Coefficient Vector Research Articles

Pattern-Reconfigurable Sparse Linear Array Synthesis Under Minimum Element Spacing Control by Alternating Sequential Quadratic Programming

A new method called alternating sequential quadratic programming (ASQP) is proposed to synthesize pattern-reconfigurable sparse linear arrays with minimum element spacing control. The method can find the common element positions and multiple sets of excitations for generating multiple reconfigurable patterns which accurately meet their given upper and lower pattern bounds. In addition, by introducing auxiliary weighting coefficients and collective excitation coefficient vectors and choosing them as optimization variables alternately, the proposed method can appropriately incorporate the minimum element spacing constraint into the pattern synthesis. Synthesized results show that the proposed method can give satisfactory reconfigurable pattern performance but save much more elements compared with some existing methods.

PLS1-MD: A partial least squares regression algorithm for solving missing data problems

In this article, we propose a methodology that modifies the partial least squares (PLS) regression algorithm. Certain steps of the algorithm are adjusted to address the estimation problem in multiple linear regression when there are missing data (MD). The modified algorithm is called PLS1-MD and is based on the available data principle, allowing for multiple regression analysis even when there are missing values in the response or some of the explanatory variables, without the need for imputation. PLS1-MD can be applied under conditions of multicollinearity (where the explanatory variables are correlated, resulting in linear combinations among columns of the design matrix) and high dimensionality (where the number of individuals is less than the number of variables). The PLS1-MD algorithm ensures orthogonality, orthonormality of the coefficient vector, and optimality at each stage. The procedure is illustrated using the Cornell and Yarn datasets, which are widely known in the context of PLS1 regression. For this purpose, 10% of the data is randomly deleted and labeled as MD. The results indicate that the estimates obtained with the PLS1-MD algorithm are very similar to those generated when applying PLS1 to the set of observations with no MD. This new algorithm does not require imputing missing values, thus preserving the properties of centrality and orthogonality. We compare the results obtained using our approach with those obtained using the R libraries named pls and plsdepot. Under the scenario of no MD, we obtain the same results. In the presence of MD, the library pls cannot be used and only plsdepot solves the problem when there are MD in the explanatory variables.

Tail-dependence, exceedance sets, and metric embeddings

There are many ways of measuring and modeling tail-dependence in random vectors: from the general framework of multivariate regular variation and the flexible class of max-stable vectors down to simple and concise summary measures like the matrix of bivariate tail-dependence coefficients. This paper starts by providing a review of existing results from a unifying perspective, which highlights connections between extreme value theory and the theory of cuts and metrics. Our approach leads to some new findings in both areas with some applications to current topics in risk management.We begin by using the framework of multivariate regular variation to show that extremal coefficients, or equivalently, the higher-order tail-dependence coefficients of a random vector can simply be understood in terms of random exceedance sets, which allows us to extend the notion of Bernoulli compatibility. In the special but important case of bivariate tail-dependence, we establish a correspondence between tail-dependence matrices and L^1- and ell _1-embeddable finite metric spaces via the spectral distance, which is a metric on the space of jointly 1-Fréchet random variables. Namely, the coefficients of the cut-decomposition of the spectral distance and of the Tawn-Molchanov max-stable model realizing the corresponding bivariate extremal dependence coincide. We show that line metrics are rigid and if the spectral distance corresponds to a line metric, the higher order tail-dependence is determined by the bivariate tail-dependence matrix.Finally, the correspondence between ell _1-embeddable metric spaces and tail-dependence matrices allows us to revisit the realizability problem, i.e. checking whether a given matrix is a valid tail-dependence matrix. We confirm a conjecture of Shyamalkumar and Tao (2020) that this problem is NP-complete.

Optimal coefficient selection in Compute and Forward relaying using improved Schnorr–Euchner search algorithm

Physical layer Network Coding with Compute and Forward relaying (CF) is a promising transmission strategy that effectively exploits the natural linear computation of the multiuser wireless channel. In CF relaying, the relay nodes receive a linear combination of transmitted signals with additive noise and each relay node computes an integer linear combination of transmitted codewords which are then forwarded to the destination. After receiving enough independent equations from multiple relay nodes, the destination could decode individual source nodes’ messages. The source nodes use nested lattice codes which have the property that an integer linear combination of codewords is a valid codeword in the codeset. The simulation set up includes a K×K×1 network model with K source nodes, K relay nodes and 1 destination node. Relay nodes are assumed to have perfect channel state information, which is used in computing the linear equation. The success of CF relaying lies in choosing the optimal coefficient in computing the independent linear equation at each relay node. Optimal coefficient selection aims to maximize the computation rate which can be achieved when the equation coefficients are matched with complex-valued channel gains. This paper proposes an iterative algorithm for finding the optimal coefficient vector in the Gaussian integer domain using an improved Schnorr–Euchner search strategy. The performance of the proposed coefficient search algorithm in terms of computation complexity and the achievable rate is compared with other existing algorithms through MATLAB simulation. Simulation is performed for networks with 2, 4, 8 and 16 numbers of source and relay nodes. The proposed coefficient selection algorithm is validated for varying Signal to Noise Power under Rayleigh fading channel environment.

