Random Vector Research Articles

Generalized complex fractional moment for the probabilistic characteristic of random vectors

A definition of multi-variate complex quantities called Generalized Complex Fractional Moment (GCFM) based on the multi-dimensional Mellin transform is proposed in this paper, which is also related to the multi-dimensional Riesz fractional integral evaluated in zero. The equivalence property between GCFM, for both multi-dimensional probability density functions and multi-dimensional characteristic functions is established. Furthermore, a method for obtaining marginal probability distributions from GCFM is presented. The validity of the GCFM method is verified through an example involving α-stable random vectors. Additionally, another example using GCFM to reconstruct the non-stationary PDF of the stochastic dynamic system highlights the prospect of applying the GCFM method in engineering.

Moderate deviations for multidimensional aggregate claims with arbitrary dependence between claim sizes and waiting times

Consider a multidimensional renewal risk model, in which the claim sizes X k , k ≥ 1 , form a sequence of independent and identically distributed random vectors with non negative components allowed to be dependent on each other, and the inter-arrival times form a sequence of p-extended negatively dependent random variables. By allowing arbitrary dependence between claim sizes and waiting times, we obtain the moderate deviations for the multidimensional aggregate claims with consistently varying tails.

Alzheimer’s Disease Diagnosis via Intuitionistic Fuzzy Random Vector Functional Link Network

Alzheimer's disease (AD) is a prominent neurodegenerative disorder, which leads to memory loss and cognitive impairment. The progression is irreversible and shows atrophies in cerebral cortex. Multiple studies revealed that the early diagnosis and early treatment can slow the progress of dementia, and hence, further atrophies can be controlled. Brain imaging data, such as magnetic resonance imaging (MRI), have been prominently used for the diagnosis of AD. Multiple approaches have been proposed for the diagnosis of AD. We propose a novel intuitionistic fuzzy random vector functional link network (IFRVFL) for the diagnosis of AD. Unlike standard random vector functional link (RVFL) network, extreme learning machine (ELM), and kernel ridge regression (KRR), which uses a uniform weighting approach for generating the optimal classifier, the proposed IFRVFL uses a fuzzy weighted approach for generating the optimal classifier. A uniform weighting scheme assumes that all the data samples are equally important; however, in real-world scenarios, this assumption may not hold true due to the presence of outliers and noise. Hence, it results in lower generalization. The proposed IFRVFL assigns each sample an intuitionistic fuzzy number (IFN), which is a function of membership and nonmembership score of a sample. The membership score is a function of the sample distance from the centroid of its corresponding class and the nonmembership score is a function of sample distance from the centroid as well as the neighborhood of the given sample. The proposed IFRVFL effectively reduces the influence of outliers. To evaluate the efficiency of the proposed IFRVFL model, we employed it for the diagnosis of AD. Experimental results demonstrate that the proposed IFRVFL model is superior in mild cognitive impairment (MCI) versus AD case. Thus, IFRVFL can be used in the clinical setting for the early diagnosis of AD. Furthermore, to check the robustness of the proposed IFRVFL model, we also evaluated it on benchmark datasets. Experimental results and the statistical tests reveal that the proposed IFRVFL is better in comparison to baseline models. The source code of the proposed IFRVFL formulation is available at https://github.com/mtanveer1/.

Enhanced data preprocessing with novel window function in Raman spectroscopy: Leveraging feature selection and machine learning for raspberry origin identification

In this study, a simple and accurate approach is proposed for enhancing the origin identification of raspberry samples using a combination of innovative Raman spectral preprocessing techniques, feature selection, and machine learning algorithms. Window function was creatively introduced and combined with baseline removal technique to preprocess the Raman spectral data, reducing the dimensionality of the raw data and ensuring the quality of the processed data. An optimization process was conducted to determine the optimal parameter for the window function, resulting in a binning window width of 5 that yielded the highest accuracy. After applying three feature selection techniques, it was found that the information gain model had the best performance in extracting discriminative spectral features. Finally, ten different machine learning algorithms were employed to construct predictive models, and the optimal models were selected. Linear Support Vector Classifier (LinearSVC), Multi-Layer Perceptron Classifier (MLPClassifier), and Linear Discriminant Analysis (LDA) achieve accuracy, precision, recall, and F1 values above 0.96, while the Random Vector Functional Link Network Classifier (RVFLClassifier) surpasses 0.93 for these performance metrics. These results demonstrate the effectiveness of the proposed approach in identifying the origin of raspberry samples with high accuracy and robustness, providing a valuable tool for agricultural product authentication and quality control.

