Topological Invariants-driven Spatial Interaction Network Representation Learning

Spatial interaction networks are crucial to understanding the interaction of spatial units.They are abstract representations of the secondorder effects of spatial relationships and can help us uncover the complex properties of geographic phenomena.Spatial interaction network representation learning is a cutting-edge paradigm that enables the learning of lowdimensional,dense representation vectors of spatial interaction networks from big data.It can distill the latent knowledge embedded in spatial interaction networks into interpretable,inferable,and predictable representations.This enables better solutions to spatial interaction network tasks such as interaction prediction,clustering,and spatial partitioning.Topological invariants are invariant under continuous variation and high-order topological structures are stable under dynamic conditions.Based on that,we develop the following study on the invariance representation learning of spatial interaction networks in terms of scale variation,regional differences,and dynamic evolution.(1)Topology-invariant-based method for quantifying the scale effects of spatial interaction networksThe scale effect in the modifiable areal unit problem is a fundamental problem in studying spatial interaction networks,while there is still lacking a method that quantifies scale effects in spatial interaction studies.This study hypothesizes that the variation of the spatial interaction networks aggregated at different scales portrays the scale effect.The core problems are how to characterize the spatial interaction networks aggregated at different scales and how to measure the distance between them.This study proposes a method for quantifying the scale effect on spatial interaction networks based on topological invariants.To solve the first problem,a topological summary method based on topological invariants is used to characterize the spatial interaction networks aggregated at different scales.The topological summary method can portray the topological feature information at multiple levels.To solve the second problem,the Wasserstein distance is used to calculate the distance between the representations of the different spatial interaction networks.In doing so,we are able to explore how different patterns in the data change with the scale based on different types of topological invariants.In this study,we conduct a quantitative cross-scale study of spatial interactions in five cities.We observe regular changes in clustering patterns,as well as the discovery that a critical scale exists for different cities and that the loop patterns in the data change dramatically around this critical scale,which is indicative of the choice of scale in spatial interaction network studies.(2)Topological equivalence enhanced spatial interaction network representation learning modelThe differences between spatial interaction networks in different regions pose a challenge to the out-of-distribution generalization of spatial interaction network representation models.The key to solving the problem lies in learning the essential features from the intrinsic properties of spatial interaction network data instead of relying on external labels.The recent emergence of graph self-supervised learning is to use the intrinsic properties of the data to construct positive samples instead of labeled samples,which is good for alleviating the problem of out-of-distribution generalization in graph representation learning.However,existing graph neural networks rely on continuously aggregating information from neighboring nodes to update node representations,resulting in the selection of positive samples over-relying on neighboring positive samples,i.e.,homogeneous samples,while neglecting long-range positive samples,i.e.,those that are far apart on the graph but have a high structural and semantic similarity.We call this problem ’neighbor bias.’ This neighbor bias reduces the generalization performance of the general representations of the graph.This chapter proposes a new hypothesis: the general properties of graph neural networks should be determined by a combination of homogeneous and structurally equivalent samples.This study proposes a topological signal-guided selfsupervised method for graph neural networks,which first uses a topological information-guided structural equivalence sampling strategy to extract multiscale topological features to compute the structural equivalence of node pairs using a persistent homology approach.We then additionally design a topological loss function to pull in non-direct neighbor node pairs with high structural equivalence in the representation space to alleviate neighbor bias.Finally,we adjust the effect of structural equivalence on the model in a joint training manner to suit datasets with different structural equivalence characteristics.In the spatial interaction network node classification task based on the population mobility dataset,POI data,and census data,the proposed method in this study was able to improve the model performance by up to 17.12%,with an average improvement of 10.86%,illustrating the importance of introducing the structural equivalence hypothesis for spatial interaction network representations.(3)Dynamic spatial interaction network representation learning model based on high-order topological informationThe interaction dynamic of spatial units is an essential characteristic of spatial interaction networks.Existing studies focus on considering one-toone interactions among spatial units while ignoring the many-to-many highorder interactions emerging from group interactions of spatial units.The group influence and reinforcement mechanisms arising from high-order interactions can significantly affect the new dynamics of the spatial interaction network.The dynamics of such high-order interactions are difficult to describe by a graph model based on binary interactions.Therefore,this study proposes a dynamic spatial interaction network representation model with enhanced high-order topology,using clique complex to portray highorder interactions.At the same time,since the clique describes the densest high-order relationships,it is not easily disturbed by spurious connected edges,so the influence of noise can be suppressed.To fuse the one-to-one interactions and high-order interactions,this study proposes a two-branch structure and adaptively adjusts the relative importance of both.The dynamic spatial interaction prediction experiments show that compared with the baseline model,the proposed method has a maximum improvement of15.39% and an average improvement of 7.03%? the robustness under different degrees of noise disturbance is demonstrated in the perturbation experiments.In summary,this study explores the challenges faced in the study of spatial interaction network representation in three dimensions of scale,space,and time,and proposes a topological invariant-driven framework for spatial interaction network representation.The feasibility and validity of this framework are verified through experiments on several spatial interaction networks,which have implications for future research at the intersection of geographic networks and geospatial artificial intelligence.There are 60 figures,26 tables,and 246 citations in this thesis.