Coefficient Vector Research Articles

A multi-objective effort-aware defect prediction approach based on NSGA-II

Effort-Aware Defect Prediction (EADP) technique sorts software modules by the defect density and aims to find more bugs when testing a certain number of Lines of Code (LOC). The existing EADP methods ignore the number of required inspected modules and thus resulting in more testing cost. Therefore, we propose a multi-objective effort-aware defect prediction approach based on NSGA-II named MOOAC for EADP, which aims to maximize the Proportion of the found Bugs (PofB@20%) and minimize the Proportion of Module Inspected (PMI@20%) when inspecting the top 20% LOC. MOOAC firstly trains a random forest classification model. Then, it builds a logistic regression model, and utilizes the NSGA-II algorithm to generate the coefficient vector of the model by maximizing the PofB@20% value and minimizing the PMI@20% value simultaneously. In the model prediction phase, MOOAC firstly employs the built random forest classifier to decide whether modules are defective. Next, the predicted defective modules are first inspected based on the ratio between the predicted defect probability by the logistic regression model and LOC, which can make testers to find more bugs and test as fewer LOC as possible. The clean modules are then inspected to reduce the Initial False Alarms (IFA), if there is still the testing budget left. The results show that MOOAC exhibits the best overall performance on the PofB@20% and PMI@20%. In other words, MOOAC enables testers to identify more bugs per 1% module.

Improved virtual SVPWM algorithm for CMV reduction and NPV oscillation elimination in Three-Level NPC inverter

An improved virtual space vector pulse-width modulation (IVSVPWM) strategy is presented to address simultaneously the problem of common mode voltage (CMV) with neutral point voltage (NPV) fluctuations in wind power converters. The proposed IVSVPWM method suppresses the amplitude of the common mode voltage to Udc/6 by discarding the positive small vector. Meanwhile, the new virtual vector is synthesized by selecting a vector whose neutral point current sums to zero among the retained voltage vectors. In addition, a feedback mechanism is established in the proposed strategy. According to the feedback result, the distribution coefficients of each basic vector in the virtual vector are recalculated to suppress the NPV fluctuation. Through the above control strategy, the dual effect of suppressing the CMV and balancing the NPV is achieved in the full modulation. The feasibility and effectiveness of the strategy are verified by simulation and experiment.© 2017 Elsevier Inc. All rights reserved.

Fractional-order elastic net regularization for identifying various types of unknown external forces

Force identification is an important and fundamental problem in various engineering fields, and several regularization techniques have been introduced to improve the ill-posedness of this problem. While these regularization techniques can achieve satisfactory identified accuracy, they are best suited for dealing with specific forms of external forces. The external force, in reality, is always unknown and needs to be identified, making it difficult to select an appropriate regularization technique in advance. To overcome this disadvantage, a novel regularization technique, i.e. fractional-order elastic net regularization is proposed for force identification in this study. Firstly, the relationship between acceleration response and coefficient vector of external force is established. Then, a weighted matrix is introduced to define the difference between measured and calculated acceleration responses. Meanwhile, the external force and coefficient vector are constrained by their respective norm penalties with the help of regularization parameters. As a result, an optimization problem is defined for force identification, and the corresponding geometric significance is analyzed to propose a selection way for the regularization parameters. Finally, both numerical simulations and experimental verifications are conducted to evaluate the effectiveness of the proposed method. Comparison with existing methods reveals that the proposed method has great identification accuracy and applicability for various types of external forces.

Multi-stage skewed grey cloud clustering model and its application

PurposeThe possibility function-based grey clustering model has evolved into a complete approach for dealing with uncertainty evaluation problems. Existing models still have problems with the choice dilemma of the maximum criteria and instances when the possibility function may not accurately capture the data's randomness. This study aims to propose a multi-stage skewed grey cloud clustering model that blends grey and randomness to overcome these problems.Design/methodology/approachFirst, the skewed grey cloud possibility (SGCP) function is defined, and its digital characteristics demonstrate that a normal cloud is a particular instance of a skewed cloud. Second, the border of the decision paradox of the maximum criterion is established. Third, using the skewed grey cloud kernel weight (SGCKW) transformation as a tool, the multi-stage skewed grey cloud clustering coefficient (SGCCC) vector is calculated and research items are clustered according to this multi-stage SGCCC vector with overall features. Finally, the multi-stage skewed grey cloud clustering model's solution steps are then provided.FindingsThe results of applying the model to the assessment of college students' capacity for innovation and entrepreneurship revealed that, in comparison to the traditional grey clustering model and the two-stage grey cloud clustering evaluation model, the proposed model's clustering results have higher identification and stability, which partially resolves the decision paradox of the maximum criterion.Originality/valueCompared with current models, the proposed model in this study can dynamically depict the clustering process through multi-stage clustering, ensuring the stability and integrity of the clustering results and advancing grey system theory.

