Observational studies between magnesium int- ake and risk of type 2 diabetes yielded inconsistent results. We conducted a system literature search of PubMed database through March 2015 for prospective cohort studies o...Observational studies between magnesium int- ake and risk of type 2 diabetes yielded inconsistent results. We conducted a system literature search of PubMed database through March 2015 for prospective cohort studies of magnesium intake and type 2 diabetes risk. Study-specific results were pooled in a random-effects model. Subgroup and sensitivity analysis were performed to assess the potential sources of heterogeneity and the robustness of the pooled estimation. Generalized least squares trend estimation was used to investigate the dose-response relationship. A total of 15 papers with 19 analyses were identified with 539,735 participants and 25,252 incident diabetes cases. Magnesium intake was associated with a significant lower risk of type 2 diabetes （RR： 0.77; 95% Ch 0.71-0.82） for the highest compared with lowest category. This association was not significantly modified by the pre-specified study characteristics. In the dose-response analysis, a magnesium intake increment of 100 mg/day was associated with a 16% reduction in type 2 diabetes risk （RR： 0.84; 95% Ch 0.80-0.88）. A nonlinear relationship existed between magnesium intake and type 2 diabetes （P-nonlinearity=0.003）. This meta-analysis further verified a protective effect of magnesium intake on type 2 diabetes in a nonlinear dose-response manner.展开更多
We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold i...We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approximation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.展开更多
Image feature optimization is an important means to deal with high-dimensional image data in image semantic understanding and its applications. We formulate image feature optimization as the establishment of a mapping...Image feature optimization is an important means to deal with high-dimensional image data in image semantic understanding and its applications. We formulate image feature optimization as the establishment of a mapping between highand low-dimensional space via a five-tuple model. Nonlinear dimensionality reduction based on manifold learning provides a feasible way for solving such a problem. We propose a novel globular neighborhood based locally linear embedding (GNLLE) algorithm using neighborhood update and an incremental neighbor search scheme, which not only can handle sparse datasets but also has strong anti-noise capability and good topological stability. Given that the distance measure adopted in nonlinear dimensionality reduction is usually based on pairwise similarity calculation, we also present a globular neighborhood and path clustering based locally linear embedding (GNPCLLE) algorithm based on path-based clustering. Due to its full consideration of correlations between image data, GNPCLLE can eliminate the distortion of the overall topological structure within the dataset on the manifold. Experimental results on two image sets show the effectiveness and efficiency of the proposed algorithms.展开更多
In this study,a k-nearest neighbor(kNN)method based on nonlinear directional dimension reduction is applied to gas-bearing reservoir prediction.The kNN method can select the most relevant training samples to establish...In this study,a k-nearest neighbor(kNN)method based on nonlinear directional dimension reduction is applied to gas-bearing reservoir prediction.The kNN method can select the most relevant training samples to establish a local model according to feature similarities.However,the kNN method cannot extract gas-sensitive attributes and faces dimension problems.The features important to gas-bearing reservoir prediction could not be the main features of the samples.Thus,linear dimension reduction methods,such as principal component analysis,fail to extract relevant features.We thus implemented dimension reduction using a fully connected artifi cial neural network(ANN)with proper architecture.This not only increased the separability of the samples but also maintained the samples’inherent distribution characteristics.Moreover,using the kNN to classify samples after the ANN dimension reduction is also equivalent to replacing the deep structure of the ANN,which is considered to have a linear classifi cation function.When applied to actual data,our method extracted gas-bearing sensitive features from seismic data to a certain extent.The prediction results can characterize gas-bearing reservoirs accurately in a limited scope.展开更多
A multi-degree-of-freedom device is proposed,which can achieve efficient vibration reduction as the main objective and energy harvesting as the secondary purpose.The device comprises a multiscale nonlinear vibration a...A multi-degree-of-freedom device is proposed,which can achieve efficient vibration reduction as the main objective and energy harvesting as the secondary purpose.The device comprises a multiