Un enfoque unificado para el estudio de patrones relacionales espacio-temporales

Autores/as

Resumen

En este trabajo se presenta una metodología para el análisis espacio-temporal de eventos utilizando redes complejas. Se construye una red de eventos considerando cada evento como un vértice y las relaciones espacio-temporales entre ellas como aristas. Se estudia la estructura de la red mediante la identificación de patrones recurrentes que describen comportamientos emergentes del sistema, conocidos como motifs. Para la detección de motifs, se diseña un algoritmo que permite aproximar la distribución empírica de los conteos de motifs, combinando métodos de simulación de redes espacio temporales, algoritmos de agrupamiento y la fórmula de Stirling por radio espacial y ventana de tiempo definidos. Se observa que una distribución log-normal se ajusta adecuadamente a la distribución del grado de la red de eventos, permitiendo definir la distancia en la que dos sucesos pueden estar relacionados en el espacio dentro de una ventana de tiempo. La metodología se ilustra aplicándola al caso de hurtos a personas reportados al departamento de policía local entre 2018 y 2021 en la ciudad de Pereira, Colombia. Los resultados evidencian que la metodología propuesta es eficaz en la identificación de motifs que capturan patrones espacio-temporales generando información que permite desarrollar estrategias de prevención de la delincuencia.

Palabras clave

Patrón espacio temporal, Criminalidad, Motifs, Red de eventos

Citas

Arthur, D. &. (2007). k-means++: The advantages of careful seeding. Soda, 7, 1027-1035.

Atluri G, K. A. (2018). Spatio-temporal data mining: a survey of problems and methods. ACM Comput Surv, 51.(4) 1-41. https://doi.org/10.3390/analytics2020027

Banerjee, S., Carlin, B. P., & Gelfand, A. E. (2014). Hierarchical modeling and analysis for spatial data. https://doi.org/10.1201/b17115. Chapman and Hall/CRC.

Barabási, A.-L. &. (1999). Emergence of scaling in random networks. Science, 286(5439), 509-512.

Barabási, A.-L. (2013). Network science. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371. DOI: 10.1126/science.286.5439.509.

Betancourt, B., Rodriguez, A., & BOYD, N. (2020). Modelling and prediction of financial trading networks: an application to the New York Mercantile Exchange natural gas futures market. Applied Journal of the Royal Statistical Society Series C, https://doi.org/10.1111/rssc.12387. doi:https://doi.org/10.1111/rssc.12387

Boba, R. L. (2016). Crime analysis with crime mapping. Sage publications.

Boccaletti, S., Bianconi, G., Criado, R., Del Genio, C., Gómez-Gardeñes, J., Romance, M., . . . W. Z. (2014). The structure and dynamics of multilayer networks. Physics reports, 544 (1), 1-122. doi: 10.1016/j.physrep.2014.07.001

Borgatti SP, M. A. (2009). Network analysis in the social sciences. Science, 323(5916), 892–895. DOI: 10.1126/science.116582

Broido, A. D., & y Clauset, A. (2019). Scale-free networks are rare. Nature communications, 10(1), 1017. https://doi.org/10.1038/s41467-019-08746-5

Celebi, M. E., Kingravi, H. A., & Vela, P. A. (2013). A comparative study of efficient initialization methods for the k-means clustering algorithm. Expert systems with applications, 40(1), 200-210. https://doi.org/10.1016/j.eswa.2012.07.021

Cozens, P., Love, T., & Davern, B. (2019). Geographical juxtaposition: A new direction in CPTED. En S. Sciences.

da Cunha BR, M. P. (2020). Assessing police topological efficiency in a major sting operation on the dark web. Sci Rep, 10, 1–10. https://doi.org/10.1038/s41598-019-56704-4

D'agostino, R. B. (2017). Goodness-of-fit-techniques. Routledge. https://doi.org/10.1201/9780203753064

Dang TA, C. J. (2018). A comparative study of urban mobility patterns using large-scale spatio-temporal data. IEEE international conference on data mining workshops (ICDMW). (págs. 572–579). DOI: 10.1109/ICDMW.2018.00089.

