Vector Covariance Research Articles

Data-adaptive binary classifiers in high dimensions using random partitioning

Classification in high dimensions has been highlighted for the past two decades since Fisher's linear discriminant analysis (LDA) is not optimal in a smaller sample size n comparing the number of covariates p, i.e. p>n, which is mostly due to the singularity of the sample covariance matrix. Rather than modifying how to estimate the sample covariance and sample mean vector in constructing a classifier, we build two types of high-dimensional classifiers using data splitting, i.e. single data splitting (SDS) and multiple data splitting (MDS). Moreover, we introduce a weighted version of MDS classifier that improves classification performance as illustrated in numerical studies. Each of the split data sets has a smaller size of covariates compared to the sample size so that LDA is applicable, and classification results can be combined with respect to minimizing the misclassification rate. We present theoretical justification backing up our proposed methods by comparing misclassification rates with LDA in high dimension. We also conduct a wide range of simulations and analyse four microarray data sets, which demonstrates that our proposed methods outperform some existing methods or at least yield comparable performances.

Advanced Defect Detection in Wrap Film Products: A Hybrid Approach with Convolutional Neural Networks and One-Class Support Vector Machines with Variational Autoencoder-Derived Covariance Vectors

This study proposes a novel approach that utilizes Convolutional Neural Networks (CNNs) and Support Vector Machines (SVMs) to tackle a critical challenge: detecting defects in wrapped film products. With their delicate and reflective film wound around a core material, these products present formidable hurdles for conventional visual inspection systems. The complex task of identifying defects, such as unwound or protruding areas, remains a daunting endeavor. Despite the power of commercial image recognition systems, they struggle to capture anomalies within wrap film products. Our research methodology achieved a 90% defect detection accuracy, establishing its practical significance compared with existing methods. We introduce a pioneering methodology centered on covariance vectors extracted from latent variables, a product of a Variational Autoencoder (VAE). These covariance vectors serve as feature vectors for training a specialized One-Class SVM (OCSVM), a key component of our approach. Unlike conventional practices, our OCSVM does not require images containing defects for training; it uses defect-free images, thus circumventing the challenge of acquiring sufficient defect samples. We compare our methodology against feature vectors derived from the fully connected layers of established CNN models, AlexNet and VGG19, offering a comprehensive benchmarking perspective. Our research represents a significant advancement in defect detection technology. By harnessing the latent variable covariance vectors from a VAE encoder, our approach provides a unique solution to the challenges faced by commercial image recognition systems. These advancements in our study have the potential to revolutionize quality control mechanisms within manufacturing industries, offering a brighter future for product integrity and customer satisfaction.

A Bayesian convolutional neural network-based generalized linear model.

Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical models in prediction accuracy, statistical inference, such as estimating the effects of covariates and quantifying the prediction uncertainty, is not trivial due to the highly complicated model structure and overparameterization. To address this challenge, we propose a new Bayesian approach by embedding CNNs within the generalized linear models (GLMs) framework. We use extracted nodes from the last hidden layer of CNN with Monte Carlo (MC) dropout as informative covariates in GLM. This improves accuracy in prediction and regression coefficient inference, allowing for the interpretation of coefficients and uncertainty quantification. By fitting ensemble GLMs across multiple realizations from MC dropout, we can account for uncertainties in extracting the features. We apply our methods to biological and epidemiological problems, which have both high-dimensional correlated inputs and vector covariates. Specifically, we consider malaria incidence data, brain tumor image data, and fMRI data. By extracting information from correlated inputs, the proposed method can provide an interpretable Bayesian analysis. The algorithm can be broadly applicable to image regressions or correlated data analysis by enabling accurate Bayesian inference quickly.

Joint design of transmit precoding and antenna selection for multi-user multi-target MIMO DFRC

Dual-function radar and communications (DFRC) systems based on multiple-input multiple-output (MIMO) arrays have received considerable attention in recent years due to their excellent ability to alleviate spectrum congestion. The MIMO DFRC systems enable high-resolution detection of multiple targets while communicating with multiple users simultaneously. However, MIMO arrays require numerous radio frequency (RF) units and suffer a strong mutual coupling among antennas, resulting in significant system overhead and performance degradation, respectively. In light of this, this paper investigates the joint optimization of transmit precoding and antenna selection for MIMO DFRC systems, aiming to improve the angular ambiguity function with a guaranteed communication quality of service (QoS) using a small number of antennas. To address the resultant non-convex optimization problem, both the indirect and direct precoding methods are proposed. In the former, the waveform covariance and antenna selection vector are first jointly optimized via a promoted sparsity along the covariance diagonal, followed by the precoding matrix indirectly derived from the optimal covariance. In the latter, the precoding matrix is directly optimized via an imposed group sparsity under the communication QoS and power constraints. Simulation results demonstrate that the proposed sparse MIMO DFRC system with fewer active antennas can achieve comparable dual-functional performance to that of the full array system.