Research on high‐precision synchronous output technology of multi‐reference source weighted synthesis in power system

AbstractThe massive perception data based on efficient analysis and intelligent decision have put forward higher requirements for high‐precision time synchronisation with the construction and development of smart power grid. However, multi‐reference source time‐frequency synchronisation of power system only selects the best method after comparison, which cannot make the most efficient use of the existing resources. It also cannot meet the need for high‐precision time synchronisation of future power system. The existing multi‐reference source synthesis algorithms cannot take into account both long‐term stability and high‐precision synchronous output. This article presents a multi‐reference source weighted improved noise model and the high‐precision output method. The multi‐reference source error after classification is eliminated by leading into classification vector and classification coefficient. The synthesised frequency offset or the time precision of output can be optimised as the objective function by weighted classification algorithm and genetic algorithm. A simulation example based on the synthesis of two satellite system clock sources and three local caesium reference sources shows that the peak value of long‐term output accuracy is controlled within 10 ns after classification weighted synthesis and optimisation, which is better than that of any single reference source.

DOA Estimation for Multiple Speech Sources Based on Flexible Single-Source Zones and Concentration Weighting

Direction of arrival (DOA) estimation is the key to many audio applications. Recently, sparse component analysis (SCA)-based methods have attracted much attention, in which single-source points (SSPs) and single-source zones (SSZs) where one source is dominant over the others in time-frequency domain are usually detected to construct the pooled histogram containing multi-source DOA information. Nonetheless, the SSZ size in existing methods is fixed and empirically predetermined, which cannot accommodate to the varying spectro-temporal property of speech sources. Furthermore, higher SSP concentration in a SSZ implies a locally stronger dominant source as well as more reliable DOA information extracted therein, which however is also not taken into account yet. To address these problems, a DOA estimation algorithm for multiple speech sources based on flexible SSZs and concentration weighting is presented in this paper. First, in each frame, correlation coefficients of time delay vectors across adjacent frequency bins are calculated to identify SSPs, followed by flexible SSZs construction using varying number of SSPs located at consecutive frequency bins. Next, the number of SSPs in each flexible SSZ is considered as a proxy of corresponding concentration degree, and employed as weighting factor to form the pooled histogram. Finally, a matching pursuit (MP)-based approach is utilized to obtain multi-source DOA estimates. Simulation results reveal that the proposed method significantly outperforms existing approaches in terms of noise floor in pooled histogram, angular resolution, and performance under various signal-to-noise ratio and reverberant conditions. Real-world experiments also verify its effectiveness, and meanwhile demonstrate considerably reduced computational complexity.

Multiple multi-sample testing under arbitrary covariance dependency.

Modern high-throughput biomedical devices routinely produce data on a large scale, and the analysis of high-dimensional datasets has become commonplace in biomedical studies. However, given thousands or tens of thousands of measured variables in these datasets, extracting meaningful features poses a challenge. In this article, we propose a procedure to evaluate the strength of the associations between a nominal (categorical) response variable and multiple features simultaneously. Specifically, we propose a framework of large-scale multiple testing under arbitrary correlation dependency among test statistics. First, marginal multinomial regressions are performed for each feature individually. Second, we use an approach of multiple marginal models for each baseline-category pair to establish asymptotic joint normality of the stacked vector of the marginal multinomial regression coefficients. Third, we estimate the (limiting) covariance matrix between the estimated coefficients from all marginal models. Finally, our approach approximates the realized false discovery proportion of a thresholding procedure for the marginal p-values for each baseline-category logit pair. The proposed approach offers a sensible trade-off between the expected numbers of true and false findings. Furthermore, we demonstrate a practical application of the method on hyperspectral imaging data. This dataset is obtained by a matrix-assisted laser desorption/ionization (MALDI) instrument. MALDI demonstrates tremendous potential for clinical diagnosis, particularly for cancer research. In our application, the nominal response categories represent cancer (sub-)types.

