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The alternating active-phase algorithm (AAPA) is widely recognized as being efficient for multi-material topology optimization. It has the advantages of easy implementation and broad applicability, but faces shortcomings, such as a uniform punishment intensity for all elements, excessive gray elements, and slow optimization convergence. To overcome these shortcomings, proposed here is an enhanced AAPA (EAAPA), the core ideas of which are as follows. (1) A new equal-scale Heaviside projection function (EHPF) is proposed, with the scale factor introduced to adjust the physical density adaptively to overcome the challenges of the invariance of the density sum and the uniqueness of projecting faced by the traditional Heaviside projection function. This adaptation reduces the number of gray elements and accelerates the convergence. (2) An innovative solid isotropic material with exponential sigmoid function (SIMESF) is constructed, with a penalty threshold and a steepness factor introduced to divide different penalty intensity regions and control their transition steepness. This improves the applicability and flexibility of the interpolation model, addressing the issue of a single punishment intensity in the solid isotropic material with penalization. The parameter values of the SIMESF model are explored via the design of a bridge, and the performances of AAPA and EAAPA are evaluated via the designs of simply supported and cantilever beams. The results show clearly that EAAPA has significant advantages in terms of optimization effectiveness and convergence speed. [ABSTRACT FROM AUTHOR]

Seismic data reconstruction is a crucial process involving the restoration of missing or corrupted traces to create a uniform dataset for subsequent data processing. Various factors such as equipment failures, and surface obstacles, result in irregularly located or corrupted traces. The absence of these traces can compromise the quality and accuracy of the resulting image. To address this issue, the Nonuniform Fast Fourier Transform (NUFFT) method is employed to reconstruct missing traces in datasets with non-uniformly sampled data. It works by interpolating the non-uniformly sampled data onto a regular grid, enabling the traditional Fast Fourier Transform application for data recovery. This interpolation process is adjusted using a kernel function to account for non-uniform sampling and reduce aliasing artifacts. The outcome is a collection of Fourier coefficients that can be utilized to reconstruct missing or incomplete parts of data. This problem is transformed into a linear constraint problem, which is efficiently solved using the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). In this study, we explore various techniques aimed at improving the convergence of FISTA, collectively referred to as improved FISTA methods. To validate the NUFFT+FISTA method for data reconstruction, we conducted numerical tests using 3D and 2D synthetic datasets, as well as field data. These tests show the advantages of the Greedy-FISTA in terms of convergence rate and affirm the accuracy of this approach in filling missing data traces. [ABSTRACT FROM AUTHOR]

This study proposes multivariate kernel density estimation by stagewise minimization algorithm based on U-divergence and a simple dictionary. The dictionary consists of an appropriate scalar bandwidth matrix and a part of the original data. The resulting estimator brings us data-adaptive weighting parameters and bandwidth matrices, and provides a sparse representation of kernel density estimation. We develop the non-asymptotic error bound of the estimator that we obtained via the proposed stagewise minimization algorithm. It is confirmed from simulation studies that the proposed estimator performs as well as, or sometimes better than, other well-known density estimators. [ABSTRACT FROM AUTHOR]

The quality of visual media is critically impacted by low illumination and the presence of airborne particulates, leading to challenges in brightness balance, color saturation, and texture clarity which are detrimental to various applications in image processing and computer vision. Addressing these challenges, this study introduces a novel image enhancement algorithm that significantly improves the quality of degraded images. Our proposed method, the multi-channel phase activation and multi-constraint dark channel prior (MMDCP), leverages an innovative approach by integrating the phase-adjusted Gaussian kernel function for brightness channel optimization in the Fourier transform frequency domain. This optimization is enhanced through the application of a saturated dark channel prior, achieving simultaneous brightness enhancement and color fidelity. Furthermore, we refine the dark channel prior deblurring algorithm by incorporating intensity, brightness, and color constraints to correct overexposure issues and color offsets in the reconstructed images. The efficacy of the MMDCP algorithm is demonstrated through extensive experimentation, comparing it against six contemporary image enhancement algorithms using two types of objective indicators and subjective assessments across four public datasets. The MMDCP algorithm consistently outperforms the existing methods, with a notable average improvement of 20% in PSNR and 19.6% in SSIM metrics, substantiating its superiority in enhancing brightness, detail, and color accuracy. This study's results underline the MMDCP algorithm's robustness and versatility in improving image quality across various conditions, including daytime, nighttime, indoor, and outdoor settings. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a new primal-dual second-order corrector interior-point algorithm for semidefinite optimization. The algorithm is based on Darvay–Takács neighbourhood of the central path. In the new algorithm, the search directions are determined by the Darvay–Takács's direction and a second-order corrector direction in each iteration. The iteration complexity bound is $ O(\sqrt {n}L) $ O (n L) for the Nesterov–Todd scaling direction, which coincides with the best-known complexity results for semidefinite optimization. Finally, numerical experiments show that the proposed algorithm is promising. [ABSTRACT FROM AUTHOR]

Spatiotemporally mapping winter wheat is imperative for informing and shaping global food security policies. Traditional mapping methods heavily rely on sufficient and reliable samples obtained through labor-intensive fieldwork and manual sample collection. However, these methods are time-consuming, costly, and lack timely and continuous data collection. To address these challenges and fully leverage remote sensing big data and cloud computing platforms like Google Earth Engine (GEE), this paper developed an algorithm for Auto-Generating Winter Wheat Samples for mapping (AGWWS). The AGWWS utilizes historical samples to determine the optimal migration threshold by measuring Spectral Angle Distance (SAD), Euclidean Distance (ED), and Near-Infrared band Difference Index (NIRDI). This facilitates the auto-generation of winter wheat sample sets for the years 2000, 2005, 2010, 2015, and 2021. Approximately two-thirds of the samples were allocated for training, with the remaining one-third used for validating the mapping method, employing the One-Class Support Vector Machine (OCSVM). The Huang–Huai–Hai (HHH) Plain, a major winter wheat production region, was selected to perform the algorithm and subsequent analysis on. Different combinations of the hyper-parameters, gamma and nu, of the OCSVM based on the Gaussian Radial Basis Function Kernel were tested for each year. Following correlation analysis between the winter wheat area derived from the generated maps and the national statistical dataset at the city level, the map with the highest corresponding R2 was chosen as the AGWWS map for each year (0.77, 0.77, 0.80, 0.86, and 0.87 for 2000, 2005, 2010, 2015, and 2021, respectively). The AGWWS maps ultimately achieved an average Overall Accuracy of 81.65%. The study then explores the Non-Grain Production of Winter Wheat (NGPOWW) by analyzing winter wheat change maps from 2000–2005, 2005–2010, 2005–2010, and 2015–2021 in the HHH Plain. Despite an overall increase in the total planted area of winter wheat, the NGPOWW phenomena has led to concerning winter wheat planting marginalization. Compensatory winter wheat areas are notably situated in mountainous and suburban cultivated lands with low qualities. Consequently, despite the apparent expansion in planted areas, winter wheat production is anticipated to be adversely affected. The findings highlight the necessity for improved cultivated land protection policies monitoring the land quality of the compensation and setting strict quota limits on occupations. [ABSTRACT FROM AUTHOR]

