Page 26 - Special Topic Session (STS) - Volume 1

STS346 A.H.M. Rahmatullah Imon

Figure 1. Outliers in data clusters

Spatial outliers are those observations whose characteristics are markedly
different from their spatial neighbors. The identification of spatial outliers is
important because it can reveal hidden but valuable knowledge in many
applications such as identifying aberrant genes or tumor cells, discovering
highway traffic congestion points, locating extreme meteorological events
such as tornadoes, and hurricanes etc. Although outliers could be easily
identified in univariate, bivariate, or even trivariate data through graphical
examination of the data, visual inspection does not usually work for more than
three dimensions. Not only that automated identification of outliers is tricky
even for a two dimensional data if they data form clusters as shown in Figure
1. Here the idea of majority minority simply does not work, bad clusters are
identified as outliers [see Hadi et al. (2009)] based on classification techniques.
Things could even be cumbersome in regression models where outliers can
occur along the ydimension, or along the x-dimension, or both and/or among
the relationship between x and y. An excellent review of different aspects of
spatial outliers is available in Shekhar et al. [16] and Hadi and Imon (2018).
Conceptually, spatial outliers match with outliers in big data and for this reason
outlier detection techniques designed for big data are often routinely
employed in spatial data. In big data the concept of outlier is local, not global
so as in spatial data. The distance and/or density based methods such as k–
nearest neighbourhood, local outlier factor (LOF), spatial outlier factor (SOF)
methods have become more popular. But all these methods are designed to
identify outliers along the y-axis and hence is not readily applicable for spatial
regression. For example, temperatures and amount of rainfalls of different
regions may vary due to their distances from sea or mountain. Once we fit this
relationship by regression we may observe not only strange temperature or
rainfall pattern, the distance factor may also be unusual. Attempts have been
made to identify outliers based on residuals but it only focuses on the outliers
in y, but not in x or both and the whole concept is rather global than local. To
overcome this problem in this paper we propose a method which not only

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