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
Identification of reservoir types in deep carbonates has always been a great challenge due to complex logging responses caused by the heterogeneous scale and distribution of storage spaces.Traditional cross-plot analy...Identification of reservoir types in deep carbonates has always been a great challenge due to complex logging responses caused by the heterogeneous scale and distribution of storage spaces.Traditional cross-plot analysis and empirical formula methods for identifying reservoir types using geophysical logging data have high uncertainty and low efficiency,which cannot accurately reflect the nonlinear relationship between reservoir types and logging data.Recently,the kernel Fisher discriminant analysis(KFD),a kernel-based machine learning technique,attracts attention in many fields because of its strong nonlinear processing ability.However,the overall performance of KFD model may be limited as a single kernel function cannot simultaneously extrapolate and interpolate well,especially for highly complex data cases.To address this issue,in this study,a mixed kernel Fisher discriminant analysis(MKFD)model was established and applied to identify reservoir types of the deep Sinian carbonates in central Sichuan Basin,China.The MKFD model was trained and tested with 453 datasets from 7 coring wells,utilizing GR,CAL,DEN,AC,CNL and RT logs as input variables.The particle swarm optimization(PSO)was adopted for hyper-parameter optimization of MKFD model.To evaluate the model performance,prediction results of MKFD were compared with those of basic-kernel based KFD,RF and SVM models.Subsequently,the built MKFD model was applied in a blind well test,and a variable importance analysis was conducted.The comparison and blind test results demonstrated that MKFD outperformed traditional KFD,RF and SVM in the identification of reservoir types,which provided higher accuracy and stronger generalization.The MKFD can therefore be a reliable method for identifying reservoir types of deep carbonates.展开更多
Monitoring sensors in complex engineering environments often record abnormal data,leading to significant positioning errors.To reduce the influence of abnormal arrival times,we introduce an innovative,outlier-robust l...Monitoring sensors in complex engineering environments often record abnormal data,leading to significant positioning errors.To reduce the influence of abnormal arrival times,we introduce an innovative,outlier-robust localization method that integrates kernel density estimation(KDE)with damping linear correction to enhance the precision of microseismic/acoustic emission(MS/AE)source positioning.Our approach systematically addresses abnormal arrival times through a three-step process:initial location by 4-arrival combinations,elimination of outliers based on three-dimensional KDE,and refinement using a linear correction with an adaptive damping factor.We validate our method through lead-breaking experiments,demonstrating over a 23%improvement in positioning accuracy with a maximum error of 9.12 mm(relative error of 15.80%)—outperforming 4 existing methods.Simulations under various system errors,outlier scales,and ratios substantiate our method’s superior performance.Field blasting experiments also confirm the practical applicability,with an average positioning error of 11.71 m(relative error of 7.59%),compared to 23.56,66.09,16.95,and 28.52 m for other methods.This research is significant as it enhances the robustness of MS/AE source localization when confronted with data anomalies.It also provides a practical solution for real-world engineering and safety monitoring applications.展开更多
A non-Maxwellian collision kernel is employed to study the evolution of wealth distribution in a multi-agent society.The collision kernel divides agents into two different groups under certain conditions. Applying the...A non-Maxwellian collision kernel is employed to study the evolution of wealth distribution in a multi-agent society.The collision kernel divides agents into two different groups under certain conditions. Applying the kinetic theory of rarefied gases, we construct a two-group kinetic model for the evolution of wealth distribution. Under the continuous trading limit, the Fokker–Planck equation is derived and its steady-state solution is obtained. For the non-Maxwellian collision kernel, we find a suitable redistribution operator to match the taxation. Our results illustrate that taxation and redistribution have the property to change the Pareto index.展开更多
