Adaptive multi-step piecewise interpolation reproducing kernel method for solving the nonlinear time-fractional partial differential equation arising from financial economics

This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)method which deals with this problem is very troublesome.This paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel(AMPIRK)method for the first time.This method has three obvious advantages which are as follows.Firstly,the piecewise number is reduced.Secondly,the calculation accuracy is improved.Finally,the waste time caused by too many fragments is avoided.Then four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the others.The research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics.

Short-term traffic flow online forecasting based on kernel adaptive filter

Considering that the prediction accuracy of the traditional traffic flow forecasting model is low,based on kernel adaptive filter(KAF)algorithm,kernel least mean square(KLMS)algorithm and fixed-budget kernel recursive least-square(FB-KRLS)algorithm are presented for online adaptive prediction.The computational complexity of the KLMS algorithm is low and does not require additional solution paradigm constraints,but its regularization process can solve the problem of regularization performance degradation in high-dimensional data processing.To reduce the computational complexity,the sparse criterion is introduced into the KLMS algorithm.To further improve forecasting accuracy,FB-KRLS algorithm is proposed.It is an online learning method with fixed memory budget,and it is capable of recursively learning a nonlinear mapping and changing over time.In contrast to a previous approximate linear dependence(ALD)based technique,the purpose of the presented algorithm is not to prune the oldest data point in every time instant but it aims to prune the least significant data point,thus suppressing the growth of kernel matrix.In order to verify the validity of the proposed methods,they are applied to one-step and multi-step predictions of traffic flow in Beijing.Under the same conditions,they are compared with online adaptive ALD-KRLS method and other kernel learning methods.Experimental results show that the proposed KAF algorithms can improve the prediction accuracy,and its online learning ability meets the actual requirements of traffic flow and contributes to real-time online forecasting of traffic flow.

Fast Image Segmentation Algorithm Based on Salient Features Model and Spatial-frequency Domain Adaptive Kernel

A fast image segmentation algorithm based on salient features model and spatial-frequency domain adaptive kernel is proposed to solve the accurate discriminate objects problem of online visual detection in such scenes of variable sample morphological characteristics,low contrast and complex background texture.Firstly,by analyzing the spectral component distribution and spatial contour feature of the image,a salient feature model is established in spatial-frequency domain.Then,the salient object detection method based on Gaussian band-pass filter and the design criterion of adaptive convolution kernel are proposed to extract the salient contour feature of the target in spatial and frequency domain.Finally,the selection and growth rules of seed points are improved by integrating the gray level and contour features of the target,and the target is segmented by seeded region growing.Experiments have been performed on Berkeley Segmentation Data Set,as well as sample images of online detection,to verify the effectiveness of the algorithm.The experimental results show that the Jaccard Similarity Coefficient of the segmentation is more than 90%,which indicates that the proposed algorithm can availably extract the target feature information,suppress the background texture and resist noise interference.Besides,the Hausdorff Distance of the segmentation is less than 10,which infers that the proposed algorithm obtains a high evaluation on the target contour preservation.The experimental results also show that the proposed algorithm significantly improves the operation efficiency while obtaining comparable segmentation performance over other algorithms.

Multi-channel differencing adaptive noise cancellation with multi-kernel method

Although a various of existing techniques are able to improve the performance of detection of the weak interesting sig- nal, how to adaptively and efficiently attenuate the intricate noises especially in the case of no available reference noise signal is still the bottleneck to be overcome. According to the characteristics of sonar arrays, a multi-channel differencing method is presented to provide the prerequisite reference noise. However, the ingre- dient of obtained reference noise is too complicated to be used to effectively reduce the interference noise only using the clas- sical linear cancellation methods. Hence, a novel adaptive noise cancellation method based on the multi-kernel normalized least- mean-square algorithm consisting of weighted linear and Gaussian kernel functions is proposed, which allows to simultaneously con- sider the cancellation of linear and nonlinear components in the reference noise. The simulation results demonstrate that the out- put signal-to-noise ratio （SNR） of the novel multi-kernel adaptive filtering method outperforms the conventional linear normalized least-mean-square method and the mono-kernel normalized least- mean-square method using the realistic noise data measured in the lake experiment.

