SAIL: A Learnable Generalisation of Spatial Autocorrelation over Graph-Structured Data

Key points

• In vision and scientific domains involving spatial data, a key question is whether node feature values vary independently across space or form coherent spatial structures.1
• Classical spatial autocorrelation statistics such as Moran's $I$ and Geary's $C$ quantify this phenomenon but operate on a single scalar variable with fixed neighbourhood weights, limiting their use for high-dimensional graph-like data.1
• SAIL produces interpretable local and global spatial coherence descriptors, enabling supervised prediction and unsupervised discovery of spatial autocorrelation modes and hotspots.1
• We show that SAIL exactly recovers classical spatial statistics under appropriate parametrisations and, for tasks driven by latent spatial autocorrelation, can approximate the Bayes-optimal predictor with an inductive bias matched to such tasks.1

Sources (1)

• [1]SAIL: A Learnable Generalisation of Spatial Autocorrelation over Graph-Structured Data
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 20, 06:28 PM

  We introduce SAIL (Spatial Autocorrelation Index Learner), a differentiable framework that generalises spatial autocorrelation into a learnable operator by jointly learning feature projections defining candidate scalar fields and inter-node neighbourhood affinities.

  In vision and scientific domains involving spatial data, a key question is whether node feature values vary independently across space or form coherent spatial structures.

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