Title: ELSA: Local spatial autocorrelation of embeddings
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: spatial autocorrelation, embeddings, spatial statistics, metrics

Abstract: Spatial autocorrelation is a popular concept in geography to measure the neighborhood dependencies of continuous random variables with geographic coordinates, such as temperature measures or house prices. However, in the real world, the data associated with a given location is often more complex than a simple scalar value and may contain e.g. images or text. Here, we introduce Embedding Local Spatial Autocorrelation, a new statistic to measure spatial interdependencies of data embeddings at a given location. ELSA adapts and expands one of the most central concepts in geography for the age of AI and its central data structure: embeddings. We highlight the utility of ELSA as a measure of spatial homo- and heterogeneity. Focusing on image embeddings, we provide experiments on using ELSA to test for spatial (in)dependence of distributions, for the detection of outliers and for sampling optimal training datasets. We also comment on further potential applications of ELSA and discuss the shortcomings of our approach.