Spatial Neighborhood Discovery
Let us consider an example in the domain of water monitoring using sensors placed in a river stream (Adam et al., 2004; Janeja et al., 2010). The sensor network comprises of sensors placed in the various parts of the stream, with the goal of detecting anomalous levels of toxicity in a water body. In order to find outliers in the form of anomalous readings in sensors or sensors that may be malfunctioning, it is first required to discover a spatial neighborhood comprising of the relevant sensors with a similar behavior. Each sensor is characterized by a set of attributes or features in proximity such as a factory, bridge, railroad, stream, certain type of vegetation, etc. Such information can be accumulated with the help of domain experts. Indeed, in many cases such studies precede sensor placement.
In addition to spatial proximity, this feature information is used to identify relationships between the sensors to place them in similarly behaving spatial neighborhoods. The study (Adam et al., 2004; Janeja et al., 2010) measures similarities, across the sensors, between feature vectors using the Jaccard coefficient. This facilitates the quantification of the heterogeneity in the neighborhood resulting from the impact of the various features. The study shows the impact of refining the neighborhood, using such similarity coefficients, on the outliers discovered.