Spatial Functional Outlier Detection in Multivariate Spatial Functional Data

Multivariate spatial functional data consists of multiple functions of time-dependent attributes observed at each spatial point. This study focuses on detecting spatial outliers in spatial functional data. Firstly, we develop a new method called Mahalanobis Distance Spatial Outlier (MDSO) to detect functional outliers in the data. The method introduces the multivariate functional Mahalanobis semi-distance and multivariate pairwise functional Mahalanobis semi-distance metrics based on the multivariate functional principal components analysis to calculate the dissimilarity between functions at each spatial point. Via simulation, we show that MDSO performs better than the other competing methods. Secondly, MDSO has been extended to detect spatial functional outliers as well. The functional outliers can now be categorized as global or/and local functional outliers. The appropriate number of neighbors and the cut-off point for the degree of isolation are determined via simulation. Finally, we demonstrate the application of the MDSO on a water quality data set obtained from Sungai Klang basin in Malaysia. The results can be used to support the authority in making better decisions on the management of the river basin or other spatial data with time-independent attributes.