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Rethinking the null hypothesis in significant colocation pattern mining of spatial flows

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Abstract

Spatial flows represent spatial interactions or movements. Mining colocation patterns of different types of flows may uncover the spatial dependences and associations among flows. Previous studies proposed a flow colocation pattern mining method and established a significance test under the null hypothesis of independence for the results. In fact, the definition of the null hypothesis is crucial in significance testing. Choosing an inappropriate null hypothesis may lead to misunderstandings about the spatial interactions between flows. In practice, the overall distribution patterns of different types of flows may be clustered. In these cases, the null hypothesis of independence will result in unconvincing results. Thus, considering the overall spatial pattern of flows, in this study, we changed the null hypothesis to random labeling to establish the statistical significance of flow colocation patterns. Furthermore, we compared and analyzed the impacts of different null hypotheses on flow colocation pattern mining through synthetic data tests with different preset patterns and situations. Additionally, we used empirical data from ride-hailing trips to show the practicality of the method.

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Data and codes availability

The synthetic data and codes are available in ‘figshare.com’ with the identifier(s): https://figshare.com/s/d881eee178d956d3a336.

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Acknowledgements

We would like to thank DiDi Chuxing company for the provision of the original dataset.

Funding

This research was funded by National Natural Science Foundation of China (41901314), Natural Science Foundation of Hunan Province, 2023JJ40447, RGC Postdoctoral Fellowship awarded by the Research Grants Council of Hong Kong (PDFS2223-4H01), and Scientific research project of Hunan Provincial Department of Education 23B0093.

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Authors and Affiliations

  1. School of Geographical Sciences, Hunan Normal University, Changsha, 410081, Hunan, China

    Mengjie Zhou, Mengjie Yang & Zhe Chen

  2. Hunan Key Laboratory of Geospatial Big Data Mining and Application, Changsha, China

    Mengjie Zhou

  3. School of Resource and Environment Sciences, Wuhan University, Wuhan, China

    Tinghua Ai

  4. Institute of Space and Earth Information Science, The Chinese University of Hong Kong, Shenzhen, Hong Kong, China

    Jiannan Cai

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  1. Mengjie Zhou
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  2. Mengjie Yang
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  3. Tinghua Ai
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  4. Jiannan Cai
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  5. Zhe Chen
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Correspondence to Mengjie Zhou.

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Appendix. Process for generating synthetic data

Appendix. Process for generating synthetic data

We derive synthetic datasets from simulations of different preset patterns and situations to test our method. There are ten flow datasets with different preset interaction patterns (colocation, not colocation) and different situations (random, clustered, abundance of flow instances), as shown in Fig. 

Fig. 8
figure 8

Synthetic datasets

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8. Cases 1–5, 9–10 are flow datasets with two categories. Among them, the spatial flows in Cases 1–3 do not have an imposed colocation pattern, while Cases 4–10 do. Cases 6 and 7 are flow datasets with five categories. The study area in each case is a unit square, and the interaction distance \(R\) is set to 0.1.

The process to generate synthetic data are described as follows. In the synthetic data, random flow patterns were generated with a homogeneous spatial Poisson process (Shu et al. 2020). In practice, we first generated random points using a Poisson process and then randomly paired them. Clustered flow patterns were generated with a similar Matérn’s cluster process. We first generated flow cluster centers from a homogeneous spatial Poisson process. Then, we replaced the cluster centers with a number of offspring flows, where the offspring flows were generated from a Poisson process and distributed inside a distance of cluster radius \(r\) centered at flow cluster centers.

For Case 1, we first generated 100 randomly distributed red flows, and then generated 100 randomly distributed blue flows. For Case 2, we first generated 100 randomly distributed red flows, and then generated 100 clustered blue flows. For Case 3, we first generated 200 clustered flows and then randomly labeled them as red and blue. For case 4, we first generated 100 randomly distributed red flows and then randomly generated a blue flow within a distance of 0.1 for each red flow. Case 5 is similar to Case 4, but the number of the two types of flows differs greatly in Case 5. For Case 6, we first generate 150 random flows and randomly labeled them as red, purple and yellow. Then, we randomly generated a blue and a green flow within a distance of 0.1 for each red flow and ensured the generated blue and green flows were within a distance of 0.1 of each other. Finally, we randomly remove five flows of each type and randomly added five flows for each type. Case 7 is similar to Case 6, except that in the first step, we generated 150 clustered flows and randomly labeled them as red, purple and yellow. For cases 8–10, we first generated 100 clustered distributed red flows, the clustered radius \(r\) is set to 0.2, 0.4 and 0.6 respectively. Then, we randomly generated a blue flow within a distance of 0.1 for each red flow (interaction distance is preset to 0.1). Finally, we randomly remove ten flows of each type and randomly added ten flows for each type.

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Zhou, M., Yang, M., Ai, T. et al. Rethinking the null hypothesis in significant colocation pattern mining of spatial flows. J Geogr Syst (2024). https://doi.org/10.1007/s10109-024-00439-y

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