Mathematical methods for anomaly grouping in hyperspectral images

The topological anomaly detection (TAD) algorithm differs from other anomaly detection algorithms in that it does not rely on the data\u27s being normally distributed. We have built on this advantage of TAD by extending the algorithm so that it gives a measure of the number of anomalous objects, rather than the number of anomalous pixels, in a hyperspectral image. We have done this by identifying and integrating clusters of anomalous pixels, which we accomplished with a graph-theoretical method that combines spatial and spectral information. By applying our method, the Anomaly Clustering algorithm, to hyperspectral images, we have found that our method integrates small clusters of anomalous pixels, such as those corresponding to rooftops, into single anomalies; this improves visualization and interpretation of objects. We have also performed a local linear embedding (LLE) analysis of the TAD results to illustrate its application as a means of grouping anomalies together. By performing the LLE algorithm on just the anomalies identified by the TAD algorithm, we drastically reduce the amount of computation needed for the computationally-heavy LLE algorithm. We also propose an application of a shifted QR algorithm to improve the speed of the LLE algorithm