Signal diffusion features for automatic target recognition in synthetic aperture sonar

Given a high dimensional dataset, one would like to be able to represent this data using fewer parameters while preserving relevant signal information, previously this was done with principal component analysis, factor analysis, or basis pursuit. However, if we assume the original data actually exists on a lower dimensional manifold embedded in a high dimensional feature space, then recently popularized approaches based in graph-theory and differential geometry allow us to learn the underlying manifold that generates the data. One such manifold-learning technique, called Diffusion Maps, is said to preserve the local proximity between data points by first constructing a representation for the underlying manifold. This work examines binary target classification problems using Diffusion Maps to embed inverse imaged synthetic aperture sonar signal data with various diffusion kernel representations for automatic target recognition. Results over three sonar datasets demonstrate that the resulting diffusion maps capture suitable discriminating information from the signals to improve target recognition and drastically lower the false alarm rate.