Contextual neural gas for spatial clustering and analysis

Abstract

This study aims to introduce contextual Neural Gas (CNG), a variant of the Neural Gas algorithm, which explicitly accounts for spatial dependencies within spatial data. The main idea of the CNG is to map spatially close observations to neurons, which are close with respect to their rank distance. Thus, spatial dependency is incorporated independently from the attribute values of the data. To discuss and compare the performance of the CNG and GeoSOM, this study draws from a series of experiments, which are based on two artificial and one real-world dataset. The experimental results of the artificial datasets show that the CNG produces more homogenous clusters, a better ratio of positional accuracy, and a lower quantization error than the GeoSOM. The results of the real-world dataset illustrate that the resulting patterns of the CNG are theoretically more sound and coherent than that of the GeoSOM, which emphasizes its applicability for geographic analysis tasks.

Keywords:

• machine learning
• self-organizing maps
• spatial cluster analysis

Acknowledgments

We acknowledge the valuable feedback received from our colleagues at our institute. Additionally, we acknowledge the constructive comments and feedback from the anonymous reviewers. Marco Helbich was funded by the Alexander von Humboldt Foundation.

Notes

1. Bação et al. (2004) suggest to include also the weighted spatial distance for the final BMU search to obtain a continuum of models between the GeoSOM and the basic SOM. However, for this it is necessary to determine adequate weights for hardly comparable dimensions.

2. In general, other ordering criteria than spatial distance can be used alternatively to incorporate autocorrelation for other dimensions such as time.

3. It is also possible to cluster the neurons or the map, respectively, in an additional post-processing step (for SOM see e.g. Murtagh 1995; Vesanto 1999; Ultsch 2005). However, post-processing may alter the results of the underlying clustering algorithms and thus makes their comparison difficult.