Recognition of mineralogical and technological varieties of iron ore on the basis of ultrasound backscatter spectrograms

The research is aimed to the analysis and modeling of the process of propagation of ultrasonic waves in iron ore samples to assess its mineralogical varieties. The paper analyzes domestic and foreign experience in modeling of ultrasonic waves propagation; methods of mathematical and computer modeling were used, as well as methods of mathematical statistics and probability theory for analysis of the results. Scientific novelty consists in developing and substantiating a method for recognizing the mineralogical and technological varieties of iron ore of a developed deposit based on spectrograms of a backscattered ultrasonic probing signal. Practical valueconsists in developing a methodology for non-contact non-destructive mineralogical analysis of iron ore to improve the efficiency and quality of its further processing and preparation for metallurgical processing. results. As measurable characteristic estimates of textural and structural features of iron ore varieties the results of spectral analysis of the reversed radiant ultrasonic signal were used. To implement the measurement results classification procedure, Adaptive Neuro-Fuzzy Inference System is used. At the vector of parameters of membership functions of terms of input variables and the vector of coefficients of linear functions in the conclusions of the rules was formed based on the characteristics of the processed ore and the spectrograms of the backscattered ultrasonic signal. The average accuracy of recognition of magnetite, chlorite-carbonate-magnetite, hematite-magnetite, magnetite-cummngtonite-chlorite-siderite mineral varieties of iron ore of the studied deposit was 93%.

A physics-based machine learning technique rapidly reconstructs the wall-shear stress and pressure fields in coronary arteries.

With the global rise of cardiovascular disease including atherosclerosis, there is a high demand for accurate diagnostic tools that can be used during a short consultation. In view of pathology, abnormal blood flow patterns have been demonstrated to be strong predictors of atherosclerotic lesion incidence, location, progression, and rupture. Prediction of patient-specific blood flow patterns can hence enable fast clinical diagnosis. However, the current state of art for the technique is by employing 3D-imaging-based Computational Fluid Dynamics (CFD). The high computational cost renders these methods impractical. In this work, we present a novel method to expedite the reconstruction of 3D pressure and shear stress fields using a combination of a reduced-order CFD modelling technique together with non-linear regression tools from the Machine Learning (ML) paradigm. Specifically, we develop a proof-of-concept automated pipeline that uses randomised perturbations of an atherosclerotic pig coronary artery to produce a large dataset of unique mesh geometries with variable blood flow. A total of 1,407 geometries were generated from seven reference arteries and were used to simulate blood flow using the CFD solver Abaqus. This CFD dataset was then post-processed using the mesh-domain common-base Proper Orthogonal Decomposition (cPOD) method to obtain Eigen functions and principal coefficients, the latter of which is a product of the individual mesh flow solutions with the POD Eigenvectors. Being a data-reduction method, the POD enables the data to be represented using only the ten most significant modes, which captures cumulatively greater than 95% of variance of flow features due to mesh variations. Next, the node coordinate data of the meshes were embedded in a two-dimensional coordinate system using the t-distributed Stochastic Neighbor Embedding (-SNE) algorithm. The reduced dataset for -SNE coordinates and corresponding vector of POD coefficients were then used to train a Random Forest Regressor (RFR) model. The same methodology was applied to both the volumetric pressure solution and the wall shear stress. The predicted pattern of blood pressure, and shear stress in unseen arterial geometries were compared with the ground truth CFD solutions on "unseen" meshes. The new method was able to reliably reproduce the 3D coronary artery haemodynamics in less than 10 s.

Properties of the coefficient estimators for the linear regression model with heteroskedastic error term

In this paper we present estimated generalized least squares (EGLS) estimator for the coefficient vector β in the linear regression model y = βX + ε, where disturbance term can be heteroskedastic. For the heteroskedasticity of the changed segment type, using Monte-Carlo method, we investigate empirical properties of the proposed and ordinary least squares (OLS) estimators. The results show that the empirical covariance of the EGLS estimators is smaller than that of OLS estimators.