Innovative educational and research center for monitoring forest resources of Siberia based on laser and microwave aerospace imaging

The possibilities of creating an innovative educational and scientific center for monitoring forest resources in Siberia on the basis of the Department of Space Facilities and Technologies of the Siberian State University of Science and Technology named after Mikhail Fedorovich Reshetnev are discussed, with the aim of training highly qualified engineering personnel and conducting promising scientific research in the field of monitoring, modeling, forecasting and management of forest resources. Methodological solutions and algorithms for three-dimensional modeling of forest structure and dynamics based on laser scanning data, digital aerial and space photography are proposed. These methods contribute to operational monitoring and can significantly reduce the cost of monitoring the condition and use of forest resources over the vast territory of Siberia. Remote sensing data is presented in the form of a geotransformed database and digital photo map, compatible in formats with computer-aided design systems and with the main geographic information systems – ArcView, ArcINFO, MapINFO. The innovative monitoring center will be used for operational state control and monitoring of forest management, the state of forest lands, forest management and forest inventory, solving problems of ecology and environmental management, geoecology, formation of a forest resource inventory, aerospace methods for studying natural resources and territories, information technology. Solving these problems will allow for the training of highly qualified specialists. The center's specialists plan to create information technologies for remote sensing of natural objects with the aim of import substitution of foreign software products. The main scientific directions of the created center: development and research of methods for system analysis of large-scale multidimensional remote sensing data based on nonparametric decision-making algorithms and parallel computing technologies; testing hypotheses about the distributions of large-volume remote sensing data based on nonparametric nuclear-type pattern recognition algorithms; detection of compact groups of large-volume remote sensing data corresponding to unimodal fragments of the joint probability density of multivariate random variables.

Enhanced lithium‐ion battery state‐of‐charge estimation for Electric Vehicles using the AOA‐DNN approach

AbstractElectric vehicles (EVs) battery management systems (BMSs) rely on exact state of charge (SoC) estimations to guarantee efficient and safe operation. Lithium‐ion batteries (LIBs) are favored for EVs due to their extended lifespan, high energy density, and minimal self‐discharge and high voltage. To address these issues, this research propose a LIB SoC prediction based on an actual BMS in EVs. The main objective is improving SoC of LIB. The proposed hybrid strategy is the combined performance of both the dynamic neural networks (DNN) and arithmetic optimization algorithm (AOA). Commonly it is named as DNN‐AOA technique. The SoC of Lithium‐ion batteries are predicted using the DNN approach. The proposed AOA is used to optimize the weight parameter of DNN to enhance prediction accuracy and reliability. By then, the operational MATLAB platform has adopted the proposed framework, and existing procedures are used to compute its execution. The proposed method demonstrates superior existing like Bayesian network (DBN), random vector functional link neural network (RVFLNN) and Gaussian progress regression (GPR). The proposed method yields a lower error value of 0.1 and a higher accuracy value of 98% compared with other existing methods.

A High-Order Numerical Scheme for Efficiently Solving Nonlinear Vectorial Problems in Engineering Applications

In scientific and engineering disciplines, vectorial problems involving systems of equations or functions with multiple variables frequently arise, often defying analytical solutions and necessitating numerical techniques. This research introduces an efficient numerical scheme capable of simultaneously approximating all roots of nonlinear equations with a convergence order of ten, specifically designed for vectorial problems. Random initial vectors are employed to assess the global convergence behavior of the proposed scheme. The newly developed method surpasses methods in the existing literature in terms of accuracy, consistency, computational CPU time, residual error, and stability. This superiority is demonstrated through numerical experiments tackling engineering problems and solving heat equations under various diffusibility parameters and boundary conditions. The findings underscore the efficacy of the proposed approach in addressing complex nonlinear systems encountered in diverse applied scenarios.

