Papers by Keyword: Kernel Function

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Authors: Hong E Li, Xiao Xu Dong, Shun Chu Li, Dong Dong Gui, Cong Yin Fan
Abstract: The similar structure of solution for the boundary value problem of second order linear homogeneous differential equation has been studied. Based on the analysis of the relationship between similar structure of solution, its kernel function, the equation and boundary conditions, similar constructive method (shortened as SCM) of solution is obtained. According to the SCM, the similar structure of solution and its kernel function are constructed for the mathematical model of homogeneous reservoir which considers the influence of bottom-hole storage and skin effect under the infinite outer boundary condition. The SCM is a new and innovative way to solve boundary value problem of differential equation and seepage flow theory, which is especially used in Petroleum Engineering.
Authors: Fei Xu, Masanori Kikuchi
Abstract: Smoothed Particle Hydrodynamics (SPH) is a relatively new technique for simulating the dynamic response of solids, especially for high velocity impact and fracture problem. However, closer examination of SPH reveals some severe problems. The major difficulties are: (1) tensile instability; (2) zero-energy mode; (3) boundary deficiency; (4) less accuracy. One solution to these major difficulties with SPH is to improve the consistency of the kernel function. Based on the Reproducing Kernel Particle Method (RKPM), the concept of the proposed simplified linear consistency is introduced. The most attractive feature of the simplified linear consistency is the ease and cheapness of doing 3D calculation. One contribution of this paper is to show clearly the accuracy of solution gradually improved by increasing the order of the consistency. Simple 3D impacting models are established with different geometries and higher accurate results are obtained by using higher consistency kernel functions. Other features as numerical convergence, computational efficiency, etc. and some considerations of the simplified linear consistency kernel function are also discussed.
Authors: Jing Tang, Xian Jun Shi, Wen Guang Zhang
Abstract: A K-Means kernel density estimation was proposed and it was used in the pretreatment process of circuit fault diagnosis. The unequal division and losing division problem caused by the traditional method are solved by this method. It also avoid the singular problem which is usually caused by the high dimension of characteristic data. A kernel function is designed and it was integrated with fuzzy support vector machine method to solve the classification problem of multi-faults . At last, a solution of optimal bandwidth is given to improve the proposed method.
Authors: Yu Kai Yao, Yang Liu, Zhao Li, Xiao Yun Chen
Abstract: Support Vector Machine (SVM) is one of the most popular and effective data mining algorithms which can be used to resolve classification or regression problems, and has attracted much attention these years. SVM could find the optimal separating hyperplane between classes, which afford outstanding generalization ability with it. Usually all the labeled records are used as training set. However, the optimal separating hyperplane only depends on a few crucial samples (Support Vectors, SVs), we neednt train SVM model on the whole training set. In this paper a novel SVM model based on K-means clustering is presented, in which only a small subset of the original training set is selected to constitute the final training set, and the SVM classifier is built through training on these selected samples. This greatly decrease the scale of the training set, and effectively saves the training and predicting cost of SVM, meanwhile guarantees its generalization performance.
Authors: Ya Ting Hu, Fu Heng Qu, Yao Hong Xue, Yong Yang
Abstract: To avoid the initialization sensitivity and low computational efficiency problems of the kernelized possibilistic c-means clustering algorithm (KPCM), a new clustering algorithm called efficient and robust kernelized possibilistic c-means clustering algorithm (ERKPCM) was proposed in this paper. ERKPCM improved KPCM by two ways. First, the data are refined by the data reduction technique, which makes it keep the data structure of the original data and have higher efficiency. Secondly, weighted clustering algorithm is executed several times to estimate cluster centers accurately, which makes it more robust to initializations and get more reasonable partitions. As a by-product, ERKPCM overcomes the problem of generating coincident clusters of KPCM. The contrast experimental results with conventional algorithms show that ERKPCM is more robust to initializations, and has a relatively high precision and efficiency.
Authors: Zheng Hua Liu, Li Han
Abstract: Kernel-based density estimation technique, especially Mean-shift based tracking technique, is a successful application to target tracking, which has the characteristics such as with few parameters, robustness, and fast convergence. However, classic Mean-shift based tracking algorithm uses fixed kernel-bandwidth, which limits the performance when the target’s orientation and scale change. An Improved adaptive kernel-based object tracking is proposed, which extend 2-dimentional mean shift to 3-dimentional, meanwhile combine multiple scale theory into tracking algorithm. Such improvements can enable the algorithm not only track zooming objects, but also track rotating objects. The experimental results validate that the new algorithm can adapt to the changes of orientation and scale of the target effectively.
Authors: Hong Xia Wang, Ke Jian Yang, Feng Gao
Abstract: This paper studies a novel visual word generation method in the Bag-of-words model for object categorization. The conventional Bag-of-words algorithm represents the cluster centers as visual words, which led to the incomplete expressions of image semantic information, so an improved method for visual word generation using the soft-decision based on kernel function is proposed. First, SIFT keypoints of images are extracted. Then, after clustering SIFT keypoints, some typical SIFT keypoints are selected from a cluster by kernel density estimation using a kernel function. Finally, these selected keypoints are trained employing SVM to generate a visual word of this cluster. Experimental results show that the proposed visual word generation method enhances the expressions of image semantic information, increases the recall ratio effectively, and improves significantly the effect of object categorization.
Authors: Rui Zhang, Tong Bo Liu, Ming Wen Zheng
Abstract: In this paper, we proposed a new fuzzy support vector machine(called L2–FSVM here), which error part of object is L2–norm.Meanwhile we introduce a new method of generating fuzzy memberships so as to reduce to effects of outliers. The experimental results demonstrate that the L2-FSVM method provides improved ability to reduce to effects of outliers in comparison with traditional SVMs and FSVMs, and claim that L2–FSVM is the best way to solve the binary classification in the three methods stated above.
Authors: Hong Bing Gao, Liao Yang, Xian Zhang, Chen Cheng
Abstract: A brief introduction of the basic concepts of the classification interval, the optimal classification surface and support vector; explained derivation of SVM based on Lagrange optimization method; Sigmoid kernel function and so on. It describes three methods of C-SVM、V-SVM and least squares SVM based on Sigmoid kernel function. To a bearing failure as a example to compare three results of SVM training of the kernel linear function, polynomial kernel function, Sigmoid kernel function, The results show that satisfactory fault analysis demand the appropriate kernel function selection. Fault in the gear box, the bearing failure is 19%, In addition, the rate is as high as 30% in other rotating machinery system failure [1,2].Thus, rolling bearing condition monitoring and fault diagnosis are very important to production safety, and many scholars have done numerous studies [3,4]. Support vector machine method is a learning methods based on statistical learning theory Vapnik-Chervonenkis dimension theory and structural risk minimization [5,6].
Authors: Xiang Zhang
Abstract: In this paper, 1-D mathematical model of the coagulation process of the polyacrylonitrile (PAN) carbon fiber is established using Fick diffusion law. Boundary stabilization for a linear parabolic diffusion-reaction partial differential equation (PDE) is considered. We use the method of backstepping to implement the boundary control of the concentration diffusion in the forming process of carbon fiber. By using the coordinate transformation, we transform the original system to a standard static system. The transformation depends on a so called gain kernel function, and we can design the boundary feedback controller using the kernel function. For the model in this paper, the kernel function itself is a hyperbolic PDE, and there is no explicit formation. Therefore, we use numerical methods to obtain the kernel function, and give the simulation results for the closed-loop control response. The simulation results show that the open-loop unstable system is stabilized by a boundary feedback.
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