I will be teaching a course on Spatial Methods for Data Science at Goethe University Frankfurt during the Winter semester of 2026/2027
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.
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, and 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