Weight Vector Research Articles

Analytic Hierarchy Process to Choose the Best Sector in the Software Industry for a New Software Engineer

Objectives: To determine the best area in the software industry for a fresh engineering graduate in India. Methods: Examined the current situation of the software industry today and the datasets that were gathered and included in accordance with that. Here, five alternatives (Research and Development, Mobile solutions, Cloud computing, Big data analytics, and Government and Defence) and seven parameters (Communication, Teamwork, Coding and technical literacy, Programming languages, Problem-solving skills, Research skills, and Multitasking skills) are taken into consideration. Fuzzy AHP and fuzzy TOPSIS methods were used, and the outcomes were compared to the AHP method. Findings: Fuzzy AHP and fuzzy TOPSIS methods have been used to produce the normalized weight vector for each alternative relative to the criterion. Additionally, a normalized weight vector has been calculated and compared to every criterion and criteria alternative. Final rankings for each alternative have been determined in relation to all of these. Novelty: The novelty of the present study is to identify the best sector of the software industry in India for a recent engineering graduate based on providing a ranking of alternatives using fuzzy TOPSIS and fuzzy AHP methodologies. While other strategies may be used to do similar works, the techniques listed above may not be used. Fuzzy AHP and fuzzy TOPSIS approaches can provide more optimal solutions, which is an innovative aspect of this study. Keywords: Analytical Hierarchy Process (AHP), Comparative analysis, Fuzzy AHP method, Fuzzy TOPSIS method, Software industry

Penalty weight tuning in high dose rate brachytherapy using multi-objective Bayesian optimization

Objective. Treatment plan optimization in high dose rate brachytherapy often requires manual fine-tuning of penalty weights for each objective, which can be time-consuming and dependent on the planner's experience. To automate this process, this study used a multi-criteria approach called multi-objective Bayesian optimization with q-noisy expected hypervolume improvement as its acquisition function (MOBO-qNEHVI). Approach. The treatment plans of 13 prostate cancer patients were retrospectively imported to a research treatment planning system, RapidBrachyMTPS, where fast mixed integer optimization (FMIO) performs dwell time optimization given a set of penalty weights to deliver 15 Gy to the target volume. MOBO-qNEHVI was used to find patient-specific Pareto optimal penalty weight vectors that yield clinically acceptable dose volume histogram metrics. The relationship between the number of MOBO-qNEHVI iterations and the number of clinically acceptable plans per patient (acceptance rate) was investigated. The performance time was obtained for various parameter configurations. Main results. MOBO-qNEHVI found clinically acceptable treatment plans for all patients. With increasing the number of MOBO-qNEHVI iterations, the acceptance rate grew logarithmically while the performance time grew exponentially. Fixing the penalty weight of the tumour volume to maximum value, adding the target dose as a parameter, initiating MOBO-qNEHVI with 25 parallel sampling of FMIO, and running 6 MOBO-qNEHVI iterations found solutions that delivered 15 Gy to the hottest 95% of the clinical target volume while respecting the dose constraints to the organs at risk. The average acceptance rate for each patient was 89.74% ± 8.11%, and performance time was 66.6 ± 12.6 s. The initiation took 22.47 ± 7.57 s, and each iteration took 7.35 ± 2.45 s to find one Pareto solution.Significance. MOBO-qNEHVI combined with FMIO can automatically explore the trade-offs between treatment plan objectives in a patient specific manner within a minute. This approach can reduce the dependency of plan quality on planner’s experience and reduce dose to the organs at risk.

Towards Robust Multi-Agent Reinforcement Learning

Stochastic gradient descent (SGD) is at the heart of large-scale distributed machine learning paradigms such as federated learning (FL). In these applications, the task of training high-dimensional weight vectors is distributed among several workers that exchange information over networks of limited bandwidth. While parallelization at such an immense scale helps to reduce the computational burden, it creates several other challenges: delays, asynchrony, and most importantly, a significant communication bottleneck. The popularity and success of SGD can be attributed in no small part to the fact that it is extremely robust to such deviations from ideal operating conditions. Inspired by these findings, we ask: Are common reinforcement learning (RL) algorithms also robust to similarly structured perturbations? Perhaps surprisingly, despite the recent surge of interest in multi-agent/federated RL, almost nothing is known about the above question. This paper collects some of our recent results in filling this void.

