Analysis of signals under compositional noise with applications to SONAR data
In this paper, we consider the problem of denoising and classification of SONAR signals observed under compositional noise, i.e., they have been warped randomly along the x-axis. The traditional techniques do not account for such noise and, consequently, cannot provide a robust classification of signals. We apply a recent framework that: 1) uses a distance-based objective function for data alignment and noise reduction; and 2) leads to warping-invariant distances between signals for robust clustering and classification. We use this framework to introduce two distances that can be used for signal classification: a) a y-distance, which is the distance between the aligned signals; and b) an x-distance that measures the amount of warping needed to align the signals. We focus on the task of clustering and classifying objects, using acoustic spectrum (acoustic color), which is complicated by the uncertainties in aspect angles at data collections. Small changes in the aspect angles corrupt signals in a way that amounts to compositional noise. As a result, we demonstrate the use of the developed metrics in classification of acoustic color data and highlight improvements in signal classification over current methods.