Sparsity-based methods for two-dimensional (2D) direction-of-arrival (DOA) estimation often suffer from high computational complexity due to the large array manifold dictionaries. This paper proposes a fast 2D DOA estimator using array manifold matri...
Detecting genomes with similar expression patterns using clustering techniques plays an important role in gene expression data analysis. Non-negative matrix factorization (NMF) is an effective method for clustering the analysis of gene expression dat...
Multi-label classification has been extensively researched and utilized for several decades. However, the performance of these methods is highly susceptible to the presence of noisy data samples, resulting in a significant decrease in accuracy when n...
The Nonnegative Matrix Factorization (NMF) algorithm and its variants have gained widespread popularity across various domains, including neural networks, text clustering, image processing, and signal analysis. In the context of hyperspectral unmixin...
In this paper, we introduce a new geometric description of the manifolds of matrices of fixed rank. The starting point is a geometric description of the Grassmann manifold
Clutter suppression in heterogeneous environments is a serious challenge for airborne radar. To address this problem, a matrix-manifold-based clutter suppression method is proposed. First, the distributions of training data in heterogeneous environme...
Low-rank matrix completion aims to recover an unknown matrix from a subset of observed entries. In this paper, we solve the problem via optimization of the matrix manifold. Specially, we apply QR factorization to retraction during optimization. We de...
Tree-like structures, characterized by hierarchical relationships and power-law distributions, are prevalent in a multitude of real-world networks, ranging from social networks to citation networks and protein–protein interaction networks. Rece...
In radar target detection, constant false alarm rate (CFAR), which stands for the adaptive threshold adjustment with variation of clutter to maintain the constant probability of false alarm during the detection, plays an important role. Matrix CFAR d...
The Riemannian manifold optimization algorithms have been widely used in machine learning, computer vision, data mining, and other technical fields. Most of these algorithms are based on the geodesic or the retracement operator and use the classical...
Manifold learning tries to find low-dimensional manifolds on high-dimensional data. It is useful to omit redundant data from input. Linear manifold learning algorithms have applicability for out-of-sample data, in which they are fast and practical es...
Non-negative Matrix Factorization (NMF) has gained popularity due to its effectiveness in clustering and feature selection tasks. It is particularly valuable for managing high-dimensional data by reducing dimensionality and providing meaningful seman...
We develop novel multivariate state-space models wherein the latent states evolve on the Stiefel manifold and follow a conditional matrix Langevin distribution. The latent states correspond to time-varying reduced rank parameter matrices, like the lo...
Machine learning has been applied in continuous-variable quantum key distribution (CVQKD) systems to address the growing threat of quantum hacking attacks. However, the use of machine learning algorithms for detecting these attacks has uncovered a vu...
A direction of arrival (DOA) estimator for two-dimensional (2D) incoherently distributed (ID) sources is presented under proposed double cross arrays, satisfying both the small interval of parallel linear arrays and the aperture equalization in the e...
This paper proposes a compressive-sensing (CS) acquisition algorithm for low-power, high-dynamic GNSS receivers based on low-dimensional time-domain measurements, a non-iterative compressive-domain direct-projection peak-search pipeline, and a cohere...
Recently, we have witnessed an explosive growth in both the quantity and dimension of data generated, which aggravates the high dimensionality challenge in tasks such as predictive modeling and decision support. Up to now, a large amount of unsupervi...
The exponential growth of patent datasets poses a significant challenge in filtering relevant documents for research and innovation. Traditional semantic search methods based on keywords often fail to capture the complexity and variability in multidi...
Antenna arrays are used for signal processing in sonar and radar direction of arrival (DOA) estimation. The well-known array geometries used in DOA estimation are uniform linear array (ULA), uniform circular array (UCA), and rectangular grid array (R...
Results from the theory of the generalized hypergeometric functions of matrix argument, and the related zonal polynomials, are used to develop a new approach to study the asymptotic distributions of linear functions of uniformly distributed random ma...
Falls are one of the most critical health care risks for elderly people, being, in some adverse circumstances, an indirect cause of death. Furthermore, demographic forecasts for the future show a growing elderly population worldwide. In this context,...
We study the Hilbert geometry induced by the Siegel disk domain, an open-bounded convex set of complex square matrices of operator norm strictly less than one. This Hilbert geometry yields a generalization of the Klein disk model of hyperbolic geomet...
Electrocardiograms (ECG) analysis is one of the most important ways to diagnose heart disease. This paper proposes an efficient ECG classification method based on Wasserstein scalar curvature to comprehend the connection between heart disease and the...
We present a simple method to approximate the Fisher–Rao distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating the Fisher–Rao distances between successive nearby nor...
This paper presents a new approach to integral sliding mode control for discrete nonlinear systems with time delay. The approach is based on an event-triggered scheme and is applied to Takagi–Sugeno fuzzy models. In the first step, a new integr...