Study on applicable coverage extension of theory-based generalization errors bounds to the variants of RVFL network and ELM

This study investigates the coverage extendibility of generalized prediction error estimation for the random vector functional link (RVFL) network and generalized extreme learning machine (GELM). GELM is an ELM applying the limiting behavior of Moore–Penrose generalized inverse (M–P GI) to the output matrix of the last hidden layer of ELM. The RVFL network, the ELM, and their variants are currently employed in various areas due to their fast learning and are expected to be adopted in more applications. Additionally, obtaining prediction error bounds quickly for these networks could greatly increase their utilities. Therefore, exploring the error bounds of the variants is crucial. Recently, the upper and lower bounds of generalized prediction error and their associated tail probabilities for the RVFL network and GELM were analyzed. This study aims to extend the coverage of the existing error bounds to variants of RVFL and ELM. To this end, we investigate each solution of the objective functions for the existing RVFL and ELM variants, compare it with the solution obtained by using the limiting behavior of M–P GI, and then discuss the applicability of the probability inequalities for the prediction error to the variant. Specifically, we conceptualize a restricted solution vector and prove that the restricted solution of a variant of RVFL is identical to that of GELM, with an appropriately selected regularization parameter. The mechanism used in the proof can be applied to other variants, which have different objective functions but have similar forms of solution. Experiments are performed with the CAIDA (Center for Applied Internet Data Analysis) dataset. Numerical results verify the analysis, showing that the generalization prediction error bounds and their associated tail probabilities for ELM (RVFL) variants in applicability coverage are almost identical to those of the GELM (RVFL). In addition, performance-based network similarity is introduced and computed with the obtained results. Based on this analysis, we can conclude that the probability inequalities for prediction error derived can be directly applied to some variants of the RVFL network and ELM, such as robust regularized RVFL and ridge regression ELM. However, it cannot apply directly to the networks that use information obtained during the learning process in its learning, such as RVFL+ and its variants. The significance of this study is that it enables us to figure out the relationship between the size-restricted final weight vector of RVFL and the final weight vectors of ELM, the effect of the relationship on generalized prediction error estimation, and the performance-based similarity between networks. This study provides a theoretical basis for the generalized prediction error's upper and lower bounds and their associated tail probabilities for ELM (RVFL) variants.

Adaptive command filtered control for a class of nonlinear time delay systems with extreme learning machine

AbstractIn this paper, an extreme learning machine (ELM)‐based adaptive command filtered control method is investigated for a class of strict feedback nonlinear systems with unknown external disturbances and time delay. To begin with, the original system state equation is transformed into a new form on account of coordinate transformation. Subsequently, an ELM is adopted to approximate unknown functions which exist in the whole system states, without any prior knowledges of the ideal weight vectors and approximation errors. Secondly, a command filter is developed for the system under consideration, which can avoid the probem of “explosion of complexity” caused by repeated derivation of virtual control signals in traditional backstepping control. Meanwhile, error compensation signals are designed to conquer the shortcoming of a dynamic surface control (DSC) method. The combination of ELM and command filter technique has been used to construct corresponding controllers and adaptive laws. Effective handling of the impact of time delay terms is ensured through designing a novel Lyapunov–Krasovskii functional. The proposed strategy guarantees boundedness of all signals in the closed‐loop system and the tracking error asymptotically converges to a compact set around the origin. In the end, two continuous stirred tank reactors (CSTRs) are taken as example to further verify the efficiency of the put forward control method.