Relying upon Legendre polynomials, an improved multiwavelet orthonormal basis is constructed in the reproducing kernel space. We study boundary value problems (BVPs) based on the improved wavelet orthonormal basis and construct the ε$$ \varepsilon $$‐best approximate solution. Convergence and the stability are discussed; this method has higher order convergence. The main advantage of the wavelet based our method is its efficiency and simple applicability for a variety of boundary conditions. Some numerical tests even including singular BVPs reveal the stability and efficiency of the new algorithm. [ABSTRACT FROM AUTHOR]

Spectral clustering has become a prevalent option for data clustering as it performs well on non-convex spatial datasets with sophisticated structures. The spectral clustering effects depend on the construction of the similarity graph matrix. In this paper, in order to further enhance the clustering performance, we propose a novel similarity measure function based on neighbor relations. The proposed method is called SC-NR. It uses the Gaussian kernel function to measure the similarity between two objects. Since Euclidean distance cannot fully reflect the relation between data, this method adds a weight related to the order of nearest neighbors to the distance between two points. The similarity is better expressed by weighted-Euclidean distance. In experiments, we compared the proposed method with the previous works via the external indexes, that is, clustering accuracy (ACC), normalized mutual information (NMI), and F-measure. The comparison of indexes with state-of-the-art methods demonstrates the superiority of our algorithm. The experiment includes six synthetic datasets and twelve real-world datasets. For instance, in the PenDigits dataset F-measure metric is 16.50% higher than the current algorithms. [ABSTRACT FROM AUTHOR]

Using a kernel experimental design (KExpD) with a few of inputs (factors) and experimental trials (runs) as an initial-stage is a practical solution for obtaining prior information about the phenomenon under the experimentation that guide the experimenters to identify the active factors and select their values (levels). Based on the prior information, extending the KExpD by adding more factors, runs and/or levels for constructing extended ExpDs (EExpDs) as follow-up stages is necessary for optimizing the outputs, estimating the factor-effects without confounding, and getting further precious information. The practice demonstrated that large EExpDs are needed for many real-world multidimensional experiments and the existing algorithms loss their efficiency in such cases. This article gives a novel low complexity and highly accurate algorithm for extending small KExpDs with mixed two- and three-level factors to large EExpDs. Theoretical linkages between the KExpDs and their corresponding EExpDs are given to investigate necessary and/or sufficient conditions for optimizing the resulting EExpDs. Numerical justifications for the efficiency and simplicity of the new technique are given by comparing its performance with the existing techniques. The main results show that: (i) The new technique gives new optimal designs that are better than the existing recommended designs. (ii) Even if some existing techniques can generate designs with the same performance as the new optimal designs, the new technique takes about one second to generate its new optimal designs, whereas the existing techniques need many hours or days to generate equivalent designs. [ABSTRACT FROM AUTHOR]

This paper proposes algorithms to model fractional (dynamical) behaviors using non-singular rational kernels whose interest is first demonstrated on a pure power law function. Two algorithms are then proposed to find a non-singular rational kernel that allows the input-output data to be fitted. The first one derives the impulse response of the modeled system from the data. The second one finds the interlaced poles and zeros of the rational function that fits the impulse response found using the first algorithm. Several applications show the efficiency of the proposed work. [ABSTRACT FROM AUTHOR]

In the context of intelligent driving, pedestrian detection faces challenges related to low accuracy in target recognition and positioning. To address this issue, a pedestrian detection algorithm is proposed that integrates a large kernel attention mechanism with the YOLOV5 lightweight model. The algorithm aims to enhance long-term attention and dependence during image processing by fusing the large kernel attention module with the C3 module. Furthermore, it addresses the lack of long-distance relationship information in channel and spatial feature extraction and representation by introducing the Coordinate Attention mechanism. This mechanism effectively extracts local information and focused location details, thereby improving detection accuracy. To improve the positioning accuracy of obscured targets, the alpha CIOU bounding box regression loss function is employed. It helps mitigate the impact of occlusions and enhances the algorithm's ability to precisely localize pedestrians. To evaluate the effectiveness of trained model, experiments are conducted on the BDD100K pedestrian dataset as well as the Pascal VOC dataset. Experimental results demonstrate that the improved attention fusion YOLOV5 lightweight model achieves an average accuracy of 60.3%. Specifically, the detection accuracy improves by 1.1% compared to the original YOLOV5 algorithm, and the accuracy performance index reaches 73.0%. These findings strongly indicate the proposed algorithm in significantly enhancing the accuracy of pedestrian detection in road scenes. [ABSTRACT FROM AUTHOR]

Dealing with classification problems requires the crucial step of feature selection (FS), which helps to reduce data dimensions and shorten classification time. Feature selection and support vector machines (SVM) classification method for banknote dirtiness recognition based on marine predator algorithm (MPA) with mathematical functions was proposed. The mathematical functions were mainly used to improve the optimizatio of MPA for feature parameter selection, and the loss function and kernel function parameters of the SVM are optimized by slime mold optimization algorithm (SMA) and marine predator algorithm. According to the experimental results, the accuracy of identifying dirtiness on the entire surface of the banknote reaches 89.07%. At the same time, according to the image pattern distribution of the banknoteS, the white area image in the middle left of the collected banknote is selected by the same method to select the feature parameters and identify the dirtiness of the banknoteS. The accuracy of dirtiness recognition in the middle left white area reached 86.67%, this shows that the white area in the middle left can basically completely replace the entire banknote. To confirm the effectiveness of the feature selection method, the proposed optimization method has been compared with four other swarm intelligent optimization algorithms to verify its performance. The experiment results indicate that the enhanced strategy is successful in improving the performance of MPA. Moreover, the robustness analysis proves its effectiveness. [ABSTRACT FROM AUTHOR]

