A study of the effect of alternative similarity measures on the performance of graph-based anomaly detection algorithms

We investigate an anomaly detection framework that uses manifold-based distances within the existing skeleton kernel principle component analysis (SkPCA) manifold-learning technique. SkPCA constructs a manifold from the an adjacency matrix built using a sparse subsample of the data and a similarity measure. In anomaly detection the relative abundance of the anomalous class is rare by definition and in practice anomalous samples are unlikely to be randomly selected for inclusion in the sparse data subsample. Thus, anomalies should not be well modeled by the SkPCA-constructed model. Here, we consider alternative distance measures based on viewing spectral pixels as points in projective space, that is, each pixel is a 1-dimensional line through the origin. Chordal and geodesic distances are computed between hyperspectral pixels and detection performance leveraging these distances is compared to alternative anomaly detection algorithms. In addition, we introduce Ensemble SkPCA which utilizes the ensemble of mean, normalized detection scores corresponding to multiple randomly generated skeletons. For acceptable false alarm tolerances, the ensemble detection score derived from chordaland geodesic-based methods achieves higher probability of detection than Euclidean distance-based Ensemble SkPCA or the benchmark RX algorithm.