A Robust Image Encryption Scheme Based on Block Compressive Sensing and Wavelet Transform

In this paper, a modified robust image encryption scheme is developed by combining block compressive sensing (BCS) and Wavelet Transform. It was achieved with a balanced performance of security, compression, robustness and running efficiency. First, the plain image is divided equally and sparsely represented in discrete wavelet transform (DWT) domain, and the coefficient vectors are confused using the coefficient random permutation strategy and encrypted into a secret image by compressive sensing. In pursuit of superior security, the hyper-chaotic Lorenz system is utilized to generate the updated secret code streams for encryption and embedding with assistance from the counter mode. This scheme is suitable for processing the medium and large images in parallel. Additionally, it exhibits superior robustness and efficiency compared with existing related schemes. Simulation results and comprehensive performance analyses are presented to demonstrate the effectiveness, secrecy and robustness of the proposed scheme. The compressive encryption model using BCS with Walsh transform as sensing matrix and WAM chaos system, the scrambling technique and diffusion succeeded in enhancement of secure performance.

Bayesian Identification Procedure for Triple Seasonal Autoregressive Models

Triple seasonal autoregressive (TSAR) models have been introduced to model time series date with three layers of seasonality; however, the Bayesian identification problem of these models has not been tackled in the literature. Therefore, in this paper, we have the objective of filling this gap by presenting a Bayesian procedure to identify the best order of TSAR models. Assuming that the TSAR model errors are normally distributed along with employing three priors, i.e., normal-gamma, Jeffreys’ and g priors, on the model parameters, we derive the marginal posterior distributions of the TSAR model parameters. In particular, we show that the marginal posteriors are multivariate t and gamma distributions for the TSAR model coefficients vector and precision, respectively. Using the marginal posterior distribution of the TSAR model coefficients vector, we present an identification procedure for the TSAR models based on a sequence of t-test of significance. We evaluate the accuracy of the proposed Bayesian identification procedure by conducting an extensive simulation study, followed by a real application to hourly electricity load datasets in six European countries.

Spectral Image Reconstruction Using Recovered Basis Vector Coefficients

Spectral imaging plays a crucial role in various fields, including remote sensing, medical imaging, and material analysis, but it often requires specialized and expensive equipment, making it inaccessible to many. Its application is also limited by the interdependent constraints of temporal, spatial, and spectral resolutions. In order to address these issues, and thus, obtain high-quality spectral images in a time-efficient and affordable manner, we proposed one two-step method for spectral image reconstruction from easily available RGB images under the down-sampling schemes. Specifically, we investigated how RGB values characterize spectral reflectance and found that, compared to the intuitive and straightforward RGB images themselves, their corresponding basis vector coefficients can represent the prior information of spectral images more explicitly and are better suited for spectral image reconstruction tasks. Thus, we derived one data-driven algebraic method to recover the corresponding basis vector coefficients from RGB images in an analytical form and then employed one CNN-based neural network to learn the patch-level mapping from the recovered basis vector coefficients to spectral images. To evaluate the effect of introducing the basis vector coefficient recovery step, several CNNs which typically perform well in spectral image reconstruction are chosen as benchmarks to compare the variation in reconstruction performance. Experimental results on a large public spectral image dataset and our real-world dataset demonstrate that compared to the unaltered version, those CNNs guided by the recovered basis vector coefficients can achieve significant performance improvement in the reconstruction accuracy. Furthermore, this method is plug-and-play, with very little computational performance consumption, thus maintaining a high speed of calculation.

The Effect of the Second Stage Estimator on Model Performance in Post-LASSO Method

Penalized linear regression methods are used for the accurate prediction of new observations and to obtain interpretable models. The performance of these methods depends on the properties of the true coefficient vector. The LASSO method is a penalized regression method that can simultaneously perform coefficient shrinkage and variable selection in a continuous process. Depending on the structure of the dataset, different estimators have been proposed to overcome the problems faced by LASSO. The estimation method used in the second stage of the post-LASSO two-stage regression method proposed as an alternative to LASSO has a considerable effect on model performance.
 In this study, the performance of the post-LASSO is compared with classical penalized regression methods ridge, LASSO, elastic net, adaptive LASSO and Post-LASSO by using different estimation methods in the second stage of the post-LASSO. In addition, the effect of the magnitude and position of the signal values in the real coefficient vector on the performance of the models obtained by these methods is analyzed. The mean squared error and standard deviation of the predictions calculated on the test set are used to compare the prediction performance of the models, while the active set sizes are used to compare their performance in variable selection. According to the findings obtained from the simulation studies, the choice of the second-stage estimator and the structure of the true coefficient vector significantly affect the success of the post-LASSO method compared to other methods.