Simultaneous upscaling of two properties of reservoirs in one dimension using adaptive bandwidth in kernel function method

Upscaling of primary geological models with huge cells, especially in porous media, is the first step in fluid flow simulation. Numerical methods are often used to solve the models. The upscaling method must preserve the important properties of the spatial distribution of the reservoir properties. An grid upscaling method based on adaptive bandwidth in kernel function is proposed according to the spatial distribution of property. This type of upscaling reduces the number of cells, while preserves the main heterogeneity features of the original fine model. The key point of the paper is upscaling two reservoir properties simultaneously. For each reservoir feature, the amount of bandwidth or optimal threshold is calculated and the results of the upscaling are obtained. Then two approaches are used to upscaling two properties simultaneously based on maximum bandwidth and minimum bandwidth. In fact, we now have a finalized upscaled model for both reservoir properties for each approach in which not only the number of their cells, but also the locations of the cells are equal. The upscaling error of the minimum bandwidth approach is less than that of the maximum bandwidth approach.

LKAW: A Robust Watermarking Method Based on Large Kernel Convolution and Adaptive Weight Assignment

Robust watermarking requires finding invariant features under multiple attacks to ensure correct extraction.Deep learning has extremely powerful in extracting features,and watermarking algorithms based on deep learning have attracted widespread attention.Most existing methods use 3×3 small kernel convolution to extract image features and embed the watermarking.However,the effective perception fields for small kernel convolution are extremely confined,so the pixels that each watermarking can affect are restricted,thus limiting the performance of the watermarking.To address these problems,we propose a watermarking network based on large kernel convolution and adaptive weight assignment for loss functions.It uses large-kernel depth-wise convolution to extract features for learning large-scale image information and subsequently projects the watermarking into a highdimensional space by 1×1 convolution to achieve adaptability in the channel dimension.Subsequently,the modification of the embedded watermarking on the cover image is extended to more pixels.Because the magnitude and convergence rates of each loss function are different,an adaptive loss weight assignment strategy is proposed to make theweights participate in the network training together and adjust theweight dynamically.Further,a high-frequency wavelet loss is proposed,by which the watermarking is restricted to only the low-frequency wavelet sub-bands,thereby enhancing the robustness of watermarking against image compression.The experimental results show that the peak signal-to-noise ratio(PSNR)of the encoded image reaches 40.12,the structural similarity(SSIM)reaches 0.9721,and the watermarking has good robustness against various types of noise.

Adaptive Kernel Firefly Algorithm Based Feature Selection and Q-Learner Machine Learning Models in Cloud

CC’s(Cloud Computing)networks are distributed and dynamic as signals appear/disappear or lose significance.MLTs(Machine learning Techniques)train datasets which sometime are inadequate in terms of sample for inferring information.A dynamic strategy,DevMLOps(Development Machine Learning Operations)used in automatic selections and tunings of MLTs result in significant performance differences.But,the scheme has many disadvantages including continuity in training,more samples and training time in feature selections and increased classification execution times.RFEs(Recursive Feature Eliminations)are computationally very expensive in its operations as it traverses through each feature without considering correlations between them.This problem can be overcome by the use of Wrappers as they select better features by accounting for test and train datasets.The aim of this paper is to use DevQLMLOps for automated tuning and selections based on orchestrations and messaging between containers.The proposed AKFA(Adaptive Kernel Firefly Algorithm)is for selecting features for CNM(Cloud Network Monitoring)operations.AKFA methodology is demonstrated using CNSD(Cloud Network Security Dataset)with satisfactory results in the performance metrics like precision,recall,F-measure and accuracy used.