Hyperspectral unmixing, which decomposes mixed pixels into endmembers and corresponding abundance maps of endmembers, has obtained much attention in recent decades. Most spectral unmixing algorithms based on non-negative matrix factorization (NMF) do...
Symmetric positive definite (SPD) data have become a hot topic in machine learning. Instead of a linear Euclidean space, SPD data generally lie on a nonlinear Riemannian manifold. To get over the problems caused by the high data dimensionality, dimen...
Hyperspectral images (HSI) possess abundant spectral bands and rich spatial information, which can be utilized to discriminate different types of land cover. However, the high dimensional characteristics of spatial-spectral information commonly cause...
We discuss the use of the Newton method in the computation of max(p → Εp [f]), where p belongs to a statistical exponential family on a finite state space. In a number of papers, the authors have applied first order search methods based on informatio...
Accurate localization of robots in unstructured environments poses challenges due to low localization accuracy and local trajectory oscillation caused by complex feature points when using Euclidean-based filtering methods. In this study, we propose a...
In special relativity, particle trajectories, whether mass-bearing or not, can be traced on the Minkowski spacetime manifold in (3+1)D. Meantime, in quantum mechanics, trajectories in the phase space are not strictly outlined because coordinate and l...
In brain–computer interface (BCI)-based motor imagery, the symmetric positive definite (SPD) covariance matrices of electroencephalogram (EEG) signals with discriminative information features lie on a Riemannian manifold, which is currently att...
The vibration signal of rotating machinery is usually nonlinear and non-stationary, and the feature set has information redundancy. Therefore, a high-dimensional feature reduction method based on multi-manifold learning is proposed for rotating machi...
Synthetic Aperture Rradar (SAR) provides rich ground information for remote sensing survey and can be used all time and in all weather conditions. Polarimetric SAR (PolSAR) can further reveal surface scattering difference and improve radar’s ap...
The extraction of a valuable set of features and the design of a discriminative classifier are crucial for target recognition in SAR image. Although various features and classifiers have been proposed over the years, target recognition under extended...
Due to the spectral complexity and high dimensionality of hyperspectral images (HSIs), the processing of HSIs is susceptible to the curse of dimensionality. In addition, the classification results of ground truth are not ideal. To overcome the proble...
In remote sensing, hyperspectral and polarimetric synthetic aperture radar (PolSAR) images are the two most versatile data sources for a wide range of applications such as land use land cover classification. However, the fusion of these two data sour...
The symmetric positive definite (SPD) matrix has attracted much attention in classification problems because of its remarkable performance, which is due to the underlying structure of the Riemannian manifold with non-negative curvature as well as the...
Deep neural networks are vulnerable and susceptible to adversarial examples, which can induce erroneous predictions by injecting imperceptible perturbations. Transferability is a crucial property of adversarial examples, enabling effective attacks un...
The matrix information geometric signal detection (MIGSD) method has achieved satisfactory performance in many contexts of signal processing. However, this method involves many matrix exponential, logarithmic, and inverse operations, which result in...
Estimating the state of a system by fusing sensor data is a major prerequisite in many applications. When the state is time-variant, derivatives of the Kalman filter are a popular choice for solving that task. Two variants are the square-root unscent...
A denoising algorithm was proposed for point cloud with high-density noise. The algorithm utilized geometric metrics on the statistical manifold and applied the idea of clustering K-means based on local statistical characteristics between noise and v...
Semi-supervised non-negative matrix factorization (NMF) has achieved successful results due to the significant ability of image recognition by a small quantity of labeled information. However, there still exist problems to be solved such as the inter...
Clustering plays a crucial role in data mining and knowledge discovery, where non-negative matrix factorization (NMF) has attracted widespread attention due to its effective data representation and dimensionality reduction capabilities. However, stan...
Due to the high dimensionality and high data redundancy of hyperspectral remote sensing images, it is difficult to maintain the nonlinear structural relationship in the dimensionality reduction representation of hyperspectral data. In this paper, a f...
Information geometric optimization (IGO) is a general framework for stochastic optimization problems aiming at limiting the influence of arbitrary parametrization choices: the initial problem is transformed into the optimization of a smooth function...
The problem of attitude estimation is broadly addressed using the Kalman filter formalism and unit quaternions to represent attitudes. This paper is also included in this framework, but introduces a new viewpoint from which the notions of “mult...
In this paper, a novel signal detector based on matrix information geometric dimensionality reduction (DR) is proposed, which is inspired from spectrogram processing. By short time Fourier transform (STFT), the received data are represented as a 2-D...
Features play an important role in the learning technologies and pattern recognition methods for polarimetric synthetic aperture (PolSAR) image interpretation. In this paper, based on the subspace clustering algorithms, we combine sparse representati...
In this study, theorems and proofs related to spherical and focal curves are presented in the BCV-Sasakian space. An approximate solution to the differential equation characterizing spherical curves in the BCV-Sasakian manifold
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