Spatial Correlations in Social Media Data: Identification and Quantification of Spatial Correlation Structures in Georeferenced Twitter Feeds

社交媒体推送是自愿提供地理信息的越来越多的来源之一。因此，近年来，这类数据已被证明是许多研究领域的丰富信息来源。本提案旨在促进方法上的进步，因此我们专注于Twitter数据。具体来说，我们的目标是探索在社交媒体feed中推导空间相关结构的新方法。我们的工作建立在成熟的空间自相关理论的基础上，这是测量空间结构的传统方法。第一个研究问题是如何将空间自相关理论与推文的几何随机性相结合。后者通常是用随机几何的方法来研究的。我们的目标是结合这两个领域的原理，以便在tweet中获得更准确的关联结构。在第一步，我们研究了随机几何对空间自相关测度的影响。这包括点模式建模和蒙特卡罗模拟研究。这项调查将为更好地解释自相关结果提供见解。此外，所获得的知识允许详细了解某些社会活动的推特间相关性的可变性。在这项探索性研究之后，我们研究了一种空间自相关的测量方法，该方法承认潜在几何结构的随机性，从而能够在社交媒体数据中获得有意义的模式。其次，我们研究了在推文中反映的现象的相互重叠特征。这种重叠是由用户的自主行为引起的，用户在空间和时间上同时报告多种现象。我们的目标是探索区分相关推文和不相关推文的方法。这是通过邓普斯特-谢弗理论和狄利克雷过程来完成的。因此，挑战在于解开几何上重叠的街区。在第二步中，我们通过部分自相关函数扩展空间自相关度量来识别这种重叠特征。这将防止混合不同的现象，并导致现实的依赖结构。前两个包关注的是点级别，而第三个方面关注的是合适的聚合策略。这些策略涉及传统的聚类技术和点模式分析的指标。这允许分析不同类型的复合社会活动之间的依赖关系。此外，聚合推文允许调查社会过程与其直接环境的关系。这将是该工作包的第二步。总的来说，我们的研究将通过改进的方法来分析社会技术系统中的社会活动及其各自的空间机制，从而能够获得对社会活动及其各自空间机制的更多和详细的了解。

Social media feeds are one of the growing numbers of sources of volunteered geographic information. Thereby, over recent years, this kind of data has proven to be a rich source of information for many areas of research. This proposal aims to contribute methodological advancements, whereby we focus on Twitter data. Specifically, we aim to explore novel ways to derive spatial correlation structures within social media feeds. Our work builds upon the mature theory of spatial autocorrelation, which is the traditional way of measuring spatial structure.The first research question is concerned with integrating the theory of spatial autocorrelation with the geometric stochasticity of tweets. The latter is typically investigated by means of stochastic geometry. We aim to combine principles from both fields in order to derive more accurate correlation structures within tweets. In a first step we investigate the effect of the stochastic geometries on spatial autocorrelation measures. This includes point pattern modelling and a Monte Carlo simulation study. That investigation will provide insights regarding a better interpretation of autocorrelation results. Moreover, the gained knowledge allows detailed insights into the variability of inter-tweet correlations of certain social activities. After this exploratory study, we investigate a measure of spatial autocorrelation that acknowledges the stochasticity of the underlying geometric structure and is thus able to obtain meaningful patterns within social media data.Secondly we investigate the mutually overlapping character of phenomena that are reflected within the tweets. This overlap is caused by the autonomous behaviour of the users, which report about multiple phenomena simultaneously in space and time. We aim to explore ways of separating relevant tweets from non-relevant ones. This is done by means of Dempster-Shafer theory and Dirichlet processes. The challenge thereby is to disentangle the geometrically overlapping neighbourhoods. In a second step we expand spatial autocorrelation measures towards acknowledging this overlapping character by means of partial autocorrelation functions. This will prevent mixing different phenomena and leads to realistic dependency structures.While the first two packages focus on the point level, the third aspect addresses suitable aggregation strategies. These strategies involve traditional clustering techniques and indices from point pattern analysis. This allows analysing dependencies between different kinds of compound social activities. Further, aggregating tweets allows investigating the relationship of social processes towards their immediate surroundings. This will be a second step of this work package.Overall, our research will enable for gaining an increased and detailed understanding of social activities and their respective spatial mechanisms through improved methods allowing to analyse representations of these within socio-technical systems.