This paper studies the problem applying Radial Basis Function Network(RBFN) which is trained by the Recursive Least Square Algorithm(RLSA) to the recognition of one dimensional images of radar targets. The equivalence...This paper studies the problem applying Radial Basis Function Network(RBFN) which is trained by the Recursive Least Square Algorithm(RLSA) to the recognition of one dimensional images of radar targets. The equivalence between the RBFN and the estimate of Parzen window probabilistic density is proved. It is pointed out that the I/O functions in RBFN hidden units can be generalized to general Parzen window probabilistic kernel function or potential function, too. This paper discusses the effects of the shape parameter a in the RBFN and the forgotten factor A in RLSA on the results of the recognition of three kinds of kernel function such as Gaussian, triangle, double-exponential, at the same time, also discusses the relationship between A and the training time in the RBFN.展开更多
A high-precision regional gravity field model is significant in various geodesy applications.In the field of modelling regional gravity fields,the spherical radial basis functions(SRBFs)approach has recently gained wi...A high-precision regional gravity field model is significant in various geodesy applications.In the field of modelling regional gravity fields,the spherical radial basis functions(SRBFs)approach has recently gained widespread attention,while the modelling precision is primarily influenced by the base function network.In this study,we propose a method for constructing a data-adaptive network of SRBFs using a modified Hierarchical Density-Based Spatial Clustering of Applications with Noise(HDBSCAN)algorithm,and the performance of the algorithm is verified by the observed gravity data in the Auvergne area.Furthermore,the turning point method is used to optimize the bandwidth of the basis function spectrum,which satisfies the demand for both high-precision gravity field and quasi-geoid modelling simultaneously.Numerical experimental results indicate that our algorithm has an accuracy of about 1.58 mGal in constructing the gravity field model and about 0.03 m in the regional quasi-geoid model.Compared to the existing methods,the number of SRBFs used for modelling has been reduced by 15.8%,and the time cost to determine the centre positions of SRBFs has been saved by 12.5%.Hence,the modified HDBSCAN algorithm presented here is a suitable design method for constructing the SRBF data adaptive network.展开更多
This paper is an extension of earlier papers [8, 9] on the ＂native＂ Hilbert spaces of functions on some domain Ωbelong toR^d Rd in which conditionally positive definite kernels are reproducing kernels. Here, the fo...This paper is an extension of earlier papers [8, 9] on the ＂native＂ Hilbert spaces of functions on some domain Ωbelong toR^d Rd in which conditionally positive definite kernels are reproducing kernels. Here, the focus is on subspaces of native spaces which are induced via subsets of Ω, and we shall derive a recursive subspace structure of these, leading to recur- sively defined reproducing kernels. As an application, we get a recursive Neville-Aitken- type interpolation process and a recursively defined orthogonal basis for interpolation by translates of kernels.展开更多
The spherical approximation between two nested reproducing kernels Hilbert spaces generated from different smooth kernels is investigated. It is shown that the functions of a space can be approximated by that of the s...The spherical approximation between two nested reproducing kernels Hilbert spaces generated from different smooth kernels is investigated. It is shown that the functions of a space can be approximated by that of the subspace with better smoothness. Furthermore, the upper bound of approximation error is given.展开更多
在数字高程模型(digital elevation model,DEM)建模过程中,传统插值方法以地表光滑连续为基本假设,且只考虑了采样点和待插值点之间的空间相关性,忽略了诸如断裂线等不连续地形特征带来的空间异质性影响,导致断裂线周围的高程被平滑,进...在数字高程模型(digital elevation model,DEM)建模过程中,传统插值方法以地表光滑连续为基本假设,且只考虑了采样点和待插值点之间的空间相关性,忽略了诸如断裂线等不连续地形特征带来的空间异质性影响,导致断裂线周围的高程被平滑,进而使得构建的DEM失真。针对上述问题,提出一种顾及空间异质性的多元径向基函数插值方法。该方法耦合了空间距离、高差、法向量3种地形信息,充分考虑了采样点和待插值点之间的空间相关性和地形特征异质性,确保地形断裂区DEM高精度建模。以国际摄影测量与遥感协会提供的10组公共数据和1组机载激光雷达点云数据为研究对象,将所提方法与结构张量约束的插值方法以及3种传统插值方法(包括标准径向基插值法、不规则三角网法、ANUDEM法(Australian National University DEM))进行比较,结果表明,所提方法的平均总误差最小,插值性能最优,而且还能较好地保持断裂地形特征。展开更多
针对步态识别过程易受拍摄视角、外观变化等因素影响问题,提出一种融合点云步态模型与深度学习的步态识别算法。算法通过轻量级特征描述符(lightweight feature descriptor,LFD)提取图像特征,并将其进行特征配准;基于几何-匹配核预处理...针对步态识别过程易受拍摄视角、外观变化等因素影响问题,提出一种融合点云步态模型与深度学习的步态识别算法。算法通过轻量级特征描述符(lightweight feature descriptor,LFD)提取图像特征,并将其进行特征配准;基于几何-匹配核预处理增强识别技术(gait model-key point recognition and extraction,GM-KPRE)提取人体关键点信息,在支持向量机算法中引入径向基函数核进行步态分类和识别;在公开数据集CASIA-B和Market-1501-v15.09.15上进行实验验证,实验结果表明,算法能有效提高步态识别准确率和效率。展开更多
基金Supported by the National Natural Science Foundationthe Doctoral Foundation of the State Education Commission of China
文摘This paper studies the problem applying Radial Basis Function Network(RBFN) which is trained by the Recursive Least Square Algorithm(RLSA) to the recognition of one dimensional images of radar targets. The equivalence between the RBFN and the estimate of Parzen window probabilistic density is proved. It is pointed out that the I/O functions in RBFN hidden units can be generalized to general Parzen window probabilistic kernel function or potential function, too. This paper discusses the effects of the shape parameter a in the RBFN and the forgotten factor A in RLSA on the results of the recognition of three kinds of kernel function such as Gaussian, triangle, double-exponential, at the same time, also discusses the relationship between A and the training time in the RBFN.
