Learning Geographical Manifolds: A Kernel Trick for Geographical Machine Learning

Levi John Wolf, Elijah Knaap

Dimension reduction is one of the oldest concerns in geographical analysis. Despite significant, longstanding attention in geographical problems, recent advances in non-linear techniques for dimension reduction, called manifold learning, have not been adopted in classic data-intensive geographical problems. More generally, machine learning methods for geographical problems often focus more on applying standard machine learning algorithms to geographic data, rather than applying true “spatially-correlated learning,” in the words of Kohonen. As such, we suggest a general way to incentivize geographical learning in machine learning algorithms, and link it to many past methods that introduced geography into statistical techniques. We develop a specific instance of this by specifying two geographical variants of Isomap, a non-linear dimension reduction, or “manifold learning,” technique. We also provide a method for assessing what is added by incorporating geography and estimate the manifold’s intrinsic geographic scale. To illustrate the concepts and provide interpretable results, we conducting a dimension reduction on geographical and high-dimensional structure of social and economic data on Brooklyn, New York. Overall, this paper’s main endeavor–defining and explaining a way to “geographize” many machine learning methods–yields interesting and novel results for manifold learning the estimation of intrinsic geographical scale in unsupervised learning.