Robust Off-Grid DOA Estimation for Noncircular Signals With Virtual SDCA

In this letter, a robust off-grid direction of arrival estimation algorithm based on sum-difference co-array (SDCA) under nonuniform noise environment is proposed for noncircular signals. The proposed method combines the coprime array (CA)’s features with those of noncircular signals, and it is further expanded to produce an SDCA with a larger array aperture. The off-grid data model is obtained after the spatial discretization. And the variational signal model is reconstructed by using the covariance vector with nonuniform noise. And then, the grid refine process based on the expanded covariance vector model is derived, which enables high-resolution DOA estimation. The proposed method can realize underdetermined DOA estimation with small physical array elements. Numerous simulations are run to make sure the suggested strategy is reliable and strong in nonuniform noise environments.

Polarization Domain Spectrum Sensing Algorithm Based on AlexNet.

In this paper, we propose a spectrum sensing algorithm based on the Jones vector covariance matrix (JCM) and AlexNet model, i.e., the JCM-AlexNet algorithm, by taking advantage of the different state characteristics of the signal and noise in the polarization domain. We use the AlexNet model, which is good at extracting matrix features, as the classification model and use the Jones vector, which characterizes the polarization state, to calculate its covariance matrix and convert it into an image and then use it as the input to the AlexNet model. Then, we calculate the likelihood ratio test statistic (AlexNet-LRT) based on the output of the model to achieve the classification of the signal and noise. The simulation analysis shows that the JCM-AlexNet algorithm performs better than the conventional polarization detection (PSD) algorithm and the other three (LeNet5, long short-term memory (LSTM), multilayer perceptron (MLP)) excellent deep-learning-based spectrum sensing algorithms for different signal-to-noise ratios and different false alarm probabilities.

An efficient numerical representation of genome sequence: natural vector with covariance component.

BackgroundThe characterization and comparison of microbial sequences, including archaea, bacteria, viruses and fungi, are very important to understand their evolutionary origin and the population relationship. Most methods are limited by the sequence length and lack of generality. The purpose of this study is to propose a general characterization method, and to study the classification and phylogeny of the existing datasets.MethodsWe present a new alignment-free method to represent and compare biological sequences. By adding the covariance between each two nucleotides, the new 18-dimensional natural vector successfully describes 24,250 genomic sequences and 95,542 DNA barcode sequences. The new numerical representation is used to study the classification and phylogenetic relationship of microbial sequences.ResultsFirst, the classification results validate that the six-dimensional covariance vector is necessary to characterize sequences. Then, the 18-dimensional natural vector is further used to conduct the similarity relationship between giant virus and archaea, bacteria, other viruses. The nearest distance calculation results reflect that the giant viruses are closer to bacteria in distribution of four nucleotides. The phylogenetic relationships of the three representative families, Mimiviridae, Pandoraviridae and Marsellieviridae from giant viruses are analyzed. The trees show that ten sequences of Mimiviridae are clustered with Pandoraviridae, and Mimiviridae is closer to the root of the tree than Marsellieviridae. The new developed alignment-free method can be computed very fast, which provides an effective numerical representation for the sequence of microorganisms.

A novel variational SBL approach for off-grid DOA detection under nonuniform noise

In this paper, a novel variational sparse Bayesian learning (SBL) approach is proposed for off-grid direction of arrival (DOA) estimation in the presence of nonuniform noise. In the proposed approach, a variational off-grid sparse model over the array covariance vector is first constructed, where the nonuniform noise covariance is modeled into a variational signal vector. At the same time, the grid refining procedure based on the variational off-grid sparse model is re-derived for reducing off-grid error, in which the spatial grid points are linear approximated and iteratively updated. Benefit from the constructed variational off-grid sparse model, the proposed approach does not require a separate estimation for the nonuniform noise variance. Numerous simulation experiments illustrate that the proposed approach has strong robustness to both off-grid error and nonuniform noise, and has superior performance on DOA detection with nonuniform noise.

