Topological Learning for Semi-Supervised Anomaly Detection in Hyperspectral Imagery

Herein, we develop a probabilistic methodology that enables the application of semi-supervised learning over a data architecture for knowledge representation. The data architecture, proposed here, is known as the Topological Hierarchal Decomposition (THD) and is derived from the use of topological compression to decompose data into subsets of increasing attribute similarity. We demonstrate the use of the THD and a probabilistic model for interrogating the THD for object detection in hyperspectral imagery. In particular, we develop a classifier to identify objects that share similar topological attributes with a training reference object.