This paper is the sequel to our study of heat kernel on Ricci shrinkers[29].In this paper,we improve many estimates in[29]and extend the recent progress of Bamler[2].In particular,we drop the compactness and curvature...This paper is the sequel to our study of heat kernel on Ricci shrinkers[29].In this paper,we improve many estimates in[29]and extend the recent progress of Bamler[2].In particular,we drop the compactness and curvature boundedness assumptions and show that the theory of F-convergence holds naturally on any Ricci flows induced by Ricci shrinkers.展开更多
The extended kernel ridge regression(EKRR)method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models.These are:(i)the isospin-dependent A^(...The extended kernel ridge regression(EKRR)method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models.These are:(i)the isospin-dependent A^(1∕3) formula,(ii)relativistic continuum Hartree-Bogoliubov(RCHB)theory,(iii)Hartree-Fock-Bogoliubov(HFB)model HFB25,(iv)the Weizsacker-Skyrme(WS)model WS*,and(v)HFB25*model.In the last two models,the charge radii were calculated using a five-parameter formula with the nuclear shell corrections and deformations obtained from the WS and HFB25 models,respectively.For each model,the resultant root-mean-square deviation for the 1014 nuclei with proton number Z≥8 can be significantly reduced to 0.009-0.013 fm after considering the modification with the EKRR method.The best among them was the RCHB model,with a root-mean-square deviation of 0.0092 fm.The extrapolation abilities of the KRR and EKRR methods for the neutron-rich region were examined,and it was found that after considering the odd-even effects,the extrapolation power was improved compared with that of the original KRR method.The strong odd-even staggering of nuclear charge radii of Ca and Cu isotopes and the abrupt kinks across the neutron N=126 and 82 shell closures were also calculated and could be reproduced quite well by calculations using the EKRR method.展开更多
Although it is recognized that the post-harvest system is most responsible for the loss of soybean quality,the real impact of this loss is still unknown.Brazilian regulation allows 15%and 30%of broken soybean for grou...Although it is recognized that the post-harvest system is most responsible for the loss of soybean quality,the real impact of this loss is still unknown.Brazilian regulation allows 15%and 30%of broken soybean for group I and group II(quality groups),respectively.However,the industry is not informed about the loss in the quality parameters of soybeans and its impacts during long-term storage.Therefore,the objective was to evaluate the effect of the breakage kernel percentage of soybean stored for 12 months.Content of 15% of breakage kernels did not affect soybean quality.However,content of 30% of breakage kernels affected significantly soybean quality,which was evidenced by the increase of up to 75% in moldy soybeans,72% in acidity,50% in leached solids,27% in electrical conductivity,and the decrease of up to 12% in soluble protein,6.4% in germination and 3.5% in thousand kernel weight after 8 months of storage.Although the legislation establishes a percentage limit,it is recommended to store soybeans with up to 15% breakage kernels.On the contrary,values higher than that can cause a significant reduction in soybean quality,resulting in commercial losses.展开更多
The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, fo...The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, for a class of kernels 9 which is singular at zero, the exponential decay rate of the solution energy. The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009. This work improves earlier results.展开更多
On the basis of the reproducing kernel particle method （RKPM）, a new meshless method, which is called the complex variable reproducing kernel particle method （CVRKPM）, for two-dimensional elastodynamics is present...On the basis of the reproducing kernel particle method （RKPM）, a new meshless method, which is called the complex variable reproducing kernel particle method （CVRKPM）, for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM.展开更多
设l∈N,δ=k/p-k+1/2,以及<p<1.本文的主要结果是建立广义BochnerRiesz平均的核的某种分解: ((1-|ξ|~l)~σ+)^(x)=sum from f=1 to J(k,l,p) b_f((1-|ξ|~2)ь+ζ)^(x)+T(|x|),其中T满足 T^(n+1)(s)≤cmin{(1+s)_(k-n-2),(1+s)^(...设l∈N,δ=k/p-k+1/2,以及<p<1.本文的主要结果是建立广义BochnerRiesz平均的核的某种分解: ((1-|ξ|~l)~σ+)^(x)=sum from f=1 to J(k,l,p) b_f((1-|ξ|~2)ь+ζ)^(x)+T(|x|),其中T满足 T^(n+1)(s)≤cmin{(1+s)_(k-n-2),(1+s)^(-k,p)},0<s<∞以及n=[K(1/p-1)]·作为上述分解的一个直接结果,我们得到:临界阶广义Bochner-Riesz平均在H^p(R^k)上的a.e.收敛性。展开更多
