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Top1. Introduction
The focus of this approach is to identify anomalous spatial windows using clustering-based methods. Anomalous spatial windows (Shi and Janeja 2009, Janeja and Atluri 2008, Das and Schneider 2007) are formed by a set of contiguous spatial nodes which are unusual with respect to the rest of the data. Many scan statistics based approaches (Kulldorff 1997, Kulldorff et al. 2007) have been proposed to identify such windows. Clustering on the other hand is used to identify similarly behaving groups of nodes. There are many parallels in these two classes of techniques. For example, the spatial circular scan statistic method (Kulldorff 1997) scans the region with a circular shape while intrinsically is looking for spatial proximity, which some clustering methods also look for. However, scan statistics based methods do not look at the similarity of other attributes as clustering methods would do. In this paper, we bridge this gap between scan statistic methods and clustering methods. There is a huge amount of work done in scan statistics as well as in clustering. But scan statistics type framework has not been applied to clustering methods yet, to discover spatial anomalous windows.
In this paper, we examine if the framework of anomaly detection could be applied to the spatial clustering methods. Particularly, we focus on adopting a density based clustering method (Ester et al. 1998) to identify spatial anomalous windows. Density is an intuitive way to represent spatial nodes. We use the density-based clustering method because it is very similar to the existing spatial circular scan statistics. Density based methods use the concept of dense neighborhoods to identify clusters which is similar to circular scan statistic (Kulldorff 1997) based method. Circular scan statistics uses a circle of a particular radius, as a starting point and then expands the circle to scan the region. Similarly, density-based clustering method uses a circular neighborhood which is preset and remains fixed. We apply the variable circular scan window to density-based neighborhood.
Motivating Domain: Location has a very significant impact on crime in the United States. While some places are nearly free of serious crime, others are plagued by some of the highest crime rates. It is therefore clear that the risk of being victimized by crime in the United States varies greatly from one location to another. Hence, we aim to find a group of locations that is unusual as compared to the rest of the data. Usually, the crime rankings that are available are based on cities of various populations, metropolitan areas or states. The ‘crime rate’ is considered to rank the spatial units (cities, metropolitan areas, or states). However, these rankings/approaches do not identify contiguous neighborhoods which are high in a particular type of crime say, murders. What we aim to find is a group of contiguous nodes or neighborhoods, instead of just individual spatial unit, which are unusual with respect to the rest of the data.
Scan statistics based methods can be used to address this problem. Similarly, there are several clustering methods that can be used to identify unusually shaped clusters. However, they do not identify the unusual nature of the clusters as compared to the rest of the data. Thus, we modeled clustering as a scan statistics problem to bridge the gap between clustering and scan statistics framework.