We consider the problem of detecting features in spatial point processes in the presence of substantial clutter. One example is the detection of mine elds using reconnaissance aircraft images that erroneously identify many objects that are not mines. Another is the detection of seismic faults on the basis of earthquake catalogs: earthquakes tend to be clustered close to the faults, but there are many that are farther away. Our solution uses model-based clustering based on a mixture model for the process, in which features are assumed to generate points according to highly linear multivariate normal densities, and the clutter arises according to a spatial Poisson process. Very nonlinear features are represented by several highly linear multivariate normal densities, giving a piecewise linear representation. The model is estimated in two stages. In the rst stage, hierarchical model-based clustering is used to provide a rst estimate of the features. In the second stage, this clustering is re ned using the EM algorithm. The number of features is found using an approximation to the posterior probability of each number of features. For the mine eld problem, this method yields high detection rates and low false positive rates. For the seismic fault problem, the method accurately recovers the documented faults in the San Francisco Bay area.
The model-based method REF hypothesizes a model for each cluster and finds the best fit of the data to the given model.
Detecting Features in Spatial Point Processes with Clutter via Model-Based Clustering
Journal of the American Statistical Association
Mathematics