This paper employs two data-driven methods, Random Forest (RF) and Support Vector Machines (SVM), to develop mineral prospectivity models for an epithermal Au deposit. Four distinct models are presented for comparison: one employing RF and three using SVM with different kernel functions—namely linear, Radial Basis Function (RBF), and polynomial. The analysis leverages a compact training dataset, encompassing just 20 deposits, with deposit and non-deposit locations chosen from known mineral occurrences. Fourteen predictor maps are constructed based on the available data and the exploration model. The findings indicate that RF is more stable and robust than SVM, regardless of the kernel function implemented. While all SVM models outperformed the RF model in terms of classification capability on the training dataset achieving an accuracy exceeding 89% versus 78% for the RF model, the success rate curves suggest superior predictive abilities of RF over SVM models. This implies that the SVM models may be overfitting the training data due to the limited quantity of training deposits. [ABSTRACT FROM AUTHOR]

The thermal management system is one of the important assemblies that ensure the secure operation of electric vehicles (EVs). Using intelligent algorithms to optimize the control strategy of the thermal management system can reduce energy consumption under the premise of effective heat dissipation of EVs. This paper attempts to construct the control strategy of EV thermal management system by coupling the modified genetic algorithm (MGA) and support vector regression (SVR). Firstly, the double-population adaptive mutation method and a novel optimization process are adopted to obtain MGA. Afterward, the performance of MGA is verified by four benchmark functions compared with three typical algorithms, which are genetic algorithm (GA), double-population genetic algorithm (DPGA), and quantum genetic algorithm (QGA). The results demonstrate that the accuracy and stability of MGA are obviously better than the other three algorithms. Secondly, MGA is applied to modify parameters of SVR kernel function, and the accuracy of MGA-SVR algorithm is verified by the Auto-MPG and Computer Hardware data sets. The mean square deviations of the SVR algorithm test set are 0.0186 and 0.0806, respectively, and the mean square deviations of the MGA-SVR algorithm test set are 0.0099 and 0.0054, respectively, which fully shows that MGA-SVR have more accurate forecasting capabilities. Finally, the thermal management system model of EV is built by the one-dimensional simulation software KULI. Under the Chinese working condition, fan speed which meets the cooling requirements of the motor and controller is obtained from the KULI model, and the database is constructed. Then, MGA-SVR is trained by database and employed to predict fan speed under the Chinese working condition and obtain control strategy of the thermal management system. Compared with traditional control strategy, the thermal management system based on MGA-SVR control strategy can not only meet the radiating requirements, but also effectively reduce the power consumption of fans. [ABSTRACT FROM AUTHOR]

This paper considers linear and nonlinear fractional delay Volterra integrodifferential equation of order ρ in the Atangana–Beleanu–Caputo (ABC) sense. We used continuous Laplace transform (CLT) to find equivalent Volterra integral equations that have been used together with the Arzela–Ascoli theorem and Schauder's fixed point theorem to prove the local existence solution. Moreover, the obtained Volterra integral equations and the contraction mapping theorem have been successfully applied to construct and prove the global existence and uniqueness of the solution for the considered fractional delay integrodifferential equation (FDIDE). The Galerkin algorithm instituted within shifted Legendre polynomials (SLPs) is applied in the approximation procedure for the corresponding delay equation. Indeed, by this algorithm, we get algebraic system models and by solving this system we gained the approximated nodal solution. The reliability of the method and reduction in the size of the computational work give the algorithm wider applicability. Linear and nonlinear examples are included with some tables and figures to show the effectiveness of the method in comparison with the exact solutions. Finally, some valuable notes and details extracted from the presented results were presented in the last part, with the sign to some of our future works. [ABSTRACT FROM AUTHOR]

A multilayer soil structure model is fundamental to design grounding systems. A new method is presented to invert the structure parameters of horizontal multilayer soil. The structure parameters of soil are determined by analyzing the kernel function of the integral equation of the apparent resistivity. The essence of the proposed method avoids the difficulties encountered in general optimization methods; namely, the calculation of the apparent resistivity and its derivative. [ABSTRACT FROM AUTHOR]

In this paper, we propose a predictor–corrector interior-point method for symmetric cone optimization. The proposed algorithm is based on a new one-norm neighbourhood, which is an even wider neighbourhood than a given negative infinity neighbourhood. The convergence is shown for a commutative class of search directions, which includes the Nesterov–Todd direction and the xs and sx directions. We show that the algorithm has O (r (c o n d (G)) 1 / 4 log ⁡ ϵ − 1) iteration complexity bound which is better than that of the usual wide neighbourhood algorithm O (r c o n d (G) log ⁡ ϵ − 1). To our knowledge, these are the best complexity results obtained so far for the solution of symmetric cone optimization. We prove that beside the predictor steps, each corrector step also reduces the duality gap by a rate of 1 − 1 O (r) . Finally, numerical experiments show that the proposed algorithm is efficient and reliable. [ABSTRACT FROM AUTHOR]

To solve the problem that the existing semi-supervised FISHER discriminant analysis algorithm (FDA) cannot effectively use both labeled and unlabeled data for learning, we propose a semi-supervised Kernel local FDA Algorithm based on density peak clustering pseudo-labels (SDPCKLFDA). First, the proposed algorithm adopts the density peak clustering algorithm to generate the pseudo cluster labels for labeled and unlabeled data, and then the generated pseudo-labels are explored to construct two regularization strategies. The two regularization strategies are used to regularize the corresponding within-class scatter matrix and between-class scatter matrix of the local Fisher discriminant analysis, and finally the optimal projection vector is obtained by solving the objective function of the local Fisher discriminant analysis. The two constructed regularization strategies can not only effectively enhance the discriminant performance of the extracted feature but also make the proposed algorithm suitable for multimodal and noisy data. In addition, to accommodate nonlinear and non-Gaussian datasets, we also develop a kernel version of the proposed algorithm with the help of kernel trick. In the experiment, the proposed algorithm is compared with the FDA and its improved algorithms on some benchmark artificial datasets and UCI datasets. The experimental results show that the discriminant performance of the proposed algorithm has been significantly improved compared with the other algorithms. [ABSTRACT FROM AUTHOR]

In view of the problems of sensitive initial value, inapplicability of discrete data and large error in the existing differential privacy clustering location protection methods, a differential privacy fuzzy clustering location protection method is proposed in this study. Firstly, the points are mapped to the feature space by Gaussian kernel function, and the computational efficiency is significantly improved due to the relatively small amount of computation. Secondly, the differential privacy is combined with the improved fuzzy C-means clustering algorithm, so that each group of input data no longer belongs to a specific class, but to the degree of membership. Finally, the Laplacian noise satisfying the differential privacy constraint is added to the centroid of the clustering set to obtain the disturbance position of each point, and the disturbance position is used to query. The experimental results show that the differential privacy fuzzy clustering location protection method reduces the query error and improves the efficiency of the algorithm under the premise of ensuring the location privacy security. [ABSTRACT FROM AUTHOR]

