Unsupervised Learning Discriminative MIG Detectors in Nonhomogeneous Clutter

TL;DR

This paper introduces a novel unsupervised learning approach using discriminative matrix information geometry detectors for signal detection in nonhomogeneous clutter environments, improving separation and detection performance.

Contribution

It develops a new class of MIG detectors based on Riemannian geometry, utilizing a two-step mini-max optimization and geometric measures to enhance detection in complex environments.

Findings

Performance surpasses conventional detectors in simulations.

Effective in nonhomogeneous environments.

Utilizes Riemannian gradient descent for optimization.

Abstract

Principal component analysis (PCA) is a commonly used pattern analysis method that maps high-dimensional data into a lower-dimensional space maximizing the data variance, that results in the promotion of separability of data. Inspired by the principle of PCA, a novel type of learning discriminative matrix information geometry (MIG) detectors in the unsupervised scenario are developed, and applied to signal detection in nonhomogeneous environments. Hermitian positive-definite (HPD) matrices can be used to model the sample data, while the clutter covariance matrix is estimated by the geometric mean of a set of secondary HPD matrices. We define a projection that maps the HPD matrices in a high-dimensional manifold to a low-dimensional and more discriminative one to increase the degree of separation of HPD matrices by maximizing the data variance. Learning a mapping can be formulated as a two-step mini-max optimization problem in Riemannian manifolds, which can be solved by the Riemannian gradient descent algorithm. Three discriminative MIG detectors are illustrated with respect to different geometric measures, i.e., the Log-Euclidean metric, the Jensen--Bregman LogDet divergence and the symmetrized Kullback--Leibler divergence. Simulation results show that performance improvements of the novel MIG detectors can be achieved compared with the conventional detectors and their state-of-the-art counterparts within nonhomogeneous environments.