Spatial classification with fuzzy lattice reasoning

This work extends the Fuzzy Lattice Reasoning (FLR) Classifier to manage spatial attributes, and spatial relationships. Specifically, we concentrate on spatial entities, as countries, cities, or states. Lattice Theory requires the elements of a Lattice to be partially ordered. To match such requirement, spatial entities are represented as a graph, whose number of nodes is equal to the amount of unique values of the spatial attribute elements. Then, the graph nodes are linearly arranged to formulate a partially ordered set; and thus be included in the Fuzzy Lattice classifier. The overall problem of incorporating spatial attributes in FLR was deduced to a Minimum Linear Arrangement problem. A corresponding open-source implementation in R has been made available on CRAN repository. The proposed method was evaluated using an open spatial dataset from the National Ambient Air Quality Standards (NAAQS). We investigated whether the addition of the spatial attribute contributed to any improvements in classification accuracy; and how linear arrangement alternatives may affect it. Experimental results showed that classification accuracy is above 85% in all cases, and the use of spatial attributes resulted to an increased accuracy of 92%. Alternative linear arrangements did not contribute significantly in improving classification accuracy in this case study.