This paper designs a maritime anomaly detection algorithm based on a support vector machine (SVM) that considers the spatiotemporal and motion features of trajectories. Since trajectories are two-dimensional, it is difficult to present their motion features. To accurately describe trajectory features, a novel trajectory feature extraction method based on statistical theory is proposed in this paper. This method maps trajectories onto a high-dimensional space, which can account for both the spatiotemporal features and motion features of the trajectories. With the proposed feature extraction method, the density-based spatial clustering of applications with noise algorithm is employed to recognize vessel traffic patterns by simultaneously considering the spatiotemporal and motion features. Then, an improved SVM is designed by employing a weighted hybrid kernel function and differential operator to detect anomalous behaviours from recognized vessel traffic patterns that include the spatiotemporal and motion characteristics. Compared with standard SVM, it can adaptively determine the optimal kernel function according to sample set. Finally, a numerical example based on automatic identification system data from the waters off Chengshan Jiao is fulfilled to verify the proposed algorithm effectiveness and accuracy. [ABSTRACT FROM AUTHOR]

In view of the shortcomings of existing artificial neural network (ANN) and support vector regression (SVR) in the application of three-dimensional displacement back analysis, Gaussian process regression (GPR) algorithm is introduced to make up for the shortcomings of existing intelligent inversion methods. In order to improve the generality of the standard GPR algorithm with single kernel function, an improved Gaussian process regression (IGPR) algorithm with combined kernel function is proposed by adding two single kernel functions. In addition, in the training process of IGPR model, the particle swarm optimization (PSO) is combined with the IGPR model (PSO-IGPR) to optimize the parameters of the IGPR model. After the IGPR model can accurately map the relationship between geomechanical parameters and rock mass deformation, the PSO algorithm is directly used to search the best geomechanical parameters to match the deformation calculated by igpr model with the measured deformation of rock mass. The application case of Beikou tunnel shows that the combined kernel function GPR has higher identification accuracy than the single kernel function GPR and SVR model, the IGPR model with automatic correlation determination (ARD) kernel function can obtain higher identification accuracy than the IGPR model with isotropic (ISO) kernel function, and the PSO-IGPR hybrid model based on ARD kernel function has the highest identification accuracy. Therefore, this paper proposes a displacement back analysis method of the PSO-IGPR hybrid algorithm based on ARD kernel function, which can be used to identify the geomechanical parameters of rock mass and solve other engineering problems. [ABSTRACT FROM AUTHOR]

The experts' decisions and evaluating the patients' data are the most significant parts affecting the breast cancer analysis. For early breast cancer detection, numerous techniques of machine learning not only can assist in examining and diagnosis the medical data quickly but also decrease the potential errors that could be occurred due to inexpert or unskilled decision-makers. Support vector machine is one of the famous classifiers that has already made an important contribution to the field of cancer classification. However, configurations of different kernel function and their parameters can significantly affect the performance of the SVM classifier. To further improve the classification accuracy of the SVM classifier for breast cancer diagnosis, an intelligent cancer classification method is proposed based on selecting a feature subset and optimizing the relevant parameters (i.e., penalty factor parameter (c ) and kernel parameter γ ) of the SVM classifier concurrently through an intelligent algorithm using the Jaya algorithm. Then, this method (Jaya-SVM) was applied to precisely characterize the breast cancer dataset, including 699 samples, which are 458 and 241 for benign and malignant, respectively. Furthermore, to evaluate the effectiveness of the proposed Jaya-SVM classifier, it is compared in terms of the computational complexity and the classification accuracy with several combinatorial metaheuristic classifiers, namely the genetic algorithm (GA), differential evolution (DE), particle swarm optimization (PSO), and cuckoo search (CS) based-SVM. Apart from this, a Breast Cancer Coimbra Dataset taken from the UCI library is used to validate the effectiveness of the proposed method. The results are presented, explained, and conclusions are drawn. [ABSTRACT FROM AUTHOR]

Over the years, research on fuzzy clustering algorithms has attracted the attention of many researchers, and they have been applied to various areas, such as image segmentation and data clustering. Various fuzzy clustering algorithms have been put forward based on the initial Fuzzy C-Means clustering (FCM) with Euclidean distance. However, the existing fuzzy clustering approaches ignore two problems. Firstly, clustering algorithms based on Euclidean distance have a high error rate, and are more sensitive to noise and outliers. Secondly, the parameters of the fuzzy clustering algorithms are hard to determine. In practice, they are often determined by the user's experience, which results in poor performance of the clustering algorithm. Therefore, considering the above deficiencies, this paper proposes a novel fuzzy clustering algorithm by combining the Gaussian kernel function and Grey Wolf Optimizer (GWO), called Kernel-based Picture Fuzzy C-Means clustering with Grey Wolf Optimizer (KPFCM-GWO). In KPFCM-GWO, the Gaussian kernel function is used as a symmetrical measure of distance between data points and cluster centers, and the GWO is utilized to determine the parameter values of PFCM. To verify the validity of KPFCM-GWO, a comparative study was conducted. The experimental results indicate that KPFCM-GWO outperforms other clustering methods, and the improvement of KPFCM-GWO is mainly attributed to the combination of the Gaussian kernel function and the parameter optimization capability of the GWO. What is more, the paper applies KPFCM-GWO to analyzes the value of an airline's customers, and five levels of customer categories are defined. [ABSTRACT FROM AUTHOR]

• We propose an priori information extraction method based on filter combination. • We construct a comprehensive sample library containing various priori information. • We propose a similarity measure based on prior information for adaptive filtering. • A robust infrared small target detection algorithm is proposed. • Our algorithm detects low signal to clutter ratio targets with good performance. Infrared small target detection in complex backgrounds remains a big challenge due to its small size and weak energy, which makes it easy to be submerged in complex backgrounds. Common filtering algorithms are difficult to apply to various complex scenes and generate many false alarms and poor robustness. Therefore, this paper proposes an infrared small target detection algorithm based on filter kernel combination optimization learning method. For the sample image block use typical filter kernels and weight coefficients to calculate the combination of filtering results, and construct the loss function of the results and the true value. The optimal weight coefficients are learned using an optimization method, which effectively achieves the fusion of multiple features, then we build a sample library containing comprehensive priori information. In the implementation, an online inference method based on similarity measure is proposed to match test images with sample library image blocks to obtain optimal combination weights. By utilizing the comprehensive priori information to enhance the adaptive ability of the algorithm for various complex backgrounds. Finally, get the position of the infrared small target. The experimental results show that our algorithm has excellent detection performance for infrared small targets with complex background and low signal to clutter ratio, and the AUC value is 0.9980, which is more robust than other comparative algorithms. [ABSTRACT FROM AUTHOR]