Reduced-order state-space models for two-dimensional discrete systems via bivariate discrete orthogonal polynomials

This paper investigates the new model order reduction (MOR) methods via bivariate discrete orthogonal polynomials for two-dimensional (2-D) discrete systems. The 2-D discrete system is described by the Kurek model. First, we deduce algebraically the shift-transformation matrix of the classical discrete orthogonal polynomials of one variable. By means of the shift-transformation matrices, 2-D discrete systems are expanded in the spaces spanned by bivariate discrete orthogonal polynomials. The coefficient matrices are calculated from matrix equations. Then the reduced-order systems are produced by the orthogonal projection matrices defined by the coefficient matrices. Theoretical analysis shows that the reduced-order systems can match a certain number of coefficient vectors of the original outputs. Finally, one numerical example is simulated to demonstrate the feasibility and effectiveness of the proposed methods.

Selection of Logistics Service Provider for port enterprises: Combination of the weighting-grey synthetic decision-making method

The purpose of this paper is to explore how port enterprises can scientifically select a better logistic service provider (LSP) to achieve a high efficiency. An empirical study is conducted to verify the effectiveness of the combination weighting-grey synthetic decision-making method by helping the LSP selection of a port enterprise in China. Data are collected from questionnaires administered to port logistics’ industry professionals. The method is proposed, which associates the analysis network process method with the entropy method to determine the combined weights of the evaluation indexes. The improved centre-point triangular whitenization weight function is introduced to cluster the alternative port LSPs and judge the corresponding grey classes. Subsequently, the synthetic weighted decision-making vectors are used to determine the grey synthetic decision-making coefficient vectors. The grey synthetic clustering decision-making coefficients are calculated to establish a synthetic decision-making rank of the alternative plans. The combined method can help the port enterprises realize the selection of better LSPs in a scientific manner.

Using support vector machine regression to reduce cloud security risks in developing countries

The use of the cloud by governments throughout the world is being aggressively investigated to increase efficiency and reduce costs. The majority of cloud computing risk management programs prioritize addressing cloud security issues that government organizations may face when they choose to adopt cloud computing systems, but these programs lack evidence of security risks, and problems with using cloud computing in developing nations are uncommon, so they called for more research in this area. The objective of this paper is to use quantitative models namely Spearman's Rank correlation coefficient, simple regression, and support vector machine regression (SVMR) for estimating cloud security issues based on cloud control factors for improving the mitigation of cloud computing security issues based on control factors using intelligent models in a government organization. Identify the proper cloud control factors for every cloud security issue from estimation errors using a standard for performance measurement like mean square error (MSE) and root mean square error (RMSE), performance measurement to evaluate and validate proposed models. SVMR is an approach to enhance practices for cloud security platforms to mitigate risks and infrastructure for cloud adoption in developing countries in this paper.

An Approach to Canonical Correlation Analysis Based on Rényi's Pseudodistances.

Canonical Correlation Analysis (CCA) infers a pairwise linear relationship between two groups of random variables, X and Y. In this paper, we present a new procedure based on Rényi's pseudodistances (RP) aiming to detect linear and non-linear relationships between the two groups. RP canonical analysis (RPCCA) finds canonical coefficient vectors, a and b, by maximizing an RP-based measure. This new family includes the Information Canonical Correlation Analysis (ICCA) as a particular case and extends the method for distances inherently robust against outliers. We provide estimating techniques for RPCCA and show the consistency of the proposed estimated canonical vectors. Further, a permutation test for determining the number of significant pairs of canonical variables is described. The robustness properties of the RPCCA are examined theoretically and empirically through a simulation study, concluding that the RPCCA presents a competitive alternative to ICCA with an added advantage in terms of robustness against outliers and data contamination.

LogBTF: gene regulatory network inference using Boolean threshold network model from single-cell gene expression data.