Multiscale collaborative representation for face recognition via class-information fusion

One of the most challenging issues in face recognition is having only a limited number of training images. Multiscale patch collaborative representation (MSPCRC) is an effective approach to address this problem. However, the existing MSPCRC methods only defined a single patch-scale weight vector for all classes to indicate the importance of different patch scales, ignoring the role of class information when fusing multiscale recognition results. In this work, we consider the effect of class information on face recognition and propose a novel multiscale collaborative-representation face recognition method. Specifically, we first construct the multiscale decision matrices of image subsets from different classes according to patch collaborative representation, and define a patch-scale weight vector for each class to describe the importance of different patch scales. Each element in a scale-weight vector represents the weight value of a certain scale in the corresponding class. Then, we construct the respective optimization objective function for each class, which takes into account the classification information both from the same class and from different classes. Finally, we propose a multiscale fusion-recognition output rule based on the patch-weight vectors. Experimental results demonstrate that the proposed method enhances classification accuracy by approximately 2% to 5% across multiple datasets, surpassing the majority of the competing methods.

Adaptive Fuzzy Fixed-Time Control for Nonlinear Systems with Unmodeled Dynamics

This article concentrates on the problem of fixed-time tracking control for a certain class of nonlinear systems with unmodeled dynamics. Unmodeled dynamics are prevalent in practical engineering systems, such as axially symmetric systems like robotic arms, spacecraft, and missiles. In this paper, the fuzzy-logic systems (FLSs) are implemented to address the challenge of accurately approximating the unknown nonlinear terms that arise during the derived control algorithm process. By employing fixed-time command filters (FTCF), the “explosion of complexity” issues encountered in traditional backstepping methods will be effectively resolved. Moreover, error compensation mechanisms are derived to effectively mitigate the filtering errors that may arise from the FTCFs. The computational burden associated with FLSs is reduced through the utilization of the weight vector estimation method based on the maximal norm and an adaptive approach. A fixed-time adaptive fuzzy tracking controller is developed within the backstepping control framework to ensure the boundedness of all signals and achieve fixed-time convergence of the tracking error for the controlled system. Illustrative examples are conducted to illustrate the viability of the derived controller.

Discriminative label correlation based robust structure learning for multi-label feature selection

Feature selection is a key technique to tackle the curse of dimensionality in multi-label learning. Lots of embedded multi-label feature selection methods have been developed. However, they face challenges in identifying and excluding redundant features. To address these issues, this paper proposes a multi-label feature selection method that combines robust structural learning and discriminative label regularization. The proposed method starts from the feature space rather than data space, motivated by the principle that redundant features have high similarity or strong correlation. To exclude redundant features, a regularization on the feature selection matrix is designed by combining ℓ2,1-norm penalty with inner products of feature weight vectors. This regularization can help to learn a robust structure in the feature selection matrix. Meanwhile, both of the similarity and dissimilarity of labels of instances are involved in exploring discriminative label correlations. Extensive experiments verified the effectiveness of the proposed model for feature selection.

Simple subspace based adaptive beamforming under Toeplitz covariances

When uncorrelated signals are incident on a uniform linear array, the array covariance matrix is of the Toeplitz form. An adaptive beamforming method is proposed based on the signal-plus-interference (SI) subspace via the Toeplitz rectification of the sample matrix. The rectified matrix is shown to be more accurate in a norm sense than the modified matrix according to the centro-Hermitian property. Since the former also is centro-Hermitian we can efficiently obtain its eigen-decomposition from a real matrix and then the weight vector in the estimated SI subspace. The proposed method, showing robustness to pointing errors, is not only computationally efficient but also very quickly converges to the optimum performance as demonstrated in the simulation.