Using a variable ℓ p ≥ 1 -norm penalty on the slacks, the recently introduced ℓ p -norm Support Vector Data Description (ℓ p -SVDD) method has improved the performance in novelty detection over the baseline approach, sometimes remarkably. This work extends this modelling formalism in multiple aspects. First, a large-margin extension of the ℓ p -SVDD method is formulated to enhance generalisation capability by maximising the margin between the positive and negative samples. Second, based on the Frank–Wolfe algorithm, an efficient yet effective method with predictable accuracy is presented to optimise the convex objective function in the proposed method. Finally, it is illustrated that the proposed approach can effectively benefit from a multiple kernel learning scheme to achieve state-of-the-art performance. The proposed method is theoretically analysed using Rademacher complexities to link its classification error probability to the margin and experimentally evaluated on several datasets to demonstrate its merits against existing methods. • The l p -SVDD approach is extended to a large-margin setting. • An efficient method is presented for the optimisation of the proposed objective function. • The proposed method can benefit from a multiple kernel learning framework. • The proposed method is theoretically analysed using Rademacher complexities. • Experimental evaluation results confirm the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

In view of the disadvantages of the existing pose estimation algorithm, which has low real-time performance and the positioning accuracy will be greatly reduced in dynamic scene, a compound deep learning and parallel computing algorithm (DP-PE) is proposed. The detection algorithm based on deep learning is used to detect dynamic objects in the environment, and the dynamic feature points are removed before the matching of feature points to reduce the impact of dynamic objects on the positioning accuracy; A method for distinguishing "pseudo-dynamic objects" is proposed to solve the problem that the stationary vehicles and pedestrians in the environment are regarded as dynamic objects. The parallel computing framework for feature point extraction and matching is established on CPU-GPU heterogeneous platform to speed up DP-PE; In the localization part of DP-PE, we propose a 3D interior point detection strategy to achieve parallel search of map points, and the saturated linear kernel function is used to act on reprojection error to realize the parallelization of pose optimization. We verify the algorithm on KITTI dataset, the experimental results show that average speedup ratio of feature point extraction and matching is 6.5 times, and the overall computational efficiency of DP-PE is about 7 times higher than that before acceleration, which can realize high precision and efficient pose estimation in dynamic scene. [ABSTRACT FROM AUTHOR]

We analyse the scaling matrix, search direction, and neighbourhood used in MOSEK's algorithm for nonsymmetric conic optimization [J. Dahl and E.D. Andersen, A primal-dual interior-point algorithm for nonsymmetric exponential-cone optimization, preprint (2019)]. It is proven that these can be used to compute a near-optimal solution to the homogeneous self-dual model in polynomial time. This provides a theoretical foundation for MOSEK's nonsymmetric conic algorithm. The main steps in the analysis are sandwiching MOSEK's scaling matrix between the primal and dual barrier's Hessians, and using this information to carefully check all the neighbourhood conditions after a small, improving step is taken. [ABSTRACT FROM AUTHOR]

Wireless sensor network is an ad hoc network with sensing capability. Usually, a large number of sensor nodes are randomly deployed in an unreachable environment or complex area for data collection and transmission, which can realize the perception and monitoring of the target area or specific objects and transmit the obtained data to the remote end of the system. Human health activity recognition algorithm is a hot topic in the field of computer. Based on the small sample problem and the linear indivisibility of real samples encountered in metric learning, this paper proposes a human activity recognition algorithm for wireless sensor networks. Human activity recognition algorithm for wireless sensor networks uses human activity recognition algorithm to solve the singularity of intraclass divergence matrix, so as to reduce the impact of small sample problem. The algorithm maps two different feature spaces to the high-dimensional linearly separable kernel space through the corresponding kernel function, calculates the distance between samples in the two projected feature subspaces to obtain two distance measurement functions, and finally linearly combines them with weights to obtain the final distance measurement function. [ABSTRACT FROM AUTHOR]

Combining multiple biomarkers to provide predictive models with a greater discriminatory ability is a discipline that has received attention in recent years. Choosing the probability threshold that corresponds to the highest combined marker accuracy is key in disease diagnosis. The Youden index is a statistical metric that provides an appropriate synthetic index for diagnostic accuracy and a good criterion for choosing a cut-off point to dichotomize a biomarker. In this study, we present a new stepwise algorithm for linearly combining continuous biomarkers to maximize the Youden index. To investigate the performance of our algorithm, we analyzed a wide range of simulated scenarios and compared its performance with that of five other linear combination methods in the literature (a stepwise approach introduced by Yin and Tian, the min-max approach, logistic regression, a parametric approach under multivariate normality and a non-parametric kernel smoothing approach). The obtained results show that our proposed stepwise approach showed similar results to other algorithms in normal simulated scenarios and outperforms all other algorithms in non-normal simulated scenarios. In scenarios of biomarkers with the same means and a different covariance matrix for the diseased and non-diseased population, the min-max approach outperforms the rest. The methods were also applied on two real datasets (to discriminate Duchenne muscular dystrophy and prostate cancer), whose results also showed a higher predictive ability in our algorithm in the prostate cancer database. [ABSTRACT FROM AUTHOR]

In view of the shortcomings of existing artificial neural network (ANN) and support vector regression (SVR) in the application of three-dimensional displacement back analysis, Gaussian process regression (GPR) algorithm is introduced to make up for the shortcomings of existing intelligent inversion methods. In order to improve the generality of the standard GPR algorithm with single kernel function, an improved Gaussian process regression (IGPR) algorithm with combined kernel function is proposed by adding two single kernel functions. In addition, in the training process of IGPR model, the particle swarm optimization (PSO) is combined with the IGPR model (PSO-IGPR) to optimize the parameters of the IGPR model. After the IGPR model can accurately map the relationship between geomechanical parameters and rock mass deformation, the PSO algorithm is directly used to search the best geomechanical parameters to match the deformation calculated by igpr model with the measured deformation of rock mass. The application case of Beikou tunnel shows that the combined kernel function GPR has higher identification accuracy than the single kernel function GPR and SVR model, the IGPR model with automatic correlation determination (ARD) kernel function can obtain higher identification accuracy than the IGPR model with isotropic (ISO) kernel function, and the PSO-IGPR hybrid model based on ARD kernel function has the highest identification accuracy. Therefore, this paper proposes a displacement back analysis method of the PSO-IGPR hybrid algorithm based on ARD kernel function, which can be used to identify the geomechanical parameters of rock mass and solve other engineering problems. [ABSTRACT FROM AUTHOR]