How to fit a properly nonlinear classification model from conventional well logs to lithofacies is a key problem for machine learning methods.Kernel methods(e.g.,KFD,SVM,MSVM)are effective attempts to solve this issue...How to fit a properly nonlinear classification model from conventional well logs to lithofacies is a key problem for machine learning methods.Kernel methods(e.g.,KFD,SVM,MSVM)are effective attempts to solve this issue due to abilities of handling nonlinear features by kernel functions.Deep mining of log features indicating lithofacies still needs to be improved for kernel methods.Hence,this work employs deep neural networks to enhance the kernel principal component analysis(KPCA)method and proposes a deep kernel method(DKM)for lithofacies identification using well logs.DKM includes a feature extractor and a classifier.The feature extractor consists of a series of KPCA models arranged according to residual network structure.A gradient-free optimization method is introduced to automatically optimize parameters and structure in DKM,which can avoid complex tuning of parameters in models.To test the validation of the proposed DKM for lithofacies identification,an open-sourced dataset with seven con-ventional logs(GR,CAL,AC,DEN,CNL,LLD,and LLS)and lithofacies labels from the Daniudi Gas Field in China is used.There are eight lithofacies,namely clastic rocks(pebbly,coarse,medium,and fine sand-stone,siltstone,mudstone),coal,and carbonate rocks.The comparisons between DKM and three commonly used kernel methods(KFD,SVM,MSVM)show that(1)DKM(85.7%)outperforms SVM(77%),KFD(79.5%),and MSVM(82.8%)in accuracy of lithofacies identification;(2)DKM is about twice faster than the multi-kernel method(MSVM)with good accuracy.The blind well test in Well D13 indicates that compared with the other three methods DKM improves about 24%in accuracy,35%in precision,41%in recall,and 40%in F1 score,respectively.In general,DKM is an effective method for complex lithofacies identification.This work also discussed the optimal structure and classifier for DKM.Experimental re-sults show that(m_(1),m_(2),O)is the optimal model structure and linear svM is the optimal classifier.(m_(1),m_(2),O)means there are m KPCAs,and then m2 residual units.A workflow to determine an optimal classifier in DKM for lithofacies identification is proposed,too.展开更多
对农作物品种正确分类是作物分类学的重要内容,为考察X-ray成像技术对小麦品种分类研究的有效性,基于软X-ray成像仪采集的3品种(Kama,Rosa and Canadian)每个品种70个籽粒,共210个籽粒样本的X-ray扫描图像,并针对其7个形态几何特征(面...对农作物品种正确分类是作物分类学的重要内容,为考察X-ray成像技术对小麦品种分类研究的有效性,基于软X-ray成像仪采集的3品种(Kama,Rosa and Canadian)每个品种70个籽粒,共210个籽粒样本的X-ray扫描图像,并针对其7个形态几何特征(面积、周长、紧致度、籽粒长度、宽度、偏斜度、种子腹沟长度),提出了一种使用Kernel-ICA的方法先对特征进行优化,再进行小麦品种的聚类与识别的方法,并与K-means、C-means 2种聚类方法以及基于工神经网络(ANN)和支持向量机(SVM)2种识别方法的分类结果进行比较,结果发现:分类正确率从高到低分别为:Kernel-ICA、SVM、C-means、K-means、BP-ANN,分类正确率分别为:91.9%、90.5%、89.5%、87.1%、86.9%。研究提出的Kernel-ICA的方法,聚类优化和识别能力较强,对软X-ray成像的小麦品种进行分类,已基本上满足农艺上对小麦品种分类需要,对农作物种质资源鉴别和作物品种分类研究具有积极意义。展开更多
This paper presents a classifier named kernel-based nonlinear representor (KNR) for optimal representation of pattern features. Adopting the Gaussian kernel, with the kernel width adaptively estimated by a simple tech...This paper presents a classifier named kernel-based nonlinear representor (KNR) for optimal representation of pattern features. Adopting the Gaussian kernel, with the kernel width adaptively estimated by a simple technique, it is applied to eigenface classification. Experimental results on the ORL face database show that it improves performance by around 6 points, in classification rate, over the Euclidean distance classifier.展开更多
Aiming at the large cost of calculating variable bandwidth kernel particle filter and the high complexity of its algorithm,a self-adjusting kernel function particle filter is presented. Kernel density estimation is fa...Aiming at the large cost of calculating variable bandwidth kernel particle filter and the high complexity of its algorithm,a self-adjusting kernel function particle filter is presented. Kernel density estimation is facilitated to iterate and obtain new particle set. And the standard deviation of particle is introduced in the kernel bandwidth. According to the characteristics of particle distribution,the bandwidth is dynamically adjusted,and the particle distribution can thus be more close to the posterior probability density model of the system. Meanwhile,the kernel density is used to estimate the weight of updating particle and the system state. The simulation results show the feasibility and effectiveness of the proposed algorithm.展开更多
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.