Motion-guided large aperture ULA to enhance DOA estimation: An inverse synthetic aperture perspective

Direction-of-arrival (DOA) estimation is a critical issue in array signal processing, especially in radar applications. However, the array aperture of high-frequency radars is constrained by the site and platform, which in turn leads to limited DOA estimation performance. In this paper, inspired by the inverse synthetic aperture radar, we design a novel DOA estimation method based on motion-guided large-aperture uniform linear array (ULA). Referring to the concept of inverse synthetic aperture, the novel method utilizes the relative motion between the radar and the target to construct a larger ULA. We demonstrate that the key condition for reconstructing ULAs is suitable data segmentation and reshaping within the coherent integration time. However, the correct segmentation position is related to the target's motion trajectory. For non-cooperative targets, the uncertain segmentation position is regarded as a mismatch problem between the steering and weighting vectors, such that the spatial spectrum becomes a product of two sinc-like functions. With the analysis of the main lobe and grating lobes, the maximum peak-to-grating-lobe ratio criterion is introduced to find the ambiguity-free DOA. The experimental results demonstrate the performance advantages of the proposed DOA estimation algorithm in terms of noise robustness and resolution.

A lightweight feature attention fusion network for pavement crack segmentation

AbstractThe occurrence of pavement cracks poses a significant potential threat to road safety, thus the rapid and accurate acquisition of pavement crack information is of paramount importance. Deep learning methods have the capability to offer precise and automated crack detection solutions based on crack images. However, the slow detection speed and huge model size in high‐accuracy models are still the main challenges required to be addressed. Therefore, this research presents a lightweight feature attention fusion network for pavement crack segmentation. This structure employs FasterNet as the backbone network, ensuring performance while reducing model inference time and memory overhead. Additionally, the receptive field block is incorporated to simulate human visual perception, enhancing the network's feature extraction capability. Ultimately, our approach employs the feature fusion module (FFM) to effectively combine decoder outputs with encoder's low‐level features using weight vectors. Experimental results on public crack datasets, namely, CFD, CRACK500, and DeepCrack, demonstrate that compared to other semantic segmentation algorithms, the proposed method achieves both accurate and comprehensive pavement crack extraction while ensuring speed.

Group decision making with incomplete triangular fuzzy multiplicative preference relations for evaluating third-party reverse logistics providers

The strategic management of reverse logistics (RL) is essential for enterprises to enhance their operational efficiency, customer satisfaction, and sustainability performance in today's competitive marketplace. Many manufacturing firms have to cooperate with professional RL providers to overcome resource constraints and technological limitations, ultimately driving business success. Thus, it is critical for every enterprise to select the most suitable third-party RL provider (3PRLP). This paper provides a novel group decision making (GDM) method with incomplete triangular fuzzy multiplicative preference relations (TFMPRs) to cope with the selection of the most optimal 3PRLP. Firstly, a definition of acceptable incomplete TFMPRs is given. Then, the sufficient and necessary condition of an acceptable incomplete TFMPR is proposed. By analyzing the properties of consistent TFMPRs, a graph-based algorithm is designed to estimate the unknown elements in incomplete TFMPRs. Based on the proposed acceptable consistency definition of TFMPRs, an optimization model is set up to improve the consistency degree of inconsistent TFMPRs. The optimal normalized triangular fuzzy multiplicative weight vector (Tri-MWV) is obtained by computing two analytic expressions and solving a linear programming model. To measure the closeness degree of two TFMPRs, the concept of logarithmic correlation coefficient (LCC) between two TFMPRs is proposed. Combining the incomplete preference information in incomplete TFMPRs with the LCCs of any two TFMPRs, an algorithm of computing experts’ weights is displayed. Subsequently, a novel method of GDM with incomplete TFMPRs is presented. Lastly, a practical example of evaluating 3PRLPs is conducted to illustrate the effectiveness of the proposed GDM method with incomplete TFMPRs.

