Adaptive Reference-Related Graph Embedding for Hyperspectral Anomaly Detection

Graph embedding (GE) provides an effective way to reveal the intrinsic feature of high-dimensional data on the foundation of preserving topological properties. Under the framework of GE, the hyperspectral image can be represented by a weighted graph, where pixels and similarities among them are treated as vertices and edge weights, respectively. In this article, an adaptive reference-related GE (ARGE) method is proposed to efficaciously obtain the low-dimensional feature and improve computational efficiency. The ARGE method is composed of two primary processes. The key to connecting these two processes is the reference vertices set, which is the abstraction of graph topological features. First, the reference vertices are adaptively selected through a three-step adaptive reference set selection (ARSS) algorithm. Second, the original high-dimensional graph is embedded as a low-dimensional graph through preserving the reference-related structure. Specifically, the pairwise similarities between vertices and reference vertices are preserved in embedding space. In addition, a new hybrid dissimilarity measure of Rao distance and spectral information divergence (RD-SID) is designed to depict the spectral difference between pixels. To evaluate the effectiveness of the proposed method, the obtained low-dimensional feature is fed into the anomaly detector to detect anomalous pixels. The experimental results on five real and one synthetic hyperspectral datasets demonstrate the superiority of the proposed ARGE method over the compared feature extraction methods.