From a systematic perspective, it is crucial to infer and analyze gene regulatory network (GRN) from high-throughput single-cell RNA sequencing data. However, most existing GRN inference methods mainly focus on the network topology, only few of them consider how to explicitly describe the updated logic rules of regulation in GRNs to obtain their dynamics. Moreover, some inference methods also fail to deal with the over-fitting problem caused by the noise in time series data. In this article, we propose a novel embedded Boolean threshold network method called LogBTF, which effectively infers GRN by integrating regularized logistic regression and Boolean threshold function. First, the continuous gene expression values are converted into Boolean values and the elastic net regression model is adopted to fit the binarized time series data. Then, the estimated regression coefficients are applied to represent the unknown Boolean threshold function of the candidate Boolean threshold network as the dynamical equations. To overcome the multi-collinearity and over-fitting problems, a new and effective approach is designed to optimize the network topology by adding a perturbation design matrix to the input data and thereafter setting sufficiently small elements of the output coefficient vector to zeros. In addition, the cross-validation procedure is implemented into the Boolean threshold network model framework to strengthen the inference capability. Finally, extensive experiments on one simulated Boolean value dataset, dozens of simulation datasets, and three real single-cell RNA sequencing datasets demonstrate that the LogBTF method can infer GRNs from time series data more accurately than some other alternative methods for GRN inference. The source data and code are available at https://github.com/zpliulab/LogBTF.

Off-Grid DOA Estimation Based on Compressed Sensing on Multipath Environment

Due to the existence of multipath propagation, the array will receive the multipath propagation signals at the same time while receiving the target signal and the performance of directional of arrival (DOA) estimation will be influenced. In this paper, an off-grid DOA estimation technique based on compressed sensing (CS) on multipath environment is proposed. To deal with the off-grid problem and the multipath propagation problem, we present a compressed sensing based method. This method regards the multipath propagation coefficients vector as a superparameter and the grid as an adjustable parameter. Then, the problem of multipath propagation coefficients estimation is converted to the estimation of an error matrix and the grid is refined iteratively. The simulation results show that the method can achieve off-grid DOA estimation in the presence of the multipath propagation signals.

PMSSC: Parallelizable multi-subset based self-expressive model for subspace clustering

Subspace clustering methods which embrace a self-expressive model that represents each data point as a linear combination of other data points in the dataset provide powerful unsupervised learning techniques. However, when dealing with large datasets, representation of each data point by referring to all data points via a dictionary suffers from high computational complexity. To alleviate this issue, we introduce a parallelizable multi-subset based self-expressive model (PMS) which represents each data point by combining multiple subsets, with each consisting of only a small proportion of the samples. The adoption of PMS in subspace clustering (PMSSC) leads to computational advantages because the optimization problems decomposed over each subset are small, and can be solved efficiently in parallel. Furthermore, PMSSC is able to combine multiple self-expressive coefficient vectors obtained from subsets, which contributes to an improvement in self-expressiveness. Extensive experiments on synthetic and real-world datasets show the efficiency and effectiveness of our approach in comparison to other methods.

Adaptive group-wise modeling of thermally induced errors of a turning center

Traditional multivariate regression analysis-based thermal error models use only one polynomial of several temperature variables to predict thermal errors, which will produce lower local prediction accuracy for a longer machining process with sudden changes of machining parameters, and hence the group-wise modeling method is proposed in this paper. Resorting to hard break points and soft break points, the grouping work is completed in two steps: hard grouping and soft grouping. The positions of hard break points are optimized using the genetic algorithm toolbox in Matlab software to realize adaptive grouping. The mechanism for updating the thermal error model coefficients vectors for different soft groups is developed. The modeling test is carried out on a turning center for which the positions of thermal key points are optimized. The prediction results for radial and axial thermal errors show that four hard break points can basically meet the requirements at the di value of 80%, so the group-wise modeling method is helpful to advance the prediction accuracy of thermal errors.

Modeling Under-Dispersed Count Data by the Generalized Poisson Distribution via Two New MM Algorithms

Under-dispersed count data often appear in clinical trials, medical studies, demography, actuarial science, ecology, biology, industry and engineering. Although the generalized Poisson (GP) distribution possesses the twin properties of under- and over-dispersion, in the past 50 years, many authors only treat the GP distribution as an alternative to the negative binomial distribution for modeling over-dispersed count data. To our best knowledge, the issues of calculating maximum likelihood estimates (MLEs) of parameters in GP model without covariates and with covariates for the case of under-dispersion were not solved up to now. In this paper, we first develop a new minimization–maximization (MM) algorithm to calculate the MLEs of parameters in the GP distribution with under-dispersion, and then we develop another new MM algorithm to compute the MLEs of the vector of regression coefficients for the GP mean regression model for the case of under-dispersion. Three hypothesis tests (i.e., the likelihood ratio, Wald and score tests) are provided. Some simulations are conducted. The Bangladesh demographic and health surveys dataset is analyzed to illustrate the proposed methods and comparisons with the existing Conway–Maxwell–Poisson regression model are also presented.

