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

社交媒体馈送是越来越多的自愿地理信息来源之一。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。这项提议旨在促进方法上的进步，从而使我们专注于Twitter数据。具体地说，我们的目标是探索在社交媒体订阅源中派生空间相关性结构的新方法。我们的工作建立在成熟的空间自相关理论的基础上，空间自相关是衡量空间结构的传统方法。第一个研究问题涉及将空间自相关理论与推文的几何随机性相结合。后者通常是通过随机几何来研究的。我们的目标是将这两个领域的原则结合起来，以便在推文中得出更准确的关联结构。在第一步中，我们研究了随机几何对空间自相关度量的影响。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，所获得的知识可以详细地洞察某些社会活动的推文间相关性的变异性。在这项探索性研究之后，我们调查了一种空间自相关度量，该度量承认了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，我们调查了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造成的，用户在空间和时间上同时报告多种现象。我们的目标是探索将相关推文与无关推文区分开来的方法。这是通过Dempster-Shafer理论和Dirichlet过程来实现的。因此，面临的挑战是理清几何重叠的街区。在第二步中，我们通过偏自相关函数将空间自相关度量扩展到承认这种重叠特征。这将防止混合不同的现象，并导致现实的依赖结构。前两个包侧重于点级别，而第三个方面解决了合适的聚合策略。这些策略涉及传统的聚类技术和来自点模式分析的索引。这使得能够分析不同类型的复合社会活动之间的依赖关系。此外，聚合推文可以调查社交过程与其周围环境的关系。这将是这项工作的第二步。总体而言，我们的研究将使我们能够通过改进方法来分析社会活动在社会技术系统中的表现，从而对社会活动及其各自的空间机制有更多和更详细的了解。

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.