categorical Data Using a Fuzzy Geographically Weighted Colocation Quotient Method" ISPRS International Journal of Geo-Information 14, no. 8: 296. https://doi.org/10.3390/ijgi14080296
APA StyleLi, L., Duan, L., Li, M., & Mai, X. (2025). Exploring the Spatial Association Between Spatial Categorical Data Using a Fuzzy Geographically Weighted Colocation Quotient Method. ISPRS International Journal of Geo-Information, 14(8), 296. https://doi.org/10.3390/ijgi14080296