WeakIdent: Weak formulation for identifying differential equation using narrow-fit and trimming

Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential terms, the identification problem can be formulated as solving a linear system, with the feature matrix consisting of linear and nonlinear terms multiplied by a coefficient vector. This product is equal to the time derivative term, and thus generates dynamical behaviors. The goal is to identify the correct terms that form the equation to capture the dynamics of the given data. We propose a general and robust framework to recover differential equations using a weak formulation with two new mechanisms, narrow-fit and trimming, for both ordinary and partial differential equations (ODEs and PDEs). The weak formulation facilitates an efficient and robust way to handle noise, and two new mechanisms, narrow-fit and trimming, improve the coefficient support and value recoveries respectively. For each sparsity level, Subspace Pursuit is utilized to find an initial set of support from the large dictionary. Then, we focus on highly dynamic regions (rows of the feature matrix), and error normalize the feature matrix in the narrow-fit step. The support is further updated via trimming the terms that contribute the least. Finally, the support set of features with the smallest Cross-Validation error is chosen as the result. A comprehensive set of numerical experiments are presented for both systems of ODEs and PDEs with various noise levels. The proposed method gives a robust recovery of the coefficients, and a significant denoising effect which can handle up to 100% noise-to-signal ratio for some equations. We compare the proposed method with several state-of-the-art algorithms for the recovery of differential equations.

Parametric modelling of vibration response for high-speed gear transmission system

In the process of dynamic modelling and vibration response simulation for the high-speed gear transmission system, complex structures with a high degree of freedom (DOF) often lead to very large calculation errors, especially under conditions with unpredictable internal and external excitations. In this paper, a novel parametric probabilistic regression (p-PR) model based on data-driven and parametric modelling theories are proposed for the vibration signals of the high-speed gear transmission system. Based on the proper orthogonal decomposition (POD) method, the dataset of vibration signals is constructed, and a new truncated parametric reduced-order model (PROM) of the dataset is given for the gear vibration, with the truncated modes and corresponding coefficient vectors obtained. Through training the PROM and operating parameters using probabilistic regression, maximum likelihood estimation, and the parametric mode reconstruction, the p-PR model of vibration data for the gear transmission system is established. To validate the parametric modelling theories and the p-PR model, a bevel gear transmission experimental rig and a vibration signal test system are built, and the constant-speed test (CST) experiment and speed-up frequency sweep (SUFS) experiment are conducted. Based on the results of the CST experiment, the p-PR model for the experimental system is established and compared with the SUFS results. Results show that the p-PR model can accurately predict the vibration signals in both the time-domain and the frequency-domain, and the maximum predictive error for the experiment is 7.8%, which validates the accuracy and feasibility of the proposed theories and methods.

PointFilterNet: A Filtering Network for Point Cloud Denoising

Point clouds obtained by 3D scanning or reconstruction are usually accompanied by noise. Filtering-based point cloud denoising methods are simple and effective, but they are limited by the manually defined coefficients. Deep learning has shown excellent ability in automatically learning parameters. In this paper, a filtering network named PointFilterNet (PFN for short) is proposed to denoise point clouds by the combination of filtering and deep learning. Instead of directly outputting denoised points using networks, PFN generates the filtering denoised points through learned coefficients. Specifically, PFN outputs three coefficient vectors. These coefficient vectors are then used to filter the coordinates of points in the neighborhood of the noisy point. PFN consists of two parts: an outlier recognizer and a denoiser, both of which generate different but indispensable filtering coefficients. The outlier recognizer reduces the interference of outliers by assigning small coefficients to them. The denoiser is designed to progressively denoise point clouds which accords to the perception process of the human visual system. The experiments on synthetic and real scanned point clouds demonstrate that PFN outperforms state-of-the-art point cloud denoising works. Compared with DMR, the Chamfer distance of PFN is reduced by 22.07% on PCN-dataset.

Dynamic relationships among changes in prices of beef, pork, and chicken in Japan: A Bayesian approach

In this paper, we investigate the interdependence among changes in the prices of beef, pork, and chicken in Japan using a time-varying coefficient vector autoregressive model. Our empirical analysis using monthly data from January 1990 to March 2014 shows that changes in beef prices have long-term influences on changes in pork and chicken prices. Moreover, current changes in the prices of beef, pork, and chicken are closely related to changes in their prices in the preceding two months. Additionally, we do not find that the bovine spongiform encephalopathy outbreak announced by the Japanese government in September 2001 had a long-term influence on the dynamic relationships among changes in the prices of beef, pork, and chicken in Japan.