基金funded by The Fundamental Research Funds for Chinese Academy of surveying and mapping(AR2402)Open Fund of Wuhan,Gravitation and Solid Earth Tides,National Observation and Research Station(No.WHYWZ202213)。
文摘A high-precision regional gravity field model is significant in various geodesy applications.In the field of modelling regional gravity fields,the spherical radial basis functions(SRBFs)approach has recently gained widespread attention,while the modelling precision is primarily influenced by the base function network.In this study,we propose a method for constructing a data-adaptive network of SRBFs using a modified Hierarchical Density-Based Spatial Clustering of Applications with Noise(HDBSCAN)algorithm,and the performance of the algorithm is verified by the observed gravity data in the Auvergne area.Furthermore,the turning point method is used to optimize the bandwidth of the basis function spectrum,which satisfies the demand for both high-precision gravity field and quasi-geoid modelling simultaneously.Numerical experimental results indicate that our algorithm has an accuracy of about 1.58 mGal in constructing the gravity field model and about 0.03 m in the regional quasi-geoid model.Compared to the existing methods,the number of SRBFs used for modelling has been reduced by 15.8%,and the time cost to determine the centre positions of SRBFs has been saved by 12.5%.Hence,the modified HDBSCAN algorithm presented here is a suitable design method for constructing the SRBF data adaptive network.
文摘This paper is an extension of earlier papers [8, 9] on the ＂native＂ Hilbert spaces of functions on some domain Ωbelong toR^d Rd in which conditionally positive definite kernels are reproducing kernels. Here, the focus is on subspaces of native spaces which are induced via subsets of Ω, and we shall derive a recursive subspace structure of these, leading to recur- sively defined reproducing kernels. As an application, we get a recursive Neville-Aitken- type interpolation process and a recursively defined orthogonal basis for interpolation by translates of kernels.
基金the NSFC(60473034)the Science Foundation of Zhejiang Province(Y604003).
文摘The spherical approximation between two nested reproducing kernels Hilbert spaces generated from different smooth kernels is investigated. It is shown that the functions of a space can be approximated by that of the subspace with better smoothness. Furthermore, the upper bound of approximation error is given.
文摘在数字高程模型(digital elevation model,DEM)建模过程中,传统插值方法以地表光滑连续为基本假设,且只考虑了采样点和待插值点之间的空间相关性,忽略了诸如断裂线等不连续地形特征带来的空间异质性影响,导致断裂线周围的高程被平滑,进而使得构建的DEM失真。针对上述问题,提出一种顾及空间异质性的多元径向基函数插值方法。该方法耦合了空间距离、高差、法向量3种地形信息,充分考虑了采样点和待插值点之间的空间相关性和地形特征异质性,确保地形断裂区DEM高精度建模。以国际摄影测量与遥感协会提供的10组公共数据和1组机载激光雷达点云数据为研究对象,将所提方法与结构张量约束的插值方法以及3种传统插值方法(包括标准径向基插值法、不规则三角网法、ANUDEM法(Australian National University DEM))进行比较,结果表明,所提方法的平均总误差最小,插值性能最优,而且还能较好地保持断裂地形特征。
文摘针对步态识别过程易受拍摄视角、外观变化等因素影响问题,提出一种融合点云步态模型与深度学习的步态识别算法。算法通过轻量级特征描述符(lightweight feature descriptor,LFD)提取图像特征,并将其进行特征配准;基于几何-匹配核预处理增强识别技术(gait model-key point recognition and extraction,GM-KPRE)提取人体关键点信息,在支持向量机算法中引入径向基函数核进行步态分类和识别;在公开数据集CASIA-B和Market-1501-v15.09.15上进行实验验证,实验结果表明,算法能有效提高步态识别准确率和效率。