基金supported by the National Natural Science Foundation of China(No.U21B2062)the Natural Science Foundation of Hubei Province(No.2023AFB307)。
文摘Identification of reservoir types in deep carbonates has always been a great challenge due to complex logging responses caused by the heterogeneous scale and distribution of storage spaces.Traditional cross-plot analysis and empirical formula methods for identifying reservoir types using geophysical logging data have high uncertainty and low efficiency,which cannot accurately reflect the nonlinear relationship between reservoir types and logging data.Recently,the kernel Fisher discriminant analysis(KFD),a kernel-based machine learning technique,attracts attention in many fields because of its strong nonlinear processing ability.However,the overall performance of KFD model may be limited as a single kernel function cannot simultaneously extrapolate and interpolate well,especially for highly complex data cases.To address this issue,in this study,a mixed kernel Fisher discriminant analysis(MKFD)model was established and applied to identify reservoir types of the deep Sinian carbonates in central Sichuan Basin,China.The MKFD model was trained and tested with 453 datasets from 7 coring wells,utilizing GR,CAL,DEN,AC,CNL and RT logs as input variables.The particle swarm optimization(PSO)was adopted for hyper-parameter optimization of MKFD model.To evaluate the model performance,prediction results of MKFD were compared with those of basic-kernel based KFD,RF and SVM models.Subsequently,the built MKFD model was applied in a blind well test,and a variable importance analysis was conducted.The comparison and blind test results demonstrated that MKFD outperformed traditional KFD,RF and SVM in the identification of reservoir types,which provided higher accuracy and stronger generalization.The MKFD can therefore be a reliable method for identifying reservoir types of deep carbonates.
基金the financial support provided by the National Key Research and Development Program for Young Scientists(No.2021YFC2900400)Postdoctoral Fellowship Program of China Postdoctoral Science Foundation(CPSF)(No.GZB20230914)+2 种基金National Natural Science Foundation of China(No.52304123)China Postdoctoral Science Foundation(No.2023M730412)Chongqing Outstanding Youth Science Foundation Program(No.CSTB2023NSCQ-JQX0027).
文摘Monitoring sensors in complex engineering environments often record abnormal data,leading to significant positioning errors.To reduce the influence of abnormal arrival times,we introduce an innovative,outlier-robust localization method that integrates kernel density estimation(KDE)with damping linear correction to enhance the precision of microseismic/acoustic emission(MS/AE)source positioning.Our approach systematically addresses abnormal arrival times through a three-step process:initial location by 4-arrival combinations,elimination of outliers based on three-dimensional KDE,and refinement using a linear correction with an adaptive damping factor.We validate our method through lead-breaking experiments,demonstrating over a 23%improvement in positioning accuracy with a maximum error of 9.12 mm(relative error of 15.80%)—outperforming 4 existing methods.Simulations under various system errors,outlier scales,and ratios substantiate our method’s superior performance.Field blasting experiments also confirm the practical applicability,with an average positioning error of 11.71 m(relative error of 7.59%),compared to 23.56,66.09,16.95,and 28.52 m for other methods.This research is significant as it enhances the robustness of MS/AE source localization when confronted with data anomalies.It also provides a practical solution for real-world engineering and safety monitoring applications.
基金Project supported by the National Natural Science Foundation of China(Grant No.11471263)the Natural Science Foundation of Xinjiang Uygur Autonomous Region,China(Grant No.2021D01B09)+1 种基金the Initial Research Foundation of Kashi University(Grant No.022024076)“Mathematics and Finance Research Centre Funding Project”,Dazhou Social Science Federation(Grant No.SCMF202305)。
文摘A non-Maxwellian collision kernel is employed to study the evolution of wealth distribution in a multi-agent society.The collision kernel divides agents into two different groups under certain conditions. Applying the kinetic theory of rarefied gases, we construct a two-group kinetic model for the evolution of wealth distribution. Under the continuous trading limit, the Fokker–Planck equation is derived and its steady-state solution is obtained. For the non-Maxwellian collision kernel, we find a suitable redistribution operator to match the taxation. Our results illustrate that taxation and redistribution have the property to change the Pareto index.
基金supported by the YSBR-001,the NSFC(12201597)research funds from USTC(University of Science and Technology of China)and CAS(Chinese Academy of Sciences)+2 种基金supported by the YSBR-001the NSFC(11971452,12026251)a research fund from USTC.
