Multiscale Anomaly Detection Using Diffusion Maps

We propose a multiscale approach to anomaly detection in images, combining spectral dimensionality reduction and a nearest-neighbor-based anomaly score. We use diffusion maps to embed the data in a low dimensional representation, which separates the anomaly from the background. The diffusion distance between points is then used to estimate the local density of each pixel in the new embedding. The diffusion map is constructed based on a subset of samples from the image and then extended to all other pixels. Due to the interpolative nature of extension methods, this may limit the ability of the diffusion map to reveal the presence of the anomaly in the data. To overcome this limitation, we propose a multiscale approach based on Gaussian pyramid representation, which drives the sampling process to ensure separability of the anomaly from the background clutter. The algorithm is successfully tested on side-scan sonar images of sea-mines.