  Convolutional Neural Networks (CNN) possess many positive qualities when it
comes to spatial raster data. Translation invariance enables CNNs to detect
features regardless of their position in the scene. However, in some domains,
like geospatial, not all locations are exactly equal. In this work, we propose
localized convolutional neural networks that enable convolutional architectures
to learn local features in addition to the global ones. We investigate their
instantiations in the form of learnable inputs, local weights, and a more
general form. They can be added to any convolutional layers, easily end-to-end
trained, introduce minimal additional complexity, and let CNNs retain most of
their benefits to the extent that they are needed. In this work we address
spatio-temporal prediction: test the effectiveness of our methods on a
synthetic benchmark dataset and tackle three real-world wind prediction
datasets. For one of them, we propose a method to spatially order the unordered
data. We compare the recent state-of-the-art spatio-temporal prediction models
on the same data. Models that use convolutional layers can be and are extended
with our localizations. In all these cases our extensions improve the results,
and thus often the state-of-the-art. We share all the code at a public
repository.