文摘This paper is the sequel to our study of heat kernel on Ricci shrinkers[29].In this paper,we improve many estimates in[29]and extend the recent progress of Bamler[2].In particular,we drop the compactness and curvature boundedness assumptions and show that the theory of F-convergence holds naturally on any Ricci flows induced by Ricci shrinkers.
基金This work was supported by the National Natural Science Foundation of China(Nos.11875027,11975096).
文摘The extended kernel ridge regression(EKRR)method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models.These are:(i)the isospin-dependent A^(1∕3) formula,(ii)relativistic continuum Hartree-Bogoliubov(RCHB)theory,(iii)Hartree-Fock-Bogoliubov(HFB)model HFB25,(iv)the Weizsacker-Skyrme(WS)model WS*,and(v)HFB25*model.In the last two models,the charge radii were calculated using a five-parameter formula with the nuclear shell corrections and deformations obtained from the WS and HFB25 models,respectively.For each model,the resultant root-mean-square deviation for the 1014 nuclei with proton number Z≥8 can be significantly reduced to 0.009-0.013 fm after considering the modification with the EKRR method.The best among them was the RCHB model,with a root-mean-square deviation of 0.0092 fm.The extrapolation abilities of the KRR and EKRR methods for the neutron-rich region were examined,and it was found that after considering the odd-even effects,the extrapolation power was improved compared with that of the original KRR method.The strong odd-even staggering of nuclear charge radii of Ca and Cu isotopes and the abrupt kinks across the neutron N=126 and 82 shell closures were also calculated and could be reproduced quite well by calculations using the EKRR method.
基金Coordenacao de Aperfeicoamento de Pessoal de Nível Superior - Brasil (CAPES)Fundacao de Amparo à Pesquisa do Estado do Rio Grande do Sul (FAPERGS)+2 种基金Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)financed in part by Coordenacao de Aperfeicoamento de Pessoal de Nível Superior-Brasil(CAPES)-Finance code 001,Fundacao de Amparoa Pesquisa do Estado do Rio Grande do Sul(FAPERGS)-Finances code 17/2551-0000935-5,22/2551-0001051-2,21/2551-0002255-8Conselho Nacional de Desenvolvimento Científico e Tecnologico(CNPq)-Finance codes 205518/2018-4,312603/2018-5.
文摘Although it is recognized that the post-harvest system is most responsible for the loss of soybean quality,the real impact of this loss is still unknown.Brazilian regulation allows 15%and 30%of broken soybean for group I and group II(quality groups),respectively.However,the industry is not informed about the loss in the quality parameters of soybeans and its impacts during long-term storage.Therefore,the objective was to evaluate the effect of the breakage kernel percentage of soybean stored for 12 months.Content of 15% of breakage kernels did not affect soybean quality.However,content of 30% of breakage kernels affected significantly soybean quality,which was evidenced by the increase of up to 75% in moldy soybeans,72% in acidity,50% in leached solids,27% in electrical conductivity,and the decrease of up to 12% in soluble protein,6.4% in germination and 3.5% in thousand kernel weight after 8 months of storage.Although the legislation establishes a percentage limit,it is recommended to store soybeans with up to 15% breakage kernels.On the contrary,values higher than that can cause a significant reduction in soybean quality,resulting in commercial losses.
文摘The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, for a class of kernels 9 which is singular at zero, the exponential decay rate of the solution energy. The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009. This work improves earlier results.
基金supported by the National Natural Science Foundation of China (Grant No.10871124)the Innovation Program of Shanghai Municipal Education Commission,China (Grant No.09ZZ99)
文摘On the basis of the reproducing kernel particle method （RKPM）, a new meshless method, which is called the complex variable reproducing kernel particle method （CVRKPM）, for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM.
文摘设l∈N,δ=k/p-k+1/2,以及<p<1.本文的主要结果是建立广义BochnerRiesz平均的核的某种分解: ((1-|ξ|~l)~σ+)^(x)=sum from f=1 to J(k,l,p) b_f((1-|ξ|~2)ь+ζ)^(x)+T(|x|),其中T满足 T^(n+1)(s)≤cmin{(1+s)_(k-n-2),(1+s)^(-k,p)},0<s<∞以及n=[K(1/p-1)]·作为上述分解的一个直接结果,我们得到:临界阶广义Bochner-Riesz平均在H^p(R^k)上的a.e.收敛性。
基金supported by the National Natural Science Foundation of China(Grant No.42002134)China Postdoctoral Science Foundation(Grant No.2021T140735)Science Foundation of China University of Petroleum,Beijing(Grant Nos.2462020XKJS02 and 2462020YXZZ004).