Appraisal of microplastic pollution and its related risks for urban indoor environment in Bangladesh using machine learning and diverse risk evolution indices

The widespread presence of Microplastics (MPs) is increasing in the indoor environment due to increasing annual plastic usage, which is becoming a global threat to human health. Therefore, this is the first research in Bangladesh to identify, and characterize, MP pollution and its allied threats to human health in the indoor urban environment, where 80 household dust samples were collected from the whole study area. The presence of MPs in household dust of the urban indoor environment was 25.8 ± 6.43 particles/g with a significant variety, whereas the fiber shape (73%), 0.5–1.00 mm ranged MPs size (58%), blue color (21%), and polystyrene polymer (34%) was the most ubiquitous MPs category. The pollution load index (1.61–2.96) indicated significant pollution due to the high abundance of MPs. Besides, other risks evaluating indices including contamination factor (1.00–3.51), and Nemerow pollution index (1.60–3.51) represent moderate to high MP-induced pollution. The polymer hazard index (119.54 ± 70.34) indicated significant risks for the selected polymers to the indoor environment living inhabitants. Machine learning approaches, especially random forest and support random vector machine were effective in predicting the number of MPs, where EC, salinity, pH, OC, and texture classes acted as controlling factors. Children and adults might be ingesting 4.12 ± 1.01 and 2.27 ± 0.57 particles/day through the ingestion exposure route, which has significant health effects. Polymer-associated lifetime cancer risk assessment results show that there are moderate risks for both adults and children, but children tend to be more susceptible to MP risks. The overall study found that Dhaka was the most severely MPs induced risky division among the others. This study reveals that high quantities of MPs in indoor environments could pose a serious health hazard' to different exposure groups.

Rdfinet: reference-guided directional diverse face inpainting network

The majority of existing face inpainting methods primarily focus on generating a single result that visually resembles the original image. The generation of diverse and plausible results has emerged as a new branch in image restoration, often referred to as “Pluralistic Image Completion”. However, most diversity methods simply use random latent vectors to generate multiple results, leading to uncontrollable outcomes. To overcome these limitations, we introduce a novel architecture known as the Reference-Guided Directional Diverse Face Inpainting Network. In this paper, instead of using a background image as reference, which is typically used in image restoration, we have used a face image, which can have many different characteristics from the original image, including but not limited to gender and age, to serve as a reference face style. Our network firstly infers the semantic information of the masked face, i.e., the face parsing map, based on the partial image and its mask, which subsequently guides and constrains directional diverse generator network. The network will learn the distribution of face images from different domains in a low-dimensional manifold space. To validate our method, we conducted extensive experiments on the CelebAMask-HQ dataset. Our method not only produces high-quality oriented diverse results but also complements the images with the style of the reference face image. Additionally, our diverse results maintain correct facial feature distribution and sizes, rather than being random. Our network has achieved SOTA results in face diverse inpainting when writing. Code will is available at https://github.com/nothingwithyou/RDFINet.

Truncated correlation coefficient test for two random vectors

. Measuring the correlation between two random variables is a classic problem in statistics. The common textbook measures are Pearson r, Spearman ρ, and Kendall τ correlation coefficients. These three values are especially useful for two univariate variables, although they have been extended to two random vectors such as RV, which is a linear correlation coefficient for two random vectors. In this article, we propose a truncated correlation coefficient measure to test whether two random vectors are independent, together with some statistical properties. We perform extensive simulation studies to compare powers of RV and the proposed test. Results show that the proposed test is more powerful than RV to detect the independence. Finally, two real data analyses further show the performance of the proposed test.