h-ADAPTIVITY ANALYSIS BASED ON MULTIPLE SCALE REPRODUCING KERNEL PARTICLE METHOD

An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes(SNN) and local-Delaunay-triangulation(LDT) tech-niques, which were suitable and effective for h-adaptivity analysis on 2-D problems with the regular or irregular distribution of the nodes. The results of multiresolution and h-adaptivity analyses on 2-D linear elastostatics and bending plate problems demonstrate that the improper high-gradient indicator will reduce the convergence property of the h-adaptivity analysis, and that the efficiency of the LDT node refinement strategy is better than SNN, and that the presented h-adaptivity analysis scheme is provided with the validity, stability and good convergence property.

h-ADAPTIVITY ANALYSIS BASED ON MULTIPLE SCALE REPRODUCING KERNEL PARTICLE METHOD

An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes（SNN） and local-Delaunay-triangulation（LDT） techniques, which were suitable and effective for h-adaptivity analysis on 2-D problems with the regular or irregular distribution of the nodes. The results of multiresolution and h- adaptivity analyses on 2-D linear elastostatics and bending plate problems demonstrate that the improper high-gradient indicator will reduce the convergence property of the h- adaptivity analysis, and that the efficiency of the LDT node refinement strategy is better than SNN, and that the presented h-adaptivity analysis scheme is provided with the validity, stability and good convergence property.

Bandwidth adaption for kernel particle filter

A novel particle filter bandwidth adaption for kernel particle filter （BAKPF） is proposed. Selection of the kernel bandwidth is a critical issue in kernel density estimation （KDE）. The plug-in method is adopted to get the global fixed bandwidth by optimizing the asymptotic mean integrated squared error （AMISE） firstly. Then, particle-driven bandwidth selection is invoked in the KDE. To get a more effective allocation of the particles, the KDE with adap- tive bandwidth in the BAKPF is used to approximate the posterior probability density function （PDF） by moving particles toward the posterior. A closed-form expression of the true distribution is given. The simulation results show that the proposed BAKPF performs better than the standard particle filter （PF）, unscented particle filter （UPF） and the kernel particle filter （KPF） both in efficiency and estimation precision.

Active Kriging-Based Adaptive Importance Sampling for Reliability and Sensitivity Analyses of Stator Blade Regulator

The reliability and sensitivity analyses of stator blade regulator usually involve complex characteristics like highnonlinearity,multi-failure regions,and small failure probability,which brings in unacceptable computing efficiency and accuracy of the current analysismethods.In this case,by fitting the implicit limit state function(LSF)with active Kriging(AK)model and reducing candidate sample poolwith adaptive importance sampling(AIS),a novel AK-AIS method is proposed.Herein,theAKmodel andMarkov chainMonte Carlo(MCMC)are first established to identify the most probable failure region(s)(MPFRs),and the adaptive kernel density estimation(AKDE)importance sampling function is constructed to select the candidate samples.With the best samples sequentially attained in the reduced candidate samples and employed to update the Kriging-fitted LSF,the failure probability and sensitivity indices are acquired at a lower cost.The proposed method is verified by twomulti-failure numerical examples,and then applied to the reliability and sensitivity analyses of a typical stator blade regulator.Withmethods comparison,the proposed AK-AIS is proven to hold the computing advantages on accuracy and efficiency in complex reliability and sensitivity analysis problems.

Research on Adaptive TSSA-HKRVM Model for Regression Prediction of Crane Load Spectrum

For the randomness of crane working load leading to the decrease of load spectrum prediction accuracy with time,an adaptive TSSA-HKRVM model for crane load spectrum regression prediction is proposed.The heterogeneous kernel relevance vector machine model(HKRVM)with comprehensive expression ability is established using the complementary advantages of various kernel functions.The combination strategy consisting of refraction reverse learning,golden sine,and Cauchy mutation+logistic chaotic perturbation is introduced to form a multi-strategy improved sparrow algorithm(TSSA),thus optimizing the relevant parameters of HKRVM.The adaptive updatingmechanismof the heterogeneous kernel RVMmodel under themulti-strategy improved sparrow algorithm(TSSA-HKMRVM)is defined by the sliding window design theory.Based on the sample data of the measured load spectrum,the trained adaptive TSSA-HKRVMmodel is employed to complete the prediction of the crane equivalent load spectrum.Applying this method toQD20/10 t×43m×12mgeneral bridge crane,the results show that:compared with other prediction models,although the complexity of the adaptive TSSA-HKRVMmodel is relatively high,the prediction accuracy of the load spectrum under long periods has been effectively improved,and the completeness of the load information during thewhole life cycle is relatively higher,with better applicability.

