Multiple Empirical Kernel Learning with Majority Projection for imbalanced problems

Traditional Multiple Empirical Kernel Learning (MEKL) expands the expressions of the sample and brings better classification ability by using different empirical kernels to map the original data space into multiple kernel spaces. To make MEKL suit for the imbalanced problems, this paper introduces a weight matrix and a regularization term into MEKL. The weight matrix assigns high misclassification cost to the minority samples to balanced misclassification cost between minority and majority class. The regularization term named Majority Projection (MP) is used to make the classification hyperplane fit the distribution shape of majority samples and enlarge the between-class distance of minority and majority class. The contributions of this work are: (i) assigning high cost to minority samples to deal with imbalanced problems, (ii) introducing a new regularization term to concern the property of data distribution, (iii) and modifying the original PAC-Bayes bound to test the error upper bound of MEKL-MP. Through analyzing the experimental results, the proposed MEKL-MP is well suited to the imbalanced problems and has lower generalization risk in accordance with the value of PAC-Bayes bound.     

基于洛伦兹范数的医学图像超分辨率重建研究

在超分辨率图像重建(SR)模型中,为了达到良好的重建效果,选择一个合适的代价函数是研究的重点。采用SR重建模型中的差错项选择了洛伦兹范数,正则化项选择了吉洪诺夫正则化,重建过程采用了迭代方法。提出的算法可以有效地解决医学图像SR重建过程中的去异值点和图像边缘保持的两大关键问题,达到良好的重建效果。为了验证上述算法的有效性,就一系列添加了运动模糊和不同噪声的低分辨率MRI医学图像进行了SR重建,并且与基于L2范数的重建算法的重建效果进行了比较分析。实验结果显示,所提算法具有良好的实用性和有效性。     

Bandlet-based sparsity regularization in video inpainting

We present a bandlet-based framework for video inpainting in order to complete missing parts of a video sequence. The framework applies spatio-temporal geometric flows extracted by bandlets to reconstruct the missing data. First, a priority-based exemplar scheme enhanced by a bandlet-based patch fusion generates a preliminary inpainting result. Then, the inpainting task is completed by a 3D volume regularization algorithm which takes advantage of bandlet bases in exploiting the anisotropic regularities. The method does not need extra processes in order to satisfy visual consistency. The experimental results demonstrate the effectiveness of our proposed video completion technique.     

Computing the regularization of a linear differential–algebraic system

We study the regularization problem for linear differential–algebraic systems. As an improvement of former results we show that any system can be regularized by a combination of state-space and input-space transformations, behavioral equivalence transformations and a reorganization of variables. The additional state feedback which is needed in earlier publications is shown to be superfluous. We provide an algorithmic procedure for the construction of the regularization and discuss computational aspects.     

Improving the prediction of petroleum reservoir characterization with a stacked generalization ensemble model of support vector machines

The ensemble learning paradigm has proved to be relevant to solving most challenging industrial problems. Despite its successful application especially in the Bioinformatics, the petroleum industry has not benefited enough from the promises of this machine learning technology. The petroleum industry, with its persistent quest for high-performance predictive models, is in great need of this new learning methodology. A marginal improvement in the prediction indices of petroleum reservoir properties could have huge positive impact on the success of exploration, drilling and the overall reservoir management portfolio. Support vector machines (SVM) is one of the promising machine learning tools that have performed excellently well in most prediction problems. However, its performance is a function of the prudent choice of its tuning parameters most especially the regularization parameter, C. Reports have shown that this parameter has significant impact on the performance of SVM. Understandably, no specific value has been recommended for it. This paper proposes a stacked generalization ensemble model of SVM that incorporates different expert opinions on the optimal values of this parameter in the prediction of porosity and permeability of petroleum reservoirs using datasets from diverse geological formations. The performance of the proposed SVM ensemble was compared to that of conventional SVM technique, another SVM implemented with the bagging method, and Random Forest technique. The results showed that the proposed ensemble model, in most cases, outperformed the others with the highest correlation coefficient, and the lowest mean and absolute errors. The study indicated that there is a great potential for ensemble learning in petroleum reservoir characterization to improve the accuracy of reservoir properties predictions for more successful explorations and increased production of petroleum resources. The results also confirmed that ensemble models perform better than the conventional SVM implementation.     

A novel semi-analytic method for the analysis of scattering by dielectric objects immersed in uniform media

The method for the solution of scattering problems with homogeneous dielectric scatterers based on a single coordinate multipole expansion, the Stratton-Chu integral and Maxwell's equations in the integral form is proposed in this paper. Its convergence is proved. The sources of ill-conditionality of constitutive algebraic systems are established. The method of their regularization based on the use of a scalar control parameter is suggested. For the sake of validation, the numerical analysis is performed for different testing objects.     

Analysis of Over- and Underdetermined Nonlinear Differential-Algebraic Systems with Application to Nonlinear Control Problems

 We study over- and underdetermined systems of nonlinear differential-algebraic equations. Such equations arise in many applications in circuit and multibody system simulation, in particular when automatic model generation is used, or in the analysis and solution of control problems in the behavior framework.?We give a general (local) existence and uniqueness theory and apply the results to analyze when nonlinear implicit control problems can be made regular by state or output feedback.?The theoretical analysis also leads immediately to numerical methods for the simulation as well as the construction of regularizing feedbacks. Date received: February 21, 2000. Date revised: November 14, 2000.     

An optimal regularization method for space-fractional backward diffusion problem

In this paper, a space-fractional backward diffusion problem (SFBDP) in a strip is considered. By the Fourier transform, we proposed an optimal modified method to solve this problem in the presence of noisy data. The convergence estimates for the approximate solutions with the regularization parameter selected by an a priori and an a posteriori strategy are provided, respectively. Numerical experiments show that the proposed methods are effective and stable.     

基于加权空间离群点度量的随机脉冲噪声降噪算法

针对排序统计类降噪算法在随机脉冲噪声（RVIN）图像降噪过程中,对图像边缘和细节部分噪声识别不够准确以及恢复比较模糊的问题,提出了基于加权空间离群点度量（SLOM）的脉冲噪声降噪算法WSLOM-EPR。该算法以优化的空间距离差为基础,引入图像邻域均值和标准差,建立反映局部边缘细节特征的噪声检测方法,提高边缘细节处噪声的识别精度;然后以精确检测结果为基础,优化保边正则（EPR）函数,提高算法的执行效率,并增强算法保留边缘细节的能力。仿真结果显示,WSLOM-EPR算法在40%到60%噪声密度下对噪声点的误检和漏检综合表现优于对比算法,且能在两者之间保持一个较好的平衡;降噪后的峰值信噪比（PSNR）好于对比算法中的大多数情况,且边缘细节在视觉上更加清晰连续。结果表明WSLOM-EPR算法提高了噪声检测精度,有效地保持了恢复图像的边缘细节信息。