Intrinsic Riemannian functional data analysis for sparse longitudinal observations

A new framework is developed to intrinsically analyze sparsely observed Riemannian functional data. It features four innovative components: a frame-independent covariance function, a smooth vector bundle termed covariance vector bundle, a parallel transport and a smooth bundle metric on the covariance vector bundle. The introduced intrinsic covariance function links estimation of covariance structure to smoothing problems that involve raw covariance observations derived from sparsely observed Riemannian functional data, while the covariance vector bundle provides a rigorous mathematical foundation for formulating such smoothing problems. The parallel transport and the bundle metric together make it possible to measure fidelity of fit to the covariance function. They also play a critical role in quantifying the quality of estimators for the covariance function. As an illustration, based on the proposed framework, we develop a local linear smoothing estimator for the covariance function, analyze its theoretical properties and provide numerical demonstration via simulated and real data sets. The intrinsic feature of the framework makes it applicable to not only Euclidean submanifolds but also manifolds without a canonical ambient space.

Real-time estimation of roll angles by magnetometer based on two-step adaptive Kalman filter

The geomagnetic field vector information is critical to the navigation and positioning in the magnetic measurement of satellites, ships, and aircraft, however, suffers from the internal inherent error and the internal error interfering magnetic fields. Most real-time geomagnetic correction algorithms based on the specific ellipsoid fitting typically lead to the difficulty in real-time acquisition of the attitude roll angle of the projectile and the estimation accuracy. Herein, we propose a novel real-time estimation algorithm based on Magnetometer measurement involved two-step adaptive Kalman filter. The first-step adaptive Kalman filter algorithm is proposed for online error compensation of the magnetometer by using the error model and ellipsoid model of the magnetometer. The robust estimation theory is proposed to apply to the first-step adaptive Kalman filtering for ellipsoid fitting. The capability of preprocessing data and the adaptive observation vector's covariance matrix enable the real-time separation and correction of outliers. In addition, a vector-dot product invariant method is proposed to estimate the 12 coefficients in the magnetometer error model, solving the problem that the traditional method cannot ultimately determine the coefficients of the error matrix. Furthermore, the second-step adaptive Kalman is utilized to adaptively real-time estimate the roll angle. In particular, the results of the simulations and experiments show that the algorithm's parameters tend to be stable, beginning since 3 s for the data collection; and the accuracy range of the roll angle is boost to between ±0.4°. Moreover, the error parameters of the magnetometer are fully calibrated, and the estimation accuracy of roll angle is improved by 1/2 with regard to that of conventional methods. The results demonstrate the capability of compensating for the random magnetic field error caused by the motor. The results show that the two-step adaptive Kalman filter algorithm can reduce the estimation error of roll angle and could be extended to practical engineering applications.

Cox Point Process Regression

Point processes in time have a wide range of applications that include the claims arrival process in insurance or the analysis of queues in operations research. Due to advances in technology, such samples of point processes are increasingly encountered. A key object of interest is the local intensity function. It has a straightforward interpretation that allows to understand and explore point process data. We consider functional approaches for point processes, where one has a sample of repeated realizations of the point process. This situation is inherently connected with Cox processes, where the intensity functions of the replications are modeled as random functions. Here we study a situation where one records covariates for each replication of the process, such as the daily temperature for bike rentals. For modeling point processes as responses with vector covariates as predictors we propose a novel regression approach for the intensity function that is intrinsically nonparametric. While the intensity function of a point process that is only observed once on a fixed domain cannot be identified, we show how covariates and repeated observations of the process can be utilized to make consistent estimation possible, and we also derive asymptotic rates of convergence without invoking parametric assumptions.

A parametric framework for multidimensional linear measurement error regression.

The ordinary linear regression method is limited to bivariate data because it is based on the Cartesian representation y = f(x). Using the chain rule, we transform the method to the parametric representation (x(t), y(t)) and obtain a linear regression framework in which the weighted average is used as a parameter for a multivariate linear relation for a set of linearly related variable vectors (LRVVs). We confirm the proposed approach by a Monte Carlo simulation, where the minimum coefficient of variation for error (CVE) provides the optimal weights when forming a weighted average of LRVVs. Then, we describe a parametric linear regression (PLR) algorithm in which the Moore-Penrose pseudoinverse is used to estimate measurement error regression (MER) parameters individually for the given variable vectors. We demonstrate that MER parameters from the PLR and nonlinear ODRPACK methods are quite similar for a wide range of reliability ratios, but ODRPACK is formulated only for bivariate data. We identify scale invariant quantities for the PLR and weighted orthogonal regression (WOR) methods and their correspondences with the partitioned residual effects between the variable vectors. Thus, the specification of an error model for the data is essential for MER and we discuss the use of Monte Carlo methods for estimating the distributions and confidence intervals for MER slope and correlation coefficient. We distinguish between elementary covariance for the y = f(x) representation and covariance vector for the (x(t), y(t)) representation. We also discuss the multivariate generalization of the Pearson correlation as the contraction between Cartesian polyad alignment tensors for the LRVVs and weighted average. Finally, we demonstrate the use of multidimensional PLR in estimating the MER parameters for replicate RNA-Seq data and quadratic regression for estimating the parameters of the conical dispersion of read count data about the MER line.

