Spatial Methods for Data Science

Vorlesung mit Übung (4 SWS)

Course description

Many systems of societal interest can be understood in terms of some notion of space, either physical or more abstract. Examples include geographic or urban systems embedded in physical space, political systems organized by ideological distance, and social relationships shaped by demographic and value similarity. Analyzing these kinds of systems often requires methods that use notions of similarity, distance, or latent space to uncover hidden patterns.

This course provides an interdisciplinary introduction to spatial approaches to data analysis and is aimed at students from a range of quantitative and social science disciplines. The first part of the course focuses on methods for analyzing systems embedded in physical space, including how nearby locations influence one another, how interactions and flows emerge across space, and how spatial patterns can be modeled and interpreted. The second part of the course moves from physical space to more abstract notions of similarity and latent structure, introducing approaches such as dimensionality reduction, embeddings, latent space models, and network geometry. The course will combine lectures on core concepts and methods with practical programming exercises and discussion of selected applications and current research literature.

Parameters

Time: Wed 9:00 to 13:00 (lectures), Thu 10:00 to 12:00 (tutorials)
Location: TBD
Language: English
Evaluation: Final oral examination

Schedule

Part I: Physical spaces

• Week 1: Introduction
  Political, social, geographic, and urban systems Distance, similarity, and neighbourhoods. Interaction and spatial dependence.
• Week 2: Spatial data and spatial relationships
  Point, areal, raster, flow, and network data Spatial weights, contiguity and nearest-neighbours.
• Week 3: Exploratory spatial data analysis
  Spatial distributions and clustering. Spatial autocorrelation.
• Week 4: Point patterns and spatial interaction
  Point processes, spatial interaction and flow systems.
• Week 5: Spatial regression and areal dependence
  Spatial regression models. Spatial lag and CAR models.
• Week 6: Geostatistics and spatial prediction
  Continuous spatial fields. Spatial interpolation. Gaussian process regression.
• Week 7: Applications / Current literature

Part II: Latent spaces

• Week 8: Introduction
  Similarity, dissimilarity, and metric spaces. Kernels and latent geometry.
• Week 9: Linear dimensionality reduction
  Principal component analysis (PCA). Multidimensional scaling (MDS).
• Week 10: Nonlinear dimensionality reduction and manifold learning.
  Isomap and locally linear embedding. Laplacian eigenmaps and diffusion maps. t-SNE and UMAP.
• Week 11: Embeddings
  Word, document, node embeddings. Spatial partitioning and nearest-neighbour search.
• Week 12: Latent space models
  Latent position models. Distance-based relational structure.
• Week 13: Spectral methods
  Graph Laplacians and spectral embedding. Spectral clustering.
• Week 14: Network geometry
  Hidden metric spaces and similarity-based connection probabilities. Hyperbolic geometry.
• Week 15: Applications / Current literature