Spatial autocorrelation is a statistical phenomenon that describes the tendency for similar values of a variable to occur in close proximity to each other. It is measured by comparing the values of a variable at different locations to assess whether they are more similar to their neighbors than they are to random locations.

What is "auto" in spatial autocorrelation?

The prefix "auto" means "self" or "same". In spatial autocorrelation, it refers to the fact that the correlation is between values of the same variable at different locations. This is in contrast to cross-correlation, which is the correlation between values of different variables at the same location.

Here are some examples of spatial autocorrelation:

Temperature: Temperatures tend to be more similar in close proximity than they are far apart.
Rainfall: Rainfall tends to be more clustered in space than it is random.
Population density: Population density tends to be higher in urban areas and lower in rural areas.

Spatial autocorrelation can be measured using a variety of statistical methods, such as Moran's I and Geary's C. These methods are typically used to assess the strength and! direction of spatial autocorrelation.

Applications of spatial autocorrelation

Spatial autocorrelation is used in many different fields, including:

Geology: Spatial autocorrelation can be used to identify patterns in geological features, such as faults and fractures.
Ecology: Spatial autocorrelation can be used to study the distribution of plants and animals.
Urban planning: Spatial autocorrelation can be used to identify areas of high and low crime rates.
Public health: Spatial autocorrelation can be used to study the spread of disease.

Spatial autocorrelation is a powerful tool for understanding the spatial patterns of data. By understanding spatial autocorrelation, we can better understand the processes that create these patterns.

To avoid training Machine Learning models with spatially autocorrelated samples, there are multiple ways to separate the data in the feature space aswell as in the spatial space. One of them is Spatial Cross-validation, which separates the cross-validation folds into spatially independent entitites to avoid such spatial correlation.
More details can be found here : Spatially autocorrelated training and validation samples inflate performance assessment of convolutional neural networks for the particular case of CNNs.

Measuring spatial autocorrelation

There are many ways to measure spatial autocorrelation, one of them being a Correlogram.
A correlogram in spatial data science is a visual tool used to explore spatial autocorrelation. It's a graph that depicts the relationship between the similarity of observations and the distance separating them. In simpler terms, it shows how values of a variable at different locations are correlated with each other.