Neural network-aided sparse convex optimization algorithm for fast DOA estimation

In this paper, a fast sparse convex optimization algorithm based on a neural network is proposed to improve the direction of arrival estimation. First, a fast [Formula: see text]-sparse representation of the array covariance vector model based on the Hermitian Toeplitz structure of array covariance is established to reduce computational complexity in data dimension and variable number. Then, the estimation error upper bound problem is investigated, and a neural network-aided coefficient selection method is developed. The direction of arrival estimation problem is solved through spectral peak search. Finally, the algorithm is extended to the case of off-grid error. The algorithm’s advantages in accuracy, calculation speed and robustness is verified by the simulations.

RxCV-based unitary SBL algorithm for off-grid DOA estimation with MIMO radar in unknown non-uniform noise

As an indispensable part of array signal processing, direction-of-arrival (DOA) estimation has been well investigated over the past few decades, and many excellent DOA estimation methods have been proposed. In this paper, a receiving domain covariance vector (RxCV) based unitary SBL algorithm is proposed for the off-grid DOA estimation of monostatic multiple-input multiple-output (MIMO) radar in unknown non-uniform noise environment. In the proposed algorithm, the data received by MIMO radar is firstly transformed into receiving domain by a reshape operation. Then the RxCV-based unitary off-grid sparse model without non-uniform noise is constructed through unitary transformation and first-order linear approximation, where the unknown non-uniform noise is got rid off by a linear transformation. Based on the RxCV-based unitary off-grid sparse model, the sparse Bayesian learning (SBL) criterion is adopted to estimate the parameters, where signal variance and off-gird error are estimated by using expectation-maximization (EM) strategy. The DOA estimation is ultimately realized through 1-dimensional spectrum search of the received data. Results of the simulation experiments have provided the evidence of that the proposed algorithm is robustness against nonuniform noise and off-grid error, and it can maintain superior DOA estimation performance compared with other reported sparse signal representation based methods.

Acceptance Criteria of Bearings-only Passive Target Tracking Solution

In passive target tracking, target motion parameters (TMP) i.e. range, course, and speed are estimated using bearing measurements. In the simulation mode, the accuracy of the estimated solution can be calculated, as true values are available. In the actual scenario, the true values of TMP are not readily obtainable. In this research, the focus is laid on the evolution of the acceptance criterion of the TMP in the actual scenario. Detailed mathematical modeling is carried out and an unscented Kalman filter (UKF) is used to estimate TMP. The state vector covariance matrix of UKF is utilized to express the errors in estimated TMP and an acceptance criterion is derived in terms of the standard deviation of errors in estimated TMP. Submarine to submarine tracking is carried out and scenarios are chosen accordingly. Several low angle on target bow (ATB) scenarios are used in the Monte-Carlo simulation and the results are presented. A similar procedure can be carried out for medium and high ATB scenarios and a submarine to ship or vice-versa passive target tracking.

Point process models for COVID-19 cases and deaths

The study of events distributed over time which can be quantified as point processes has attracted much interest over the years due to its wide range of applications. It has recently gained new relevance due to the COVID-19 case and death processes associated with SARS-CoV-2 that characterize the COVID-19 pandemic and are observed across different countries. It is of interest to study the behavior of these point processes and how they may be related to covariates such as mobility restrictions, gross domestic product per capita, and fraction of population of older age. As infections and deaths in a region are intrinsically events that arrive at random times, a point process approach is natural for this setting. We adopt techniques for conditional functional point processes that target point processes as responses with vector covariates as predictors, to study the interaction and optimal transport between case and death processes and doubling times conditional on covariates.