Davies, T., & Marchione, E. (2015). Event networks and the identification of crime pattern motifs. PloS one, 10(11). https://doi.org/10.1371/journal.pone.0143638

Diggle, P. J. (2013). Statistical analysis of spatial and spatio-temporal point patterns. CRC press. https://doi.org/10.1201/b15326

Dorogovtsev, S. N., Goltsev, A. V., & Mendes, J. F. (2008). Critical phenomena in complex networks. Reviews of Modern Physics, 80(4), 1275. https://doi.org/10.1103/RevModPhys.80.1275

Durante, D. &. (2014). Nonparametric Bayes dynamic modelling of relational data. Biometrika, 101(4), 883-898. https://doi.org/10.1093/biomet/asu040

Dutka, J. (1991). The early history of the factorial function. Archive for history of exact sciences, 225-249. https://doi.org/10.1007/BF00389433

Estrada, E. (2012). The structure of complex networks: theory and applications. American Chemical Society, https://doi.org/10.1093/acprof:oso/9780199591756.001.0001

Felson, M., & Boba, R. L. (2012). Crime and everyday life. Sage. https://doi.org/10.4135/9781483349299

Forbes, C., Evans, M., Hastings, N., & Peacock, B. (2011). Statistical distributions. John Wiley & Sons. DOI:10.1002/9780470627242

Grubesic TH, M. E. (2008). Spatio-temporal interaction of urban crime. Journal of Quantitative Criminology, 24, 285-306.

Gupta, S., Sharma, G., & Dukkipati, A. (2019). A generative model for dynamic networks with applications. Proceedings of the AAAI Conference on Artificial Intelligence, 33, 7842-7849. https://doi.org/10.1609/aaai.v33i01.33017842

Haining, R. P. (2020). Regression Modelling Wtih Spatial and Spatial-Temporal Data: A Bayesian Approach. CRC Press. https://doi.org/10.1201/9780429088933

Higdon, D. (2006). A primer on space-time modeling from a Bayesian perspective. Monographs on Statistics and Applied Probability, 107, 217.

Higdon, P. D. (2015). Multilinear tensor regression for longitudinal relational data. The annals of applied statistics, 9(3), 1169. https://doi.org/10.1214/15-AOAS839

James, G., Witten, D., Hastie, T., Tibshirani, R., & Taylor, J. (2023). An introduction to statistical learning: With applications in python. Springer Nature. https://doi.org/10.1007/978-3-031-38747-0

Jazayeri A, Y. C. (2020). Motif discovery algorithms in static and temporal networks: a survey. https://doi.org/10.48550/arXiv.2005.09721

Jiménez-García W., R.-R. R.-S. (2023). Space-time analysis of theft from persons in Pereira (2019-2021). An approach to the theory of environmental munificence for crime. Revista Criminalidad, 65(1), 121-137. https://doi.org/10.47741/17943108.405

Jiménez-García, W. G. (2014). Hacia una tipología de lugares peligrosos. Caso de estudio de la comuna 11 de Dosquebradas, Colombia. Revista Criminalidad, 56(1), 133-156.

Kent, J. T. (2022). Spatial analysis. John Wiley & Sons. DOI:10.1002/9781118763551

Kim, B., Lee, K. H., Xue, L., & Niu, X. e. (2018). A review of dynamic network models with latent variables. Statistics surveys, 12.

Kolaczyk, E. D., & Csárdi, G. (2014). Statistical analysis of network data with R. New York: Springer. https://doi.org/10.1007/978-3-030-44129-6

Lang JC, D. S. (2018). Analytic models for sir disease spread on random spatial networks. J Complex Netw. https://doi.org/10.1093/comnet/cny004, 948–970

Latora, V., Nicosia, V., & Russo, G. (2017). Complex networks: principles, methods and applications. Cambridge University Press. https://doi.org/10.1080/00107514.2018.1450296

Leong, K., & Sung, A. (2015). A review of spatio-temporal pattern analysis approaches on crime analysis. International E-Journal of Criminal Sciences., 9.

Lloyd, S. (1982). Least squares quantization in PCM. IEEE transactions on information theory, 28(2), 129-137. DOI: 10.1109/TIT.1982.1056489

Lotero, L., Hurtado, R. G., Floría, L. M., & Gómez-Gardeñes, J. (2016). Rich do not rise early: spatio-temporal patterns in the mobility networks of different socio-economic classes. Royal Society open science, 3(10). https://doi.org/10.1098/rsos.150654

Macqueen, J. (1967). Some methods for classification and analysis of multivariate observations. Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, 1, págs. 281-297.