Design and Calculation of Evaluation Index for Urban Road Anti-Blocking Ability

Aiming at the lack of an anti-clogging ability index in the road network traffic evaluation index, an anti-clogging ability index was proposed to measure the anti-clogging ability of urban road traffic network: Κ-anti-clogging coefficient, which is used to measure the shortest path between any pair of starting and ending points on the urban road traffic network. After the current edge of the shortest path is blocked, the shortest path is selected from the current node of the shortest path. If the current edge of the shortest path is blocked again, the selection continues until the shortest path to the ending point is selected. In the case of unrecoverable congestion, the properties of the anti-clogging coefficient vector on any origin-destination pair, a path, and the whole traffic network are analysed, and the algorithm of the anti-clogging coefficient and its complexity are given. Finally, an example analysis is carried out using a local traffic network in a city.

Co-Efficient Vector Based Differential Distributed Quasi-Orthogonal Space Time Frequency Coding.

Distributed space time frequency coding (DSTFC) schemes address problems of performance degradation encountered by cooperative broadband networks operating in highly mobile environments. Channel state information (CSI) acquisition is, however, impractical in such highly mobile environments. Therefore, to address this problem, designers focus on incorporating differential designs with DSTFC for signal recovery in environments where neither the relay nodes nor destination have CSI. Traditionally, unitary matrix-based differential designs have been used to generate the differentially encoded symbols and codeword matrices. Unitary based designs are suitable for cooperative networks that utilize the amplify-and-forward protocol where the relay nodes are typically required to forego differential decoding. In considering other scenarios where relay nodes are compelled to differentially decode and re-transmit information signals, we propose a novel co-efficient vector differential distributed quasi-orthogonal space time frequency coding (DQSTFC) scheme for decode-and-forward cooperative networks. Our proposed space time frequency coding scheme relaxes the need for constant channel gain in the temporal and frequency dimensions over long symbol periods; thus, performance degradation is reduced in frequency-selective and time-selective fading environments. Simulation results illustrate the performance of our proposed co-efficient vector differential DQSTFC scheme under different channel conditions. Through pair-wise error probability analysis, we derive the full diversity design criteria for our code.

Study on a Novel Strategy for High-Quality Grinding Surface Based on the Coefficient of Friction

Surface quality has a significant impact on the service life of machine parts. Grinding is often the last process to ensure surface quality and accuracy of material formation. In this study, a high-quality surface was developed by determining the coefficient of friction in grinding a quartz fiber-reinforced silica ceramic composite. By processing the physical signals in the grinding process, a multi-objective function was established by considering grinding parameters, i.e., surface roughness, coefficient of friction, active energy consumption, and effective grinding time. The weight vector coefficients of the sub-objective functions were optimized through a multi-objective evolutionary algorithm based on the decomposition (MOEA/D) algorithm. The genetic algorithm was used to optimize the process parameters of the multi-objective function, and the optimal range for the coefficient of friction was determined to be 0.197~0.216. The experimental results indicated that when the coefficient of friction tends to 0.197, the distribution distance of the microscopic data points on the surface profile is small and the distribution uniformity is good. When the coefficient of friction tends to 0.216, the surface profile shows a good periodic characteristic. The quality of a grinding surface depends on the uniformity and periodicity of the surface’s topography. The coefficient of friction explained the typical physical characteristics of high-quality grinding surfaces. The multi-objective optimization function was even more important for the subsequent high-quality machining of mechanical parts to provide guidance and reference significance.

A comparative study of different variable selection methods based on numerical simulation and empirical analysis.

This study employs the principles of computer science and statistics to evaluate the efficacy of the linear random effect model, utilizing Lasso variable selection techniques (including Lasso, Elastic-Net, Adaptive-Lasso, and SCAD) through numerical simulation and empirical research. The analysis focuses on the model's consistency in variable selection, prediction accuracy, stability, and efficiency. This study employs a novel approach to assess the consistency of variable selection across models. Specifically, the angle between the actual coefficient vector β and the estimated coefficient vector is computed to determine the degree of consistency. Additionally, the boxplot tool of statistical analysis is utilized to visually represent the distribution of model prediction accuracy data and variable selection consistency. The comparative stability of each model is assessed based on the frequency of outliers. This study conducts comparative experiments of numerical simulation to evaluate a proposed model evaluation method against commonly used analysis methods. The results demonstrate the effectiveness and correctness of the proposed method, highlighting its ability to conveniently analyze the stability and efficiency of each fitting model.