Adaptive Metric Learning for Dimensionality Reduction

Finding a suitable space is one of the most critical problems for dimensionality reduction. Each space corresponds to a distance metric defined on the sample attributes, and thus finding a suitable space can be converted to develop an effective distance metric. Most existing dimensionality reduction methods use a fixed pre-specified distance metric. However, this easy treatment has some limitations in practice due to the fact the pre-specified metric is not going to warranty that the closest samples are the truly similar ones. In this paper, we present an adaptive metric learning method for dimensionality reduction, called AML. The adaptive metric learning model is developed by maximizing the difference of the distances between the data pairs in cannot-links and those in must-links. Different from many existing papers that use the traditional Euclidean distance, we use the more generalized l2,p-norm distance to reduce sensitivity to noise and outliers, which incorporates additional flexibility and adaptability due to the selection of appropriate p-values for different data sets. Moreover, considering traditional metric learning methods usually project samples into a linear subspace, which is overstrict. We extend the basic linear method to a more powerful nonlinear kernel case so that well capturing complex nonlinear relationship between data. To solve our objective, we have derived an efficient iterative algorithm. Extensive experiments for dimensionality reduction are provided to demonstrate the superiority of our method over state-of-the-art approaches.

Combining Adaptive Diffusion with Difference for Detecting Nonstationary Signals

时间频率分析试图构造时间和频率的密度功能与时间在要分析的信号和信号的频率的进化揭示频率部件。Wigner 分发(WD ) 是为在雷达的域里分析 nonstationary 信号的最基本、广泛地使用的方法之一，通讯，等等。然而， WD 的申请被干扰术语的存在极大地限制。适应散开方法建议由朱利恩·戈斯梅，移开 WD 的干扰术语等。是面对信号产生的干扰术语无效，其分布在 WD 的时间频率飞机一起被交织。我们为移开这些干扰术语为检测 nonstationary 信号改进科恩类的时间频率表示的分辨率和可读性把散开技术与差别方法相结合。

面向生物氧化提金槽温度监测的数据融合策略

为提高生物氧化槽温度估计的准确性,提出一种数据融合策略。利用鲁棒自适应无迹卡尔曼滤波算法对底层采集的数据进行处理,克服噪声对系统性能的影响。利用序贯自适应加权融合算法对滤波后的数据进行局部融合,保证融合结果的一致性与高精度。利用改进的斑马优化算法优化核极限学习机进行全局融合,提升算法的泛化能力与鲁棒性。实验结果表明,提出的融合方法能够提高生物氧化槽温度估计的精度,为后续的控制决策提供有力的数据保障。

Theoretical convergence analysis of complex Gaussian kernel LMS algorithm

With the vigorous expansion of nonlinear adaptive filtering with real-valued kernel functions,its counterpart complex kernel adaptive filtering algorithms were also sequentially proposed to solve the complex-valued nonlinear problems arising in almost all real-world applications.This paper firstly presents two schemes of the complex Gaussian kernel-based adaptive filtering algorithms to illustrate their respective characteristics.Then the theoretical convergence behavior of the complex Gaussian kernel least mean square（LMS） algorithm is studied by using the fixed dictionary strategy.The simulation results demonstrate that the theoretical curves predicted by the derived analytical models consistently coincide with the Monte Carlo simulation results in both transient and steady-state stages for two introduced complex Gaussian kernel LMS algonthms using non-circular complex data.The analytical models are able to be regard as a theoretical tool evaluating ability and allow to compare with mean square error（MSE） performance among of complex kernel LMS（KLMS） methods according to the specified kernel bandwidth and the length of dictionary.