An attribute ranking method based on rough sets and interval-valued fuzzy sets

Feature importance is a complex issue in machine learning, as determining a superior attribute is vague, uncertain, and dependent on the model. This study introduces a rough-fuzzy hybrid (RAFAR) method that merges various techniques from rough set theory and fuzzy set theory to tackle uncertainty in attribute importance and ranking. RAFAR utilizes an interval-valued fuzzy matrix to depict preference between attribute pairs. This research focuses on constructing these matrices from datasets and identifying suitable rankings based on these matrices. The concept of interval-valued weight vectors is introduced to represent attribute importance, and their additive and multiplicative compatibility is examined. The properties of these consistency types and the efficient algorithms for solving related problems are discussed. These new theoretical findings are valuable for creating effective optimization models and algorithms within the RAFAR framework. Additionally, novel approaches for constructing pairwise comparison matrices and enhancing the scalability of RAFAR are suggested. The study also includes experimental results on benchmark datasets to demonstrate the accuracy of the proposed solutions.

Direct integration bias-compensated maximum correntropy criterion algorithm independent of measurement noise samples

In system identification, if the filter input and the desired signal are both interfered by noise, traditional adaptive filtering algorithms will not work effectively. The recently presented bias-compensated normalized maximum correntropy criterion (BC-NMCC) algorithm, which was developed based on the information theory learning (ITL) and Taylor expansion, can deal with this case. However, it needs to use measurement noise samples to update the adaptive filter weight vector, whose values are usually unavailable. To solve this problem, we propose a direct integration bias-compensated maximum correntropy criterion (DI-BC-MCC) algorithm under an unbiasedness criterion (UC). Specifically, we utilize a direct integral approach to calculate the expected values instead of using Taylor expansion. With this idea, the update equation of DI-BC-MCC does not involve measurement noise samples, unlike BC-NMCC. The derived compensation term can reduce the impact of input noise significantly, and DI-BC-MCC can perform well in impulsive noise environments. In addition, the steady-state performance of DI-BC-MCC is analyzed under some frequently used assumptions. Finally, simulations are provided to demonstrate the good performance of DI-BC-MCC and to verify the accuracy of the theoretical analysis.

Mining Deviations in Document Writing Style through Vector Dissimilarity

Doubts arise about the originality of a document when noticing a change in its writing style. This evidence to plagiarism has made the intrinsic approach for detecting plagiarism uncover the plagiarized passages through the analysis of the writing style for the suspicious document where a reference corpus to compare with is absent. The proposed work aims at discovering the deviations in document writing style through applying several steps: Firstly, the entire document is segmented into disjointed segments wherein each corresponds to a paragraph in the original document. For the entire document and for each segment, center vectors comprising average weight of their word are constructed. Second, the degree of closeness is calculated through applying Cosine similarity to measure for each segment, the deviation of its center vector from the center vector of the entire document. Additionally, word n-gram length will be investigated to show its effect on the proposed system performance wherein, center vectors are computed considering word n-grams for different values of n (n= 1, 2, and 3). Performance evaluation of the proposed method was accomplished through the use of Precision, Recall, F-measure, Granularity, and Plagdet as evaluation measures. Moreover, PAN-PC-09 and PAN-PC-11 were used for detecting intrinsic plagiarism as evaluation corpora. It is shown that the proposed approach has achieved results that are comparable to the state-of-the-art methods. Positive impact was observed through discovering deviations in document writing style by computing weight vectors dissimilarity rather than calculating the difference between the word n-grams that exist in segments and their corresponding word n-grams in the suspicious document. Furthermore, when considering the length of word n-gram, better results were recorded for system performance when word bi-grams was used compared to word uni-grams and word tri-grams.

Benders decomposition for the discrete ordered median problem

Ordered median optimization has been proven to be a powerful tool to generalize many well-known problems from the literature. In Location Theory, the Discrete Ordered Median Problem (DOMP) is a facility location problem where clients are first ranked according to their allocation cost to the nearest open facility, and then these costs are multiplied by a suitable weight vector λ. That way, DOMP generalizes many well-known discrete location problems including p-median, p-center or centdian. In this article, we also allow negative entries of λ, allowing us to derive models for better addressing equity and fairness in facility location, for modeling obnoxious facility location problems or for including other client preference models. We present new mixed integer programming models for DOMP along with algorithmic enhancements for solving the DOMP to optimality using mixed integer programming techniques. Specifically, starting from state-of-the-art formulations from the literature, we present several Benders decomposition reformulations applied to them. Using these approaches, new state-of-the-art results have been obtained for different ordered weighting vectors.