In the lung computer-aided detection (Lung CAD) system, the region of interest (ROI) of lung nodules has more false positives, making the imbalance between positive and negative (true positive and false positive) samples more likely to lead to misclassification of true positive nodules, a cost-sensitive multikernel learning support vector machine (CS-MKL-SVM) algorithm is proposed. Different penalty coefficients are assigned to positive and negative samples, so that the model can better learn the features of true positive nodules and improve the classification effect. To further improve the detection rate of pulmonary nodules and overall recognition accuracy, a score function named F-new based on the harmonic mean of accuracy (ACC) and sensitivity (SEN) is proposed as a fitness function for subsequent particle swarm optimization (PSO) parameter optimization, and a feasibility analysis of this function is performed. Compared with the fitness function that considers only accuracy or sensitivity, both the detection rate and the recognition accuracy of pulmonary nodules can be improved by this new algorithm. Compared with the grid search algorithm, using PSO for parameter search can reduce the model training time by nearly 20 times and achieve rapid parameter optimization. The maximum F-new obtained on the test set is 0.9357 for the proposed algorithm. When the maximum value of F-new is achieved, the corresponding recognition ACC is 91%, and SEN is 96.3%. Compared with the radial basis function in the single kernel, the F-new of the algorithm in this paper is 2.16% higher, ACC is 1.00% higher and SEN is equal. Compared with the polynomial kernel function in the single kernel, the F-new of the algorithm is 3.64% higher, ACC is 1.00% higher and SEN is 7.41% higher. The experimental results show that the F-new, ACC and SEN of the proposed algorithm is the best among them, and the results obtained by using multikernel function combined with F-new index are better than the single kernel function. Compared with the MKL-SVM algorithm of grid search, the ACC of the algorithm in this paper is reduced by 1%, and the results are equal to those of the MKL-SVM algorithm based on PSO only. Compared with the above two algorithms, SEN is increased by 3.71% and 7.41%, respectively. Therefore, it can be seen that the cost sensitive method can effectively reduce the missed detection of nodules, and the availability of the new algorithm can be further verified. [ABSTRACT FROM AUTHOR]

Due to the large fluctuation of import and export volume and many influencing factors, it is difficult for the general prediction algorithm to obtain more accurate prediction results. To solve this problem, a trade forecasting method based on the Particle Swarm Optimization (PSO) optimization hybrid Relevance Vector Machine (RVM) model is proposed. The method firstly finds out the indexes that affect the import and export trade and extracts the principal factors of the indexes as the input data of the model through principal component analysis. Then, based on the single-kernel RVM model training with multiple different kernel functions, the multikernel weighting method was used to construct the hybrid kernel RVM model according to the prediction error of the single-kernel RVM model. Finally, the parameters of the hybrid kernel model were optimized by PSO to improve the prediction accuracy. Close trade will strengthen the dependence between countries, and under this premise, it becomes particularly important to study the frequency of trade between countries. In this paper, the countries along the Belt and Road are classified by the method of high-order directed graph clustering, and the trade transactions between the countries are represented by a small network subgraph. Then, the 65 trading countries are classified by cutting graph and K-means clustering method, and the classification results are obtained by running relevant codes in MATLAB. The results are represented by the lattice graph. [ABSTRACT FROM AUTHOR]

• A robust method is proposed to alleviate the effect of traffic data with outliers. • A comprehensive traffic flow prediction indicator system is established in this paper. • We hybridize polynomial and Gaussian kernel to build nonlinear version of our method. • Parameters of the proposed method are optimized by Fruit Fly Optimization Algorithm. A novel least squares twin support vector regression method is proposed based on the robust L 1 -norm distance to alleviate the negative effect of traffic data with outliers. Although there is some known work for the short-term traffic flow prediction problems, their efficacy depends heavily on the collected traffic data, which are often affected by various external factors (e.g. weather, traffic jam or accident), leading to errors and missing data. This makes it difficult to pick an effective method that accurately predicts the traffic state. As a contribution of this paper, an iterative algorithm is designed to solve the non-smooth L 1 -norm terms of our method; its convergence also proved. Further, a comprehensive traffic flow indicator system based on speed, traffic flow, occupancy and ample degree is utilized in this paper. We also extend the proposed method to a nonlinear version by hybridizing the polynomial kernel and radial basis function kernel, where the weight coefficient of hybrid kernel is determined by the change tendency of traffic data. To promote the prediction performance, the parameters of our nonlinear method are optimized by adaptive fruit fly optimization algorithm. Extensive experiments on real traffic data are performed to evaluate our model. The results indicate that the newly constructed model yields better prediction performance and robustness than other models in various experimental settings. [ABSTRACT FROM AUTHOR]

l A non-convex fractional-order variational model is proposed to restore the image blurred by an unknown blur kernel. l Quaternion FTV with l p quasinorm constrained image and L 1 -norm constrained kernel are unified to a regularization framework. l The fractional-order total variation is extended to four-directional FTV including diagonal and back diagonal gradients. l An efficient algorithm based on the alternating direction method is proposed to address the non-convex optimization problem. This paper considers a variational model for single image blind restoration. By exploiting the fractional-order total variation (FTV) and L p quasinorm relaxation, a non-convex fractional-order variational model is proposed to restore the image blurred by an unknown blur kernel. A quaternion FTV model is first put forward to exploring more directional information of an image. The new model utilizes non-convex and non-smooth quaternion FTV with L p quasinorm to constrain the image and L 1 -norm to constrain the blur kernel, which are unified to a unified regularization framework. Further, an efficient algorithm is proposed to solve the non-convex problem via using the alternating direction minimization. The extensive experiments demonstrate the efficiency and viability of the proposed method and reveal superior performances in comparison with several existing methods. [ABSTRACT FROM AUTHOR]

We present a feasible full step interior-point algorithm to solve the P ∗ (κ) horizontal linear complementarity problem defined on a Cartesian product of symmetric cones, which is not based on a usual barrier function. The full steps are scaled utilizing the Nesterov-Todd (NT) scaling point. Our approach generates the search directions leading to the full-NT steps by algebraically transforming the centring equation of the system which defines the central trajectory using the induced barrier of a so-called positive-asymptotic kernel function. We establish the global convergence as well as a local quadratic rate of convergence of our proposed method. Finally, we demonstrate that our algorithm bears a complexity bound matching the best available one for the algorithms of its kind. [ABSTRACT FROM AUTHOR]

