Wavelet, a powerful tool for signal processing, can be used to approximate the target func-tion. For enhancing the sparse property of wavelet approximation, a new algorithm was proposed by using wavelet kernel Support...Wavelet, a powerful tool for signal processing, can be used to approximate the target func-tion. For enhancing the sparse property of wavelet approximation, a new algorithm was proposed by using wavelet kernel Support Vector Machines (SVM), which can converge to minimum error with bet-ter sparsity. Here, wavelet functions would be firstly used to construct the admitted kernel for SVM according to Mercy theory; then new SVM with this kernel can be used to approximate the target fun-citon with better sparsity than wavelet approxiamtion itself. The results obtained by our simulation ex-periment show the feasibility and validity of wavelet kernel support vector machines.展开更多
By combining the wavelet decomposition with kernel method, a practical approach of universal multiscale wavelet kernels constructed in reproducing kernel Hilbert space （RKHS） is discussed, and an identification sche...By combining the wavelet decomposition with kernel method, a practical approach of universal multiscale wavelet kernels constructed in reproducing kernel Hilbert space （RKHS） is discussed, and an identification scheme using wavelet support vector machines （WSVM） estimator is proposed for nordinear dynamic systems. The good approximating properties of wavelet kernel function enhance the generalization ability of the proposed method, and the comparison of some numerical experimental results between the novel approach and some existing methods is encouraging.展开更多
To enhance the detection accuracy and deduce false positive rate of distributed denial of service （DDoS） attack detection, a new machine learning method was proposed. With the analysis of support vector machine （SV...To enhance the detection accuracy and deduce false positive rate of distributed denial of service （DDoS） attack detection, a new machine learning method was proposed. With the analysis of support vector machine （SVM） and the wavelet kernel function theory, an admissive support vector kernel, which is a wavelet kernel constructed in this article, implements the combination of the wavelet technique with SVM. Then, wavelet support vector machine （WSVM） is applied to DDoS attack detections and as a classifying means to test the validity of the wavelet kernel function. Simulation experiments show that under the same conditions, the predictive ability of WSVM is improved and the computation burden is alleviated. The detection accuracy of WSVM is higher than the traditional SVM by about 4%, while its false positive is lower than the traditional SVM. Thus, for DDoS detections, WSVM shows better detection performance and is more adaptive to the changing network environment.展开更多
The relationship among Mercer kernel, reproducing kernel and positive definite kernel in support vector machine （SVM） is proved and their roles in SVM are discussed. The quadratic form of the kernel matrix is used t...The relationship among Mercer kernel, reproducing kernel and positive definite kernel in support vector machine （SVM） is proved and their roles in SVM are discussed. The quadratic form of the kernel matrix is used to confirm the positive definiteness and their construction. Based on the Bochner theorem, some translation invariant kernels are checked in their Fourier domain. Some rotation invariant radial kernels are inspected according to the Schoenberg theorem. Finally, the construction of discrete scaling and wavelet kernels, the kernel selection and the kernel parameter learning are discussed.展开更多
针对核电多回路耦合系统在升功率运行中异常传感器检测困难、检测延时及检测精度低等问题,提出了一种自联想核回归模型(auto-associative kernel regression,简称AAKR)与修正序贯概率比检验(sequential probability ratio test,简称SPRT...针对核电多回路耦合系统在升功率运行中异常传感器检测困难、检测延时及检测精度低等问题,提出了一种自联想核回归模型(auto-associative kernel regression,简称AAKR)与修正序贯概率比检验(sequential probability ratio test,简称SPRT)相结合的方法。首先,利用小波软阈值降噪方法对监测数据预处理,获取高质量的多源传感器解调信号;其次,采用AAKR构造传感器正常运行数据的估计值,并获取多源传感器测量值与估计值之间的残差;然后,运用滑动时间窗获取不同阶段残差向量的均值和方差,设计一种SPRT检测规则对传感器残差进行异常检测;最后,用核电一、二回路耦合系统模拟机实验数据进行方法验证与性能分析。结果表明,所提传感器异常检测方法的准确率达到99.52%,异常检测延时降低了81.73%,可有效提高现有核电厂传感器异常检测的稳定性。展开更多
We present wavelet bases made of piecewise (low degree) polynomial functions with an (arbitrary) assigned number of vanishing moments. We study some of the properties of these wavelet bases;in particular we consider t...We present wavelet bases made of piecewise (low degree) polynomial functions with an (arbitrary) assigned number of vanishing moments. We study some of the properties of these wavelet bases;in particular we consider their use in the approximation of functions and in numerical quadrature. We focus on two applications: integral kernel sparsification and digital image compression and reconstruction. In these application areas the use of these wavelet bases gives very satisfactory results.展开更多
文摘Wavelet, a powerful tool for signal processing, can be used to approximate the target func-tion. For enhancing the sparse property of wavelet approximation, a new algorithm was proposed by using wavelet kernel Support Vector Machines (SVM), which can converge to minimum error with bet-ter sparsity. Here, wavelet functions would be firstly used to construct the admitted kernel for SVM according to Mercy theory; then new SVM with this kernel can be used to approximate the target fun-citon with better sparsity than wavelet approxiamtion itself. The results obtained by our simulation ex-periment show the feasibility and validity of wavelet kernel support vector machines.
