TY - JOUR

T1 - Unsupervised Learning Discriminative MIG Detectors in Nonhomogeneous Clutter

AU - Hua, Xiaoqiang

AU - Ono, Yusuke

AU - Peng, Linyu

AU - Xu, Yuting

N1 - Funding Information:
This work was supported by NSFC (Grant No. 61901479), JSPS KAKENHI (Grant No. JP20K14365), JST CREST (Grant No. JPMJCR1914), and Keio Gijuku Fukuzawa Memorial Fund.
Publisher Copyright:
© 1972-2012 IEEE.

PY - 2022/6/1

Y1 - 2022/6/1

N2 - 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.

AB - 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.

KW - Manifold projection

KW - Matrix information geometry (MIG) detectors

KW - Nonhomogeneous clutter

KW - Signal detection

KW - Unsupervised learning

UR - http://www.scopus.com/inward/record.url?scp=85129583984&partnerID=8YFLogxK

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U2 - 10.1109/TCOMM.2022.3170988

DO - 10.1109/TCOMM.2022.3170988

M3 - Article

AN - SCOPUS:85129583984

VL - 70

SP - 4107

EP - 4120

JO - IEEE Transactions on Communications

JF - IEEE Transactions on Communications

SN - 1558-0857

IS - 6

ER -