Multivariate Spatial Outlier Detection Using Robust Geographically Weighted Methods

Abstract

Outlier detection is often a key task in a statistical analysis and helps guard against poor decision-making based on results that have been influenced by anomalous observations. For multivariate data sets, large Mahalanobis distances in raw data space or large Mahalanobis distances in principal components analysis, transformed data space, are routinely used to detect outliers. Detection in principal components analysis space can also utilise goodness of fit distances. For spatial applications, however, these global forms can only detect outliers in a non-spatial manner. This can result in false positive detections, such as when an observation's spatial neighbours are similar, or false negative detections such as when its spatial neighbours are dissimilar. To avoid mis-classifications, we demonstrate that a local adaptation of various global methods can be used to detect multivariate spatial outliers. In particular, we account for local spatial effects via the use of geographically weighted data with either Mahalanobis distances or principal components analysis. Detection performance is assessed using simulated data as well as freshwater chemistry data collected over all of Great Britain. Results clearly show value in both geographically weighted methods to outlier detection.

The GWmodel R package: further topics for exploring spatial heterogeneity using geographically weighted models

“…The GW modelling paradigm provides a simple, yet powerful analytical toolkit for exploring change in a statistical model's parameters and outputs across space; a paradigm that continues to evolve (e.g. 16,21,24,45,46,47,48,52,53). Functions for these more recent advances in GW modelling will be incorporated into GWmodel in due course.…”

Local Geographic Variation of Public Services Inequality: Does the Neighborhood Scale Matter?

“…As an adaptation of the PCA approach, the GWPCA takes the spatial autocorrelation in the spatial process into account [42,93,94]. Incorporating the GWPCA within the same re-design algorithm may provide an improvement for a multivariate spatial process that has distinct non-stationary relationship properties.…”

“…Therefore, we calibrated our GWPCAs with a bi-square kernel using adaptive bandwidths whose sizes are chosen automatically and objectively via cross-validation. This methodology has been fully explained by Harris et al [93]. …”

“…Harris et al [93] integrated the GWPCA methodology with robust local Mahalonobis distances (MDs) to outline any change in the structure of a multivariate data set. Therefore, we can use this GWPCA-based detection method to investigate the local scale characteristics of a multivariate composition for (1) checking whether the data structure of the observation is unusual with respect to its close spatial neighborhood; and (2) investigating how the MAUP influences a certain spatial heterogeneity in the structure of the set of public services inequality indicators.…”

“…Therefore, we can use this GWPCA-based detection method to investigate the local scale characteristics of a multivariate composition for (1) checking whether the data structure of the observation is unusual with respect to its close spatial neighborhood; and (2) investigating how the MAUP influences a certain spatial heterogeneity in the structure of the set of public services inequality indicators. Harris et al [93] have presented the full report on this methodology.…”