Menczer, F., Fortunato, S., & Davis, C. A. (2020). A first course in network science. Cambridge University Press.

Newman, M. (2018). Networks. Oxford University Press. https://doi.org/10.1093/oso/9780198805090.001.0001

Newman, M., Barabási, A.-L., & Watts, D. J. (2011). The structure and dynamics of networks. Princeton university press.

Oberoi KS, D. M. (2021). Graph-based pattern detection in spatio-temporal phenomena. . 16th Spatial analysis and geomatics conference (SAGEO).

Oyana, T. J. (2020). Spatial analysis with R: statistics, visualization, and computational methods. CRC press. https://doi.org/10.1201/9781003021643

Pasquaretta C, D. T.-M. (2021). Analysis of temporal patterns in animal movement networks. Methods Ecol Evol, 12(1), 101-113. https://doi.org/10.1111/2041-210X.13364

Salje H, C. D. (2016). Estimating infectious disease transmission distances using the overall distribution of cases. Epidemics, 17, 10-18. https://doi.org/10.1016/j.epidem.2016.10.001

Sanabria, A. M., Bohorquez, M. P., Rentería, R. R., & Mateu, J. (2022). Identification of patterns for space-time event networks. Applied Network Science, 7(1). https://doi.org/10.1007/s41109-021-00442-y

Schubert, E., Sander, J., Ester, M., Kriegel, H.-P., & XU, X. (2017). DBSCAN revisited, revisited: why and how you should (still) use DBSCAN. ACM Transactions on Database Systems (TODS), 42(3), 1-21. https://doi.org/10.1145/3068335

Scott J, C. P. (2011). En The SAGE handbook of social network analysis. SAGE. https://doi.org/10.48550/arXiv.2005.09721.

Sewell, D. K., & Chen, Y. (2017). Latent space approaches to community detection in dynamic networks. Bayesian Analysis, 12(2), 351-377. https://doi.org/10.1214/16-BA1000

Sosa, J., & Buitrago, L. (2021). A Review of Latent Space Models for Social Networks. Revista Colombiana de Estadística, 44(1), 171-200. https://doi.org/10.15446/rce.v44n1.89369), 171-200

Sznajd-Weron, K. y. (2020). Opinion evolution in closed community. International Journal of Modern Physics C , 11(6), 1157-1165. https://doi.org/10.1142/S0129183100000936

U. M. Butt, S. L. (2020). Spatio-Temporal Crime HotSpot Detection and Prediction: A Systematic Literature Review. IEEE Access, 8. DOI: 10.1109/ACCESS.2020.3022808

Wang, K., Yang, R., Liu, C., Samarasinghalage, T., & Zang, Y. (2022). Extracting Electricity Patterns from High-dimensional Data: A comparison of K-Means and DBSCAN algorithms. IOP Conference Series: Earth and Environmental Science. IOP Publishing,.

Wernicke, S. &. (2006). FANMOD: a tool for fast network motif detection. Bioinformatics, 22(9), DOI: 10.1093/bioinformatics/btl038.

Wikle, C. K., Zammit-Mangion, A., & Cressie, N. (2019). Spatio-temporal statistics with R. Chapman and Hall/CRC.

Zhang, Y. &. (2020). Graph deep learning model for network-based predictive hotspot mapping of sparse spatio-temporal events. Computers, Environment and Urban Systems, 79. https://doi.org/10.1016/j.compenvurbsys.2019.101403

Zhao, X. &. (2017). Modeling temporal-spatial correlations for crime prediction. Proceedings of the 2017 ACM on Conference on Information and Knowledge Management, (págs. 497-506).

Publicado

15-05-2025

Cómo citar

Quintero Martinez, M. A., Sosa -Martínez, J. C., Bohorquez, M., & Rentería Ramos, R. R. (2025). Un enfoque unificado para el estudio de patrones relacionales espacio-temporales. Redes. Revista Hispana Para El análisis De Redes Sociales, 37(1), 40–58. https://doi.org/10.5565/rev/redes.1108

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