LDPP-MIG Detectors in Sample-Starved Nonhomogeneous Clutter

Abstract

Enhancing the discriminative power of points on matrix manifolds by reducing redundant information in data is an effective strategy to boost the performance of matrix information geometry (MIG) detectors. In this study, we explore a category of MIG detectors that utilize a projection method to preserve local dissimilarity. Specifically, the local dissimilarity preserving projection (LDPP) is learned in both supervised and unsupervised ways. Then, we apply the resulting decision schemes to signal detection in nonhomogeneous clutter. To achieve this goal, we leverage the properties of Hermitian positive-definite (HPD) correlation matrices of data. Given a collection of training matrices, we estimate the disturbance covariance matrix and transform the signal detection problem into a task of discrimination within the manifold of HDP matrices. Then, we introduce an LDPP method that projects HPD matrices onto a lower dimensional manifold that inherently enhances discriminability, while strictly adhering to a constraint maximizing the preservation of local dissimilarity between each HPD matrix and its neighboring matrices. The process of learning this mapping is cast as an optimization problem on the Stiefel manifold, which can be efficiently solved using the Riemannian gradient descent algorithm. Based on this discriminative lower dimensional manifold, we construct four distinct LDPP-MIG detectors, each grounded in unique geometric principles. Experimental results highlight that the proposed LDPP-MIG detectors achieve detection performance improvements with respect to their counterparts.