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In complex, high dimensional and unstructured data it is often difficult to extract meaningful patterns. This is especially the case when dealing with textual data. Recent studies in machine learning, information theory and network science…
A good understanding of cities is crucial to implement urban planning policies leading to social and economic sustainability and an efficient use of resources. While urban concentration has been associated with both positive and negative…
Modern business and economic datasets often exhibit nonlinear, multi-scale structures that traditional linear tools under-represent. Topological Data Analysis (TDA) offers a geometric lens for uncovering robust patterns, such as connected…
Quantifying the topological similarities of different parts of urban road networks (URNs) enables us to understand the urban growth patterns. While conventional statistics provide useful information about characteristics of either a single…
Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…
The article contains a methodology for social statistics assessing. The significance of minorities (groups that differ in their attributes from the majority) has grown substantially in the modern postindustrial economy and society. In the…
Gerrymandering is one of the biggest threats to American democracy. By manipulating district lines, politicians effectively choose their voters rather than the other way around. Current gerrymandering identification methods (namely the…
Migration the main process shaping patterns of human settlement within and between countries. It is widely acknowledged to be integral to the process of human development as it plays a significant role in enhancing educational outcomes. At…
The Hoover index H, derived from the distribution of population density, has a long history in population geography. But it is prone to misinterpretation and serious measurement artifacts, some of which have been recognized for years. Here…
Persistent homology is a branch of computational algebraic topology that studies shapes and extracts features over multiple scales. In this paper, we present an unsupervised approach that uses persistent homology to study divergent behavior…
Economic growth results from countries' accumulation of organizational and technological capabilities. The Economic and Product Complexity Indices, introduced as an attempt to measure these capabilities from a country's basket of exported…
Understanding how neural networks generalize on unseen data is crucial for designing more robust and reliable models. In this paper, we study the generalization gap of neural networks using methods from topological data analysis. For this…
This chapter examines the possibility to analyze and compare human activities in an urban environment based on the detection of mobile phone usage patterns. Thanks to an unprecedented collection of counter data recording the number of…
Persistent homology has been widely used to discover hidden topological structures in data across various applications, including music data. To apply persistent homology, a distance or metric must be defined between points in a point cloud…
Human settlements on Earth are scattered in a multitude of shapes, sizes and spatial arrangements. These patterns are often not random but a result of complex geographical, cultural, economic and historical processes that have profound…
Inspired by Christopher Alexanders conception of the world - space is not lifeless or neutral but a living structure involving far more small things than large ones a topological representation has been previously developed to characterize…
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…
Family planning is a global development priority and a key indicator of reproductive health. Monitoring progress is challenged by gaps in survey data across countries. The United Nations Population Division addresses this with the Family…
We follow up on the study of correlations between GDP's of rich countries. We analyze web-downloaded data on GDP that we use as individual wealth signatures of the country economical state. We calculate the yearly fluctuations of the GDP.…
This study details an approach for the analysis of social media collected political data through the lens of Topological Data Analysis, with a specific focus on Persistent Homology and the political processes they represent by proposing a…