Robust and Fast Super-Resolution SAR Tomography of Forests Based on Covariance Vector Sparse Bayesian Learning

A novel method based on covariance vector sparse Bayesian learning (CV-SBL) is proposed in this letter to reconstruct the vertical structure of forests using a small number of synthetic aperture radar (SAR) images. This method regards the inversion of forests reflectivity profiles in the wavelet domain as a sparse signal reconstruction (SSR). Based on the covariance matrix matching criterion, the backscatter power of forests signal and noise will be jointly solved adaptively. Through a few iterations, the exact positions of the closely spaced phase centers can be obtained to simplify the characterization of the vertical structure of the forests. Unlike the traditional compressive sensing (CS) method based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1} $ </tex-math></inline-formula> norm convex optimization, the novel method can obtain a real sparse solution without setting hyper-parameters and has a more reliable and accurate reconstruction performance. Besides, the computational efficiency of the new method is much higher than that of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1} $ </tex-math></inline-formula> minimization CS method, and it is more suitable for large-scale forests mapping applications. The proposed method is validated using P-band TropiSAR 2009 data set over a test site in Paracou, French Guiana. Furthermore, the reconstruction performance of the proposed method is compared with the spectral analysis methods (Beamforming and Capon) and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1} $ </tex-math></inline-formula> minimization super-resolution CS.

Adaptive Kalman filtering for closed-loop systems based on the observation vector covariance

ABSTRACT The Kalman filter is one of the most widely used methods for state estimation and control purposes. However, it requires correct knowledge of noise statistics, which are unknown or not known perfectly in real-life applications and then they need to be identified. Considering such background, this paper introduces a new adaptive Kalman filter algorithm in order to handle the unknown process noise covariance for linear discrete-time closed-loop systems. From the closed-loop joint analysis of the system and the a priori recursive form of the Kalman filter, we adaptively estimate the process noise covariance by relating it to the observation vector covariance. The latter is then obtained from an exponential moving average technique. Lastly, we also extend our adaptive methodology for a special class of nonlinear systems. The performance of the proposed adaptive method is demonstrated through numerical examples and it has been compared to other types of adaptive filtering algorithms.

Fast Underdetermined DOA Estimation Based on Generalized MRA via Original Covariance Vector Sparse Reconstruction

Minimum redundancy array (MRA) has the maximum aperture with continuous difference co-array among various sparse arrays with same number of physical sensors, but it is hard to calculate the sensor position of MRA and realize array design by using MRA. To solve those problem, generalized MRA is proposed with mutual coupling limitation and easy calculation method of sensor position. Based on proposed array configuration, a high-precision underdetermined direction of arrival (DOA) estimation method is proposed with reduced computational complexity. In this method, fast covariance matrix reconstruction is achieved by trace norm minimization with more accurate covariance estimation. Based on the Toeplitz property of covariance matrix in uniform array, a new sparse representation model is established with reduced dimension of covariance vector and faster DOA estimation is achieved via convex optimization. In addition, the proposed method can also be used for underdetermined DOA estimation of other sparse arrays. Using simulation experiments, we demonstrate that the proposed sparse array configuration has superiority over other sparse arrays and the proposed method can outperform most existing methods in terms of underdetermined DOA estimation accuracy and efficiency.

Vehicle re-identification based on unsupervised local area detection and view discrimination

Vehicle re-identification is an important part of intelligent transportation. Although much work has been done on this subject in recent years, vehicle re-identification is still a challenging task due to its obvious illumination change, high similarity between inter-class and great changes under different views. As discriminatory local areas and vehicle view information is the key to improving the above issues, it is desirable to create a model which considers both local details and cross-view situation. In this paper, we built a vehicle re-identification framework based on unsupervised local area detection and view discrimination. First, we combine the convolution features of multiple vehicle images by channel to generate joint channel features, and constructs a discriminating region detector unsupervised by clustering the channel covariance vectors generated between the joint channel features. In the next stage, the irregular shape detection results are converted to rectangular discriminative region by using a novel local region integration algorithm. These rectangular discriminative regions are fed into a multi-branch network to extract the local–global features which contains rich detail information. Furthermore, we generate the view features by regarding the detected discriminative areas as keypoints and construct the unsupervised view discriminator. By using the view information of the vehicle, we designed a view-discrimination based reranking algorithm, which effectively reduces the error rate of identification due to view variant. In order to prove the validity of our method, we have done extensive experiments on VehicleID and VERI-Wild dataset. Experimental results show that our method is superior to other existing vehicle re-identification algorithms.