基金the National 973 Key Fundamental Research Project of China (Grant No.2002CB312200)
文摘By combining the wavelet decomposition with kernel method, a practical approach of universal multiscale wavelet kernels constructed in reproducing kernel Hilbert space （RKHS） is discussed, and an identification scheme using wavelet support vector machines （WSVM） estimator is proposed for nordinear dynamic systems. The good approximating properties of wavelet kernel function enhance the generalization ability of the proposed method, and the comparison of some numerical experimental results between the novel approach and some existing methods is encouraging.
基金National Natural Science Foundation of China (60573141, 60773041)the Hi-Tech Research and Development Program of China (2006AA01Z439)+5 种基金Natural Science Foundation of Jiangsu Province (BK2005146)High Technology Research Program of Jiangsu Province (BG2005037, BG2006001)Key Laboratory of Information Technology Processing of Jiangsu Province (kjs0606)High Technology Research Program of Nanjing City (2006RZ105)State Key Laboratory of Modern Communication (9140C1101010603)Jiangsu Provincial Research Scheme of Natural Science for Higher Education Institutions (07KJB520083)
文摘To enhance the detection accuracy and deduce false positive rate of distributed denial of service （DDoS） attack detection, a new machine learning method was proposed. With the analysis of support vector machine （SVM） and the wavelet kernel function theory, an admissive support vector kernel, which is a wavelet kernel constructed in this article, implements the combination of the wavelet technique with SVM. Then, wavelet support vector machine （WSVM） is applied to DDoS attack detections and as a classifying means to test the validity of the wavelet kernel function. Simulation experiments show that under the same conditions, the predictive ability of WSVM is improved and the computation burden is alleviated. The detection accuracy of WSVM is higher than the traditional SVM by about 4%, while its false positive is lower than the traditional SVM. Thus, for DDoS detections, WSVM shows better detection performance and is more adaptive to the changing network environment.
基金Supported by the National Natural Science Foundation of China(60473035)~~
文摘The relationship among Mercer kernel, reproducing kernel and positive definite kernel in support vector machine （SVM） is proved and their roles in SVM are discussed. The quadratic form of the kernel matrix is used to confirm the positive definiteness and their construction. Based on the Bochner theorem, some translation invariant kernels are checked in their Fourier domain. Some rotation invariant radial kernels are inspected according to the Schoenberg theorem. Finally, the construction of discrete scaling and wavelet kernels, the kernel selection and the kernel parameter learning are discussed.
文摘针对核电多回路耦合系统在升功率运行中异常传感器检测困难、检测延时及检测精度低等问题,提出了一种自联想核回归模型(auto-associative kernel regression,简称AAKR)与修正序贯概率比检验(sequential probability ratio test,简称SPRT)相结合的方法。首先,利用小波软阈值降噪方法对监测数据预处理,获取高质量的多源传感器解调信号;其次,采用AAKR构造传感器正常运行数据的估计值,并获取多源传感器测量值与估计值之间的残差;然后,运用滑动时间窗获取不同阶段残差向量的均值和方差,设计一种SPRT检测规则对传感器残差进行异常检测;最后,用核电一、二回路耦合系统模拟机实验数据进行方法验证与性能分析。结果表明,所提传感器异常检测方法的准确率达到99.52%,异常检测延时降低了81.73%,可有效提高现有核电厂传感器异常检测的稳定性。
文摘We present wavelet bases made of piecewise (low degree) polynomial functions with an (arbitrary) assigned number of vanishing moments. We study some of the properties of these wavelet bases;in particular we consider their use in the approximation of functions and in numerical quadrature. We focus on two applications: integral kernel sparsification and digital image compression and reconstruction. In these application areas the use of these wavelet bases gives very satisfactory results.