Neglected Heterogeneity, Simpson’s Paradox, and the Anatomy of Least Squares

Abstract When a sample combines data from two or more groups, multivariate regression yields a matrix-weighted average of the group-specific coefficient vectors. However, it is possible that the weighted average of a specific coefficient falls outside the range of the group-specific coefficients, and it may even have a different sign compared to both group-level coefficients, a manifestation of Simpson’s paradox. The result of the combined regression is then prone to misinterpretation. The purpose of this paper is to raise awareness of this problem and to state conditions under which such non-convex weighting or sign reversal can arise, for a model with two regressors and two groups. Two illustrative examples, an investment equation estimated with panel data, and a cross-sectional earnings equation for men and women, highlight the relevance of these findings for applied work.

Evaluating Fiscal Policy Under Cyclical Balance in Developed Countries

Abstract This study investigates the cyclical patterns of fiscal policy rules using various policy variables that respond to the macroeconomic performance of developed countries over the past few decades. The study reveals that regardless of whether the economy is in a recession or a boom, fiscal policy basically displays counter-cyclical behavior. However, the degree of cyclicality varies depending on the output gap measurements chosen and the countries analyzed. Additionally, the estimates using various fiscal policy indicators demonstrate a strong time variation in fiscal cyclical behavior, resulting in a significant increase in the counter-cyclicality of the fiscal balance. The article also applies the time-varying coefficients vector autoregression model to assess the effects of fiscal policy on output and finds that a boost in the cyclically adjusted primary balance positively impacts production in the short run.

Sample canonical correlation coefficients of high-dimensional random vectors with finite rank correlations

Consider two random vectors x˜=Az+C11∕2x∈Rp and y˜=Bz+C21∕2y∈Rq, where x∈Rp, y∈Rq and z∈Rr are independent random vectors with i.i.d. entries of zero mean and unit variance, C1 and C2 are p×p and q×q deterministic population covariance matrices, and A and B are p×r and q×r deterministic factor loading matrices. With n independent observations of x˜ and y˜, we study the sample canonical correlations between them. Under the sharp fourth moment condition on the entries of x, y and z, we prove the BBP transition for the sample canonical correlation coefficients (CCCs). More precisely, if a population CCC is below a threshold, then the corresponding sample CCC converges to the right edge of the bulk eigenvalue spectrum of the sample canonical correlation matrix and satisfies the famous Tracy-Widom law; if a population CCC is above the threshold, then the corresponding sample CCC converges to an outlier that is detached from the bulk eigenvalue spectrum. We prove our results in full generality, in the sense that they also hold for near-degenerate population CCCs and population CCCs that are close to the threshold.

Laplace Distribution Based Online Identification of Linear Systems With Robust Recursive Expectation–Maximization Algorithm

The robust online identification problem of linear systems is considered in this paper using a faster robust recursive expectation-maximization (RREM) framework. To improve the convergence rate, the outliers, which would deteriorate the identified models, are accommodated with a Laplace distribution instead of Student's t-distribution. Then, the recursive transformation of the maximum likelihood function is realized with a recursive Q-function. The extensively recognized autoregressive exogenous (ARX) models are used for the description of general linear systems. As a result, the unknown parameters, including the regression coefficient vector of the ARX models, the variance of the noise without outliers, and the scale parameter of the Laplace distribution, are determined in a recursive manner. The performance of the proposed approach is tested with a simulated continuous fermentation reactor (CFR) system example and a coupled-tank experiment.

Response prediction of cantilever plates via mode superposition method and combination method of beam functions

The present work is devoted to predicting the response of cantilever plates by expanding the vibration data at limited positions to the unmeasured regions with poor accessibility. The predictive algorithm is based on the mode superposition method (MSM) and the combination method of beam functions (CMOBF). Firstly, the vibration mode function (VMF) of the cantilever plate is deduced offline according to the CMOBF. According to the VMFs calculated offline and the responses measured at limited points, the mode coefficients are updated by the MSM in real time. Finally, the displacements or accelerations of target positions are predicted by the product of the mode matrix and the vector of mode coefficients. The predictive process is achieved in the absence of specific expression and distribution of external loads. Besides, different from traditional modal decomposition and expansion methods, the present work is not dependent on the finite element (FE) model or repeated iterations. The predictive process is convenient to carry out with a small computation time online. As some application examples, the predictive method is applied to the cantilever plates under concentrated and moving loads by simulations and experiments. Both the acceleration and displacement signals are taken into account and examined.