An Improved Weighted Median Algorithm for Spatial Outliers Detection

Abstract

A spatial outlier is an object that significantly deviates from its surrounding neighbors. The median algorithm is one of the spatial outlier methods, which is robust. However, it assumes that all spatial objects have the same characteristics. Meanwhile, the Average Difference Algorithm (AvgDiff) has accommodated the differences in spatial characteristics, but it does not use statistical tests to determine the status of an object, whether it is an outlier or not. The research developed an improved version of the median algorithm and AvgDiff, called the Weighted Median Algorithm (WMA) which combined the advantages of the two methods. From the median algorithm, WMA adopted median and statistical test concepts. Meanwhile, from AvgDiff, WMA adopted the concept of using differences in objects’ spatial characteristics as weights. A combination of the two advantages was innovated by calculating WMA’s neighborhood score using a weighted median. Then, a simulation was conducted to analyze the accuracy of the method. The result confirms that when objects have heterogeneous spatial characteristics, WMA performs better than the median algorithm. The accuracy of WMA is not much higher than AvgDiff, but the use of WMA can prevent a serious false detection problem. The methods can be applied to an incidence rate of Covid-19 data in East Java.