An efficient angle-based twin random vector functional link classifier

Random vector functional link (RVFL) has always proven to be an excellent classifier in various application areas of machine learning. In this work, inspired by RVFL and its twin variant, i.e., twin RVFL (TRVFL), we propose an efficient angle-based twin random vector functional link (ATRVFL) to address the binary classification problem. ATRVFL is a general classification model in which the first optimization problem can be found by solving a quadratic programming problem (QPP). The second problem can be described as an unconstrained minimization problem (UMP) which is solved by a system of linear equations. ATRVFL finds the solution by solving a QPP and a UMP instead of solving two QPPs. Therefore, its training time is significantly less than TRVFL. To maximize the angle between the normals of the two hyperplanes, the second hyperplane is chosen to be close to its class. The objective of introducing the idea of angle is to maximise the distance between two hyperplanes to improve the ability to discriminate them in geometric spaces. Experimental analyses are performed on a leaf dataset and 25 real-world benchmark datasets (RWDs) collected from the UCI repository of various fields like medical, biological, etc. The results are evaluated based on classification accuracy, the area under the curve, G-mean and F1-score. The results of ATRVFL are compared with Support Vector Machine (SVM), RVFL, Twin-RVFL (TRVFL), RVFL with ε-insensitive Huber loss (ε-HRVFL), ensemble deep learning-based RVFL network (edRVFL) and Intuitionistic fuzzy random vector functional link classifier (IFRVFLC). The classification accuracy of the proposed model on the leaf dataset is 91.093 % and the highest F1-score of 0.768. Overall, based on experimental analysis it is evident that the proposed ATRVFL shows comparative or better performance than SVM, RVFL, TRVFL, ε-HRVFL, IFRVFLC and edRVFL.

Computing the quadratic numerical range

A novel algorithm for the computation of the quadratic numerical range is presented and exemplified yielding much better results in less time compared to the random vector sampling method. Furthermore, a bound on the probability for the random vector sampling method to produce a point exceeding a neighborhood of the expectation value in dependence on norm and size of the matrix is given.

Optimality Conditions in Control Problems with Random State Constraints in Probabilistic or Almost Sure Form

In this paper, we discuss optimality conditions for optimization problems involving random state constraints, which are modeled in probabilistic or almost sure form. Although the latter can be understood as the limiting case of the former, the derivation of optimality conditions requires substantially different approaches. We apply them to a linear elliptic partial differential equation with random inputs. In the probabilistic case, we rely on the spherical-radial decomposition of Gaussian random vectors in order to formulate fully explicit optimality conditions involving a spherical integral. In the almost sure case, we derive optimality conditions and compare them with a model based on robust constraints with respect to the (compact) support of the given distribution. Funding: The authors thank the Deutsche Forschungsgemeinschaft [Projects B02 and B04 in the “Sonderforschungsbereich/Transregio 154 Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks”] for support. C. Geiersbach acknowledges support from the Deutsche Forschungsgemeinschaft [Germany’s Excellence Strategy–the Berlin Mathematics Research Center MATH+ Grant EXC-2046/1, Project 390685689]. R. Henrion acknowledges support from the Fondation Mathématique Jacques Hadamard [Program Gaspard Monge in Optimization and Operations Research, including support to this program by Electricité de France].

Precise single step and multistep short-term photovoltaic parameters forecasting based on reduced deep convolutional stack autoencoder and minimum variance multikernel random vector functional network

Accurate prediction of photovoltaic (PV) power can significantly alleviate energy crises. However, the inherent randomness and intermittency of PV power pose challenges to the stability and safety of PV-penetrated grid systems. To address this, we have developed a novel hybrid model: a reduced deep convolutional stack autoencoder with a minimum variance multikernel random vector functional link network (RDCSAE-MVMRVFLN). This model enhances grid efficacy and safety. We extract the most informative band-limited intrinsic mode functions (BLIMFs) of highly nonlinear and nonstationary solar energy parameters using an entropy, kurtosis, and correlation coefficient-based information-oriented variational mode decomposition (IOVMD). These efficient BLIMFs are concatenated and input into the RDCSAE for rich, abstract, and discriminative representation computation. A less computationally complex MVMKRVFLN regression method, incorporating these refined representations, is proposed for superior prediction accuracy and reduced computational complexity. Our method shows exceptional performance in predicting solar temperature, irradiation, and power for multi-horizon forecasts with minimal error metrics (correlation coefficients of 0.999±0.001, 0.992±0.001, 0.986±0.02 and 0.978±0.02, and RMSE of 0.016±0.001, 0.024±0.001, 0.034±0.001 and 0.045±0.001 for the interval of 10 minutes, 30 minutes, 1 hour and 3 hours respectively) in both single-step and multi-step forecasting compared to conventional methods. The RDCSAE-MVMKRVFLN model is implemented on a high-speed Xilinx Virtex-5 FPGA embedded processor to validate its simplicity, robustness, and practicability. Additionally, we examine the prediction performance using real-time data from a 1 MW solar farm in Odisha, India, demonstrating the model’s effectiveness and superiority.