Data-Driven Adaptive Controller Based on Hyperbolic Cost Function for Non-Affine Discrete-Time Systems with Variant Control Direction

As technology evolves, more complex non-affine systems are created. These complex systems are hard to model, whereas most controllers require information on systems to be designed. This information is hard to obtain for systems with varying control directions. Therefore, this study introduces a novel data-driven estimator and controller tailored for single-input single-output non-affine discrete-time systems. This approach focuses on cases when the control direction varies over time and the mathematical model of the system is completely unknown. The estimator and controller are constructed using a Multiple-input Fuzzy Rules Emulated Network framework. The weight vectors are updated through the gradient descent optimization method, which employs a unique cost function that multiplies the error by a hyperbolic tangent. The stability analyses demonstrate that both the estimator and controller converge to uniformly ultimately bounded (UUB) functions of Lyapunov. To validate the results, we show experimental tests of force control that were executed on the z-axis of a drive-controlled 3D scanning robot. This system has a varying control direction, and we also provide comparison results with a state-of-the-art controller. The results show a mean absolute percentage tracking error smaller than one percent on the steady state and the expected variation in the system’s control direction.

Research on the Vector Space and Its Linearity

A vector space is an abelian group over a field. From the viewpoint of group theory, the tangent space is a theoretical concept. Tangent space is similar to a vector space, particularly in terms of linearity. From a field's perspective, a subfield is a subset of the original field that shares the same properties as the original field. Subfield is logically similar to a subspace of a vector space. A vector is an element of a vector space. Weight vectors can be used to describe motion, which can be applied in pattern recognition. A linear combination of weight vectors can describe a sequence of motions. Kernel graph theory treats a graph as an element of its theoretical structure. Kernel graph theory can also be applied in pattern recognition. So, basically, this article presents a perspective on applying vector space in pattern recognition. The inherent logic of vector space can be applied to both motion synthesis and graph pattern recognition. The linearity of the vector space is the main focus of this article.

Robust Bias Compensation Method for Sparse Normalized Quasi-Newton Least-Mean with Variable Mixing-Norm Adaptive Filtering

Input noise causes inescapable bias to the weight vectors of the adaptive filters during the adaptation processes. Moreover, the impulse noise at the output of the unknown systems can prevent bias compensation from converging. This paper presents a robust bias compensation method for a sparse normalized quasi-Newton least-mean (BC-SNQNLM) adaptive filtering algorithm to address these issues. We have mathematically derived the biased-compensation terms in an impulse noisy environment. Inspired by the convex combination of adaptive filters’ step sizes, we propose a novel variable mixing-norm method, BC-SNQNLM-VMN, to accelerate the convergence of our BC-SNQNLM algorithm. Simulation results confirm that the proposed method significantly outperforms other comparative works regarding normalized mean-squared deviation (NMSD) in the steady state.

Separation of variables for scalar-valued polynomials in the non-stable range

Any complex-valued polynomial on (Rn)k decomposes into an algebraic combination of O(n)-invariant polynomials and harmonic polynomials. This decomposition, separation of variables, is granted to be unique if n≥2k−1. We prove that the condition n≥2k−1 is not only sufficient, but also necessary for uniqueness of the separation. Moreover, we describe the structure of non-uniqueness of the separation in the boundary cases when n=2k−2 and n=2k−3.Formally, we study the kernel of a multiplication map ϕ carrying out separation of variables. We devise a general algorithmic procedure for describing Ker ϕ in the restricted non-stable range k≤n<2k−1. In the full non-stable range n<2k−1, we give formulas for highest weights of generators of the kernel as well as formulas for its Hilbert series. Using the developed methods, we obtain a list of highest weight vectors generating Ker ϕ.