A new fractional-order Dickson functions are introduced for solving numerically fractional optimal control and variational problems involving Mittag–Leffler nonsingular kernel. The type of fractional derivative in the proposed problems is the Atangana–Baleanu–Caputo fractional derivative. In the process of the method, we use fractional-order Dickson functions and their properties to provide an accurate computational technique for calculating operational matrices, at first. Then, with the help of operational matrices and the Lagrange multiplier method, these problems are reduced to a system of algebraic equations. At last, to demonstrate the effectiveness of the new method, we enforce the proposed algorithm for several examples. [ABSTRACT FROM AUTHOR]

We develop an exact and scalable algorithm for one-dimensional Gaussian process regression with Matérn correlations whose smoothness parameter ν is a half-integer. The proposed algorithm only requires O(ν³n) operations and O(νn) storage. This leads to a linear-cost solver since ν is chosen to be fixed and usually very small in most applications. The proposed method can be applied to multi-dimensional problems if a full grid or a sparse grid design is used. The proposed method is based on a novel theory for Matérn correlation functions. We find that a suitable rearrangement of these correlation functions can produce a compactly supported function, called a "kernel packet". Using a set of kernel packets as basis functions leads to a sparse representation of the covariance matrix that results in the proposed algorithm. Simulation studies show that the proposed algorithm, when applicable, is significantly superior to the existing alternatives in both the computational time and predictive accuracy. [ABSTRACT FROM AUTHOR]

Density Peak Clustering (DPC) is a useful algorithm for grouping data points based on their closeness and density. It is widely used in various areas of computer science. It can detect the peak density in each period of the clustering steps and assign the rest of the data to the next steps. Peak density clustering analysis is able to discover clusters of arbitrary shapes, but usually, when the data set is large, it is computationally expensive and difficult to apply to high-dimensional data. When the distance between clusters is significantly different, it is unable to distinguish adjacent clusters with different densities. To deal with such issues, a new clustering algorithm based on neighborhoods and the Apollonius kernel is proposed. The proposed algorithm can be implemented with four steps. 1) Estimation of natural neighbor, 2) Identification of core points, 3) Merging the cores of a cluster and separating the cores of different clusters, 4) Using the Apollonius kernel between the core points and the farthest points to assign the remaining points to the clusters and find the noise points. The local density estimation process based on the natural neighborhood of high-density points and their integration, as well as border point classification, allows the proposed method to reveal the local cluster structure. As a result, the adjoining clusters with distinctive densities are recognized, and the computation is substantially reduced. The proposed method is validated on some synthetic data sets and the UCI data set experimentally and has a high 10% accuracy. [ABSTRACT FROM AUTHOR]

In this work, a fast algorithm to evaluate the dynamic response of nonviscously damped systems with arbitrary distributions of damping characterised by arbitrary kernel functions (both number and form) is proposed. The proposed algorithm requires mere matrix–vector operations. It can be integrated into existing analysis tools with various time integration methods in forms of either element-based dashpots or global damping model. Compared to other existing methods, the proposed algorithm does not explicitly evaluate the convolution integral and thus does not require the storage of the whole velocity history. It shows superior accuracy while the corresponding computational cost is low. [ABSTRACT FROM AUTHOR]

• A single-step recursive algorithm of non-viscous damping forces is developed. • Rectangle-impulse responses of kernel functions determine the algorithm parameters. • The algorithm is compatible with the solution schemes of time integration methods. • The compatible algorithm retains the characteristics of time integration methods. The non-viscous damping force features the convolution integral of the velocity and the kernel function, causing the difficulty of the solutions of the system equation of motion due to the nonlocal time dependence. In accordance with the linear time-invariant system theory in signal processing, this paper presents a single-step recursive algorithm of convolution integral for efficiently computing non-viscous damping forces. The algorithm parameters are effectively identified from the discrete responses of the kernel function to the rectangular unit impulse through digital filter technologies. The proposed algorithm is compatible with the solution schemes based on existing time integration methods, which handle the nonlocal dependence using internal recursive support vectors while leaving the order of the equation of motion unchanged. The central difference method, the Newmark- ß method, and the Bathe method are employed to illustrate the use of the algorithm, proving to retain the stability characteristics of time integration methods. The single and multiple DOF examples show that the simulated results based on the compatible solution schemes compare well with those built on other existing methods, verifying high accuracy and efficiency. The proposed algorithm thus extends the application range of existing time integration methods from the viscously damped system to the non-viscously damped one, fully demonstrating its generalizability. [ABSTRACT FROM AUTHOR]

A lot of research has been conducted on many variants of the Fuzzy c-means (FCM) clustering algorithm incorporating local spatial neighborhood information to improve segmentation accuracy and robustness to noise. Among these variants, a fast and robust FCM (FRFCM) clustering algorithm performs fast and robustly to noise for both grayscale and color images. Though, FRFCM is fast but segmentation performance needs improvement. This work presents an improved variant of the FRFCM algorithm, based on the kernel metric and possibilistic fuzzy c-means approach. The proposed method named Kernel Possibilistic Fast-Robust Fuzzy c-means (KPFRFCM) algorithm overcomes the disadvantages of FRFCM i.e. the poor segmentation performance and less robustness to noise, for both grayscale and color images. Experiments performed on various types of images without noise and images degraded by different types of noises with different degrees, prove that proposed KPFRFCM is more efficient and more robust to noise when compared with existing state-of-the-art algorithms for image segmentation. • Accuracy of image segmentation is very important for higher level processing. • A variant of FCM algorithm incorporating local spatial neighborhood information. • KPFRFCM enhances accuracy, robustness to noise of FRFCM with PFCM, kernel approach. [ABSTRACT FROM AUTHOR]

The pivotal aim of present work is to design and implement an effective numerical approach, the iterative reproducing-kernel algorithm, to provide numerical solutions to the fractional Riccati and Bernoulli differential equations in the Caputo-Fabrizio sense. To achieve this, we develop an advanced operational algorithm based on creating a complete orthonormal function system utilizing the reproducing-kernel function in order to formulate the solution in the form of uniformly convergent Fourier series. Additionally, error and stability analysis of the proposed method are studied in the appropriate space W 2 , 2 (Δ). On the other hand, some meaningful numerical applications are included to demonstrate the feasibility and reliability of this approach under the qualitative effect of the Caputo-Fabrizio fractional derivative. In numerical viewpoints, the achieved results using the proposed approach indicate a high level of accuracy and rare technical skills, which qualifies it to deal with many fractional models emerging in various mathematical and physical disciplines within the frame of Caputo-Fabrizio derivatives. [ABSTRACT FROM AUTHOR]