文摘How to fit a properly nonlinear classification model from conventional well logs to lithofacies is a key problem for machine learning methods.Kernel methods(e.g.,KFD,SVM,MSVM)are effective attempts to solve this issue due to abilities of handling nonlinear features by kernel functions.Deep mining of log features indicating lithofacies still needs to be improved for kernel methods.Hence,this work employs deep neural networks to enhance the kernel principal component analysis(KPCA)method and proposes a deep kernel method(DKM)for lithofacies identification using well logs.DKM includes a feature extractor and a classifier.The feature extractor consists of a series of KPCA models arranged according to residual network structure.A gradient-free optimization method is introduced to automatically optimize parameters and structure in DKM,which can avoid complex tuning of parameters in models.To test the validation of the proposed DKM for lithofacies identification,an open-sourced dataset with seven con-ventional logs(GR,CAL,AC,DEN,CNL,LLD,and LLS)and lithofacies labels from the Daniudi Gas Field in China is used.There are eight lithofacies,namely clastic rocks(pebbly,coarse,medium,and fine sand-stone,siltstone,mudstone),coal,and carbonate rocks.The comparisons between DKM and three commonly used kernel methods(KFD,SVM,MSVM)show that(1)DKM(85.7%)outperforms SVM(77%),KFD(79.5%),and MSVM(82.8%)in accuracy of lithofacies identification;(2)DKM is about twice faster than the multi-kernel method(MSVM)with good accuracy.The blind well test in Well D13 indicates that compared with the other three methods DKM improves about 24%in accuracy,35%in precision,41%in recall,and 40%in F1 score,respectively.In general,DKM is an effective method for complex lithofacies identification.This work also discussed the optimal structure and classifier for DKM.Experimental re-sults show that(m_(1),m_(2),O)is the optimal model structure and linear svM is the optimal classifier.(m_(1),m_(2),O)means there are m KPCAs,and then m2 residual units.A workflow to determine an optimal classifier in DKM for lithofacies identification is proposed,too.
文摘对农作物品种正确分类是作物分类学的重要内容,为考察X-ray成像技术对小麦品种分类研究的有效性,基于软X-ray成像仪采集的3品种(Kama,Rosa and Canadian)每个品种70个籽粒,共210个籽粒样本的X-ray扫描图像,并针对其7个形态几何特征(面积、周长、紧致度、籽粒长度、宽度、偏斜度、种子腹沟长度),提出了一种使用Kernel-ICA的方法先对特征进行优化,再进行小麦品种的聚类与识别的方法,并与K-means、C-means 2种聚类方法以及基于工神经网络(ANN)和支持向量机(SVM)2种识别方法的分类结果进行比较,结果发现:分类正确率从高到低分别为:Kernel-ICA、SVM、C-means、K-means、BP-ANN,分类正确率分别为:91.9%、90.5%、89.5%、87.1%、86.9%。研究提出的Kernel-ICA的方法,聚类优化和识别能力较强,对软X-ray成像的小麦品种进行分类,已基本上满足农艺上对小麦品种分类需要,对农作物种质资源鉴别和作物品种分类研究具有积极意义。
文摘This paper presents a classifier named kernel-based nonlinear representor (KNR) for optimal representation of pattern features. Adopting the Gaussian kernel, with the kernel width adaptively estimated by a simple technique, it is applied to eigenface classification. Experimental results on the ORL face database show that it improves performance by around 6 points, in classification rate, over the Euclidean distance classifier.
基金Supported by the National Natural Science Foundation of China(60972059)the General Project of Science and Technology of Xuzhou City(XM12B002)
文摘Aiming at the large cost of calculating variable bandwidth kernel particle filter and the high complexity of its algorithm,a self-adjusting kernel function particle filter is presented. Kernel density estimation is facilitated to iterate and obtain new particle set. And the standard deviation of particle is introduced in the kernel bandwidth. According to the characteristics of particle distribution,the bandwidth is dynamically adjusted,and the particle distribution can thus be more close to the posterior probability density model of the system. Meanwhile,the kernel density is used to estimate the weight of updating particle and the system state. The simulation results show the feasibility and effectiveness of the proposed algorithm.