Parallel ensemble of a randomization-based online sequential neural network for classification problems using a frequency criterion

Randomization-based neural networks have gained wide acceptance in the scientific community owing to the simplicity of their algorithm and generalization capabilities. Random vector functional link (RVFL) networks and their variants are a class of randomization-based neural networks. RVFL networks have shown promising results in classification, regression, and clustering problems. For real-world applications, learning algorithms that can train with new samples over previous results are necessary because of to the constant generation of problems related to large-scale datasets. Various online sequential algorithms, commonly involving an initial learning phase followed by a sequential learning phase, have been proposed to address this issue. This paper presents a training algorithm based on multiple online sequential random vector functional link (OS-RVFL) networks for large-scale databases using a shared memory architecture. The training dataset is distributed among p OS-RVFL networks, which are trained in parallel using p threads. Subsequently, the test dataset samples are classified using each trained OS-RVFL network. Finally, a frequency criterion is applied to the results obtained from each OS-RVFL network to determine the final classification. Additionally, an equation was derived to reasonably predict the total training time of the proposed algorithm based on the learning time in the initial phase and the time scaling factor compared to the sequential learning phase. The results demonstrate a drastic reduction in training time because of data distribution and an improvement in accuracy because of the adoption of the frequency criterion.

Testing independence based on Spearman’s footrule in high dimensions

. Spearman’s footrule is a widely used tool to discover the relationship between two continuous random variables, mainly because of its robustness, natural interpretation, and simplicity of calculation. In this article, we propose a new test statistic based on the sum of squares of pairwise Spearman’s footrule, to test the mutual independence of a high dimensional random vector. The large sample properties of the proposed test method are established. Simulation results show that the new test has higher power than existing test methods under some circumstances. An example with real life data is discussed to illustrate the usefulness and effectiveness of the proposed test statistic.

Generalized kernel distance covariance in high dimensions: non-null CLTs and power universality

Abstract Distance covariance is a popular dependence measure for two random vectors $X$ and $Y$ of possibly different dimensions and types. Recent years have witnessed concentrated efforts in the literature to understand the distributional properties of the sample distance covariance in a high-dimensional setting, with an exclusive emphasis on the null case that $X$ and $Y$ are independent. This paper derives the first non-null central limit theorem for the sample distance covariance, and the more general sample (Hilbert–Schmidt) kernel distance covariance in high dimensions, in the distributional class of $(X,Y)$ with a separable covariance structure. The new non-null central limit theorem yields an asymptotically exact first-order power formula for the widely used generalized kernel distance correlation test of independence between $X$ and $Y$. The power formula in particular unveils an interesting universality phenomenon: the power of the generalized kernel distance correlation test is completely determined by $n\cdot \operatorname{dCor}^{2}(X,Y)/\sqrt{2}$ in the high-dimensional limit, regardless of a wide range of choices of the kernels and bandwidth parameters. Furthermore, this separation rate is also shown to be optimal in a minimax sense. The key step in the proof of the non-null central limit theorem is a precise expansion of the mean and variance of the sample distance covariance in high dimensions, which shows, among other things, that the non-null Gaussian approximation of the sample distance covariance involves a rather subtle interplay between the dimension-to-sample ratio and the dependence between $X$ and $Y$.