Firstly, a new sequence transformation that can be expressed in terms of a ratio of two pfaffians is derived based on a special kernel. It can be regarded as a direct generalization of Aitken's Δ2 process from the point of view of pfaffians and then the corresponding convergence acceleration algorithm is constructed. Numerical examples with applications of this algorithm are also presented. Secondly, we find a way to generalize the Shanks transformation via pfaffians so that a larger class of new sequence transformations are derived. The corresponding recursive algorithms are also proposed. [ABSTRACT FROM AUTHOR]

• The paper provides a robust regression method for interval-valued variables. • The objective function of the method considers the full interval information. • The computation of the sum of squares errors uses exponential-type kernel functions. • Outliers have a small weight for both center and radius parameter estimates. • Applications on synthetic and real data sets corroborate the proposed method. Interval-valued data are needed to manage either the uncertainty related to measurements, or the variability inherent to the description of complex objects representing group of individuals. A number of regression methods suitable to interval variables describing variability of complex objects are already available. However, less attention has been given to methods that, simultaneously, take into account the full interval information and are resistant to interval outlier observations, even with the frequent presence of atypical observations on interval-valued data sets. This paper proposes a new robust linear regression method for interval variables, where the presence of outliers either in the center or in the radius penalize both the center and the radius regression models. Moreover, the interval observations with outliers on both center and radius are more penalized than those observations with outliers only in the center (or in the radius). Besides, this paper provides a suitable iterative algorithm to estimate the parameters of the proposed method. The algorithm estimates the parameters of the center (or of the radius) model taking into account both information of the center and the radius. The convergence and time complexity of the iterative algorithm are also presented. Finally, the performance of the new method is compared with some previous robust regression approaches and evaluated on synthetic and real interval-valued data sets. [ABSTRACT FROM AUTHOR]

We propose an interpretable graph neural network framework to denoise single or multiple noisy graph signals. The proposed graph unrolling networks expand algorithm unrolling to the graph domain and provide an interpretation of the architecture design from a signal processing perspective. We unroll an iterative denoising algorithm by mapping each iteration into a single network layer where the feed-forward process is equivalent to iteratively denoising graph signals. We train the graph unrolling networks through unsupervised learning, where the input noisy graph signals are used to supervise the networks. By leveraging the learning ability of neural networks, we adaptively capture appropriate priors from input noisy graph signals. A core component of graph unrolling networks is the edge-weight-sharing graph convolution operation, which parameterizes each edge weight by a trainable kernel function whose trainable parameters are shared by all the edges. The proposed convolution is permutation-equivariant and can flexibly adjust the edge weights to various graph signals. We further consider two special cases of this class of networks, graph unrolling sparse coding (GUSC) and graph unrolling trend filtering (GUTF), by unrolling sparse coding and trend filtering, respectively. To validate the proposed methods, we conduct extensive experiments on both real-world datasets and simulated datasets, and demonstrate that our methods have smaller denoising errors than conventional denoising algorithms and state-of-the-art graph neural networks. For denoising a single smooth graph signal, the normalized mean square error of the proposed networks is around 40% and 60% lower than that of graph Laplacian denoising and graph wavelets, respectively. [ABSTRACT FROM AUTHOR]

• Gaussian Processes strongly depend on kernel functions in any application. • A kernel can be represented as a tree of basic mathematical expressions. • In this work, Genetic Programming is proposed to learn such expression trees. • This approach has been tested in several time-series forecasting problems. Choosing the best kernel is crucial in many Machine Learning applications. Gaussian Processes are a state-of-the-art technique for regression and classification that heavily relies on a kernel function. However, in the Gaussian Processes literature, kernels have usually been either ad hoc designed, selected from a predefined set, or searched for in a space of compositions of kernels which have been defined a priori. In this paper, we propose a Genetic Programming algorithm that represents a kernel function as a tree of elementary mathematical expressions. By means of this representation, a wider set of kernels can be modeled, where potentially better solutions can be found, although new challenges also arise. The proposed algorithm is able to overcome these difficulties and find kernels that accurately model the characteristics of the data. This method has been tested in several real-world time series extrapolation problems, improving the state-of-the-art results while reducing the complexity of the kernels. [ABSTRACT FROM AUTHOR]

Aiming at the shortcomings of a single machine learning model with low model prediction accuracy and insufficient generalization ability in house price index prediction, a whale algorithm optimized support vector regression model based on bagging ensemble learning method is proposed. Firstly, gray correlation analysis is used to obtain the main influencing factors of house prices, and the segmentation forecasting method is used to divide the data set and forecast the house prices in the coming year using the data of the past ten years. Secondly, the whale optimization algorithm is used to find the optimal parameters of the penalty factor and kernel function in the SVR model, and then, the WOA-SVR model is established. Finally, in order to further improve the model generalization capability, a bagging integration strategy is used to further integrate and optimize the WOA-SVR model. The experiments are conducted to forecast the house price indices of four regions, Beijing, Shanghai, Tianjin, and Chongqing, respectively, and the results show that the prediction accuracy of the proposed integrated model is better than the comparison model in all cases. [ABSTRACT FROM AUTHOR]

Gene expression data has the characteristics of high dimensionality and a small sample size and contains a large number of redundant genes unrelated to a disease. The direct application of machine learning to classify this type of data will not only incur a great time cost but will also sometimes fail to improved classification performance. To counter this problem, this paper proposes a dimension-reduction algorithm based on weighted kernel principal component analysis (WKPCA), constructs kernel function weights according to kernel matrix eigenvalues, and combines multiple kernel functions to reduce the feature dimensions. To further improve the dimensional reduction efficiency of WKPCA, t-class kernel functions are constructed, and corresponding theoretical proofs are given. Moreover, the cumulative optimal performance rate is constructed to measure the overall performance of WKPCA combined with machine learning algorithms. Naive Bayes, K-nearest neighbour, random forest, iterative random forest and support vector machine approaches are used in classifiers to analyse 6 real gene expression dataset. Compared with the all-variable model, linear principal component dimension reduction and single kernel function dimension reduction, the results show that the classification performance of the 5 machine learning methods mentioned above can be improved effectively by WKPCA dimension reduction. [ABSTRACT FROM AUTHOR]