Nyström kernel algorithm based on least logarithmic hyperbolic cosine loss

Kernel adaptive filters(KAFs)have sparked substantial attraction for online non-linear learning applications.It is noted that the effectiveness of KAFs is highly reliant on a rational learning criterion.Concerning this,the logarithmic hyperbolic cosine(lncosh)criterion with better robustness and convergence has drawn attention in recent studies.However,existing lncosh loss-based KAFs use the stochastic gradient descent(SGD)for optimization,which lack a trade-off between the convergence speed and accuracy.But recursion-based KAFs can provide more effective filtering performance.Therefore,a Nyström method-based robust sparse kernel recursive least lncosh loss algorithm is derived in this article.Experiments via measures and synthetic data against the non-Gaussian noise confirm the superiority with regard to the robustness,accuracy performance,and computational cost.

A Sparse Kernel Approximate Method for Fractional Boundary Value Problems

In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W_(0)^(4)[0,1] and W^(1)[0,1].The process of the W-POAFD is as follows:(i)choose a dictionary and implement the pre-orthogonalization to all the dictionary elements;(ii)select points in[0,1]by the weak maximal selection principle to determine the corresponding orthonormalized dictionary elements iteratively;(iii)express the analytical solution as a linear combination of these determined dictionary elements.Convergence properties of numerical solutions are also discussed.The numerical experiments are carried out to illustrate the accuracy and efficiency of W-POAFD for solving FBVPs.

基于核相关滤波和卡尔曼滤波预测的混合跟踪方法

针对核相关滤波(KCF)跟踪算法在遮挡场景中出现跟踪性能降低甚至跟踪失败的问题,提出了一种核相关滤波和卡尔曼滤波(KF)预测相结合的模型自适应抗遮挡图像目标跟踪算法KCF-KF。首先,考虑到传统KCF目标跟踪算法中缺少遮挡评估的问题,通过引入响应图的峰值旁瓣比来对图像目标的遮挡情况进行判断,并将遮挡类型划分为部分遮挡和严重遮挡。其次,根据遮挡程度采取不同的模型更新策略,当目标无遮挡或者部分遮挡时,替代传统KCF跟踪算法中采用固定学习率更新模型的方法,通过自适应地调整模型学习率来更新目标外观模型,避免跟踪漂移;当目标被严重遮挡时,停止KCF模型更新。最后,应用严重遮挡之前的运动信息构建卡尔曼滤波器状态空间和位置输出模型,设计卡尔曼滤波算法预测运动目标轨迹来估计遮挡情景下的目标位置,从而解决在遮挡场景中目标跟踪失败的问题。采用OTB-2013标准数据集进行大量实验,结果表明:所提的混合跟踪算法KCF-KF的距离精度为0.796,重叠成功率为0.692。与其他传统跟踪算法相比,该混合算法的跟踪精度和跟踪成功率均优于其他算法,并且在遇到目标遮挡挑战时具有更好的跟踪性能,有效地解决了跟踪过程中的遮挡干扰问题。

基于自适应矩阵的核联合稀疏表示高光谱图像分类

针对高光谱图像丰富的空间信息和光谱信息未充分利用的问题,提出了基于自适应矩阵的核联合稀疏表示高光谱图像分类的方法。在特征表示阶段,定义了自适应矩阵特征,通过结合自适应邻域块策略与非线性相关熵度量构成的特征来描述原始光谱像素,充分融合了形状可变的空间信息与非线性光谱信息。在分类阶段,考虑自适应矩阵和高光谱图像非线性,采用对数欧式核函数,构建了核联合稀疏表示模型,以获得重构误差。同时利用字典空间信息构建了矩阵相关性,引入平衡参数实现了稀疏重构误差与矩阵相关性的联合分类。在两个数据集上的实验结果表明,该算法充分利用了高光谱图像的空间信息、光谱信息,能够有效提高分类精度。