Multi-device wind turbine power generation forecasting based on hidden feature embedding

In recent years, the global installed capacity of wind power has grown rapidly. Wind power forecasting, as a key technology in wind turbine systems, has received widespread attention and extensive research. However, existing studies typically focus on the power prediction of individual devices. In the context of multi-turbine scenarios, employing individual models for each device may introduce challenges, encompassing data dilution and a substantial number of model parameters in power generation forecasting tasks. In this paper, a single-model method suitable for multi-device wind power forecasting is proposed. Firstly, this method allocates multi-dimensional random vectors to each device. Then, it utilizes space embedding techniques to iteratively evolve the random vectors into representative vectors corresponding to each device. Finally, the temporal features are concatenated with the corresponding representative vectors and inputted into the model, enabling the single model to accomplish multi-device wind power forecasting task based on device discrimination. Experimental results demonstrate that our method not only solves the data dilution issue and significantly reduces the number of model parameters but also maintains better predictive performance. Future research could focus on using more interpretable space embedding techniques to observe representation vectors of wind turbine equipment and further explore their semantic features.

Ensemble Deep Random Vector Functional Link Network Using Privileged Information for Alzheimer's Disease Diagnosis.

Alzheimer's disease (AD) is a progressive brain disorder. Machine learning models have been proposed for the diagnosis of AD at early stage. Recently, deep learning architectures have received quite a lot attention. Most of the deep learning architectures suffer from the issues of local minima, slow convergence and sensitivity to learning rate. To overcome these issues, non-iterative learning based deep randomized models especially random vector functional link network (RVFL) with direct links have proven to be successful. However, deep RVFL and its ensemble models are trained only on normal samples. In this paper, deep RVFL and its ensembles are enabled to incorporate privileged information, as the standard RVFL model and its deep models are unable to use privileged information. To fill this gap, we have incorporated learning using privileged information (LUPI) in deep RVFL model, and propose deep RVFL with LUPI framework (dRVFL+). Privileged information is available while training the models. As RVFL is an unstable classifier, we propose ensemble deep RVFL+ with LUPI framework (edRVFL+) which exploits the LUPI as well as the diversity among the base leaners for better classification. Unlike traditional ensemble approach wherein multiple base learners are trained, the proposed edRVFL+ model optimises a single network and generates an ensemble via optimization at different levels of random projections of the data. Both dRVFL+ and edRVFL+ efficiently utilise the privileged information which results in better generalization performance. In LUPI framework, half of the available features are used as normal features and rest as the privileged features. However, we propose a novel approach for generating the privileged information. We utilise different activation functions while processing the normal and privileged information in the proposed deep architectures. To the best of our knowledge, this is first time that a separate privileged information is generated. The proposed dRVFL+ and edRVFL+ models are employed for the diagnosis of Alzheimer's disease. Experimental results demonstrate the superiority of the proposed dRVFL+ and edRVFL+ models over baseline models. Thus, the proposed edRVFL+ model can be utilised in clinical setting for the diagnosis of AD.

Reliability Analysis of a System Designed to Withstand a Specified Shock Magnitude Range

The system under consideration has 𝑛 independent components, and its operation relies on the functioning of at least 𝑘 components, 1 ≤ 𝑘 ≤ 𝑛. The system experiences (𝑛 + 1) distinct shocks. Shock 𝑗 impacts the 𝑗!" component, 𝑗 = 1, 2, . . . , 𝑛, while shock (𝑛 + 1) simultaneously impacts all components. Any shock is lethal if its magnitude is below or above the component-designed thresholds 𝑑# or 𝑑$, respectively. A shock is characterized by its magnitude and arrival time, forming a bivariate random vector. The bivariate random vectors specifying the magnitudes and the arrival times of the shocks are assumed to be independent and follow non-identical bivariate distributions. The reliability of a 𝑘-out-of-𝑛: 𝐺 system under the influence of this type of shocks is derived. The reliability of parallel and series systems is obtained as special situations. The bivariate Pareto type I distribution is applied as an example of the bivariate distribution of the magnitude and arrival time of the shocks. Furthermore, numerical illustrations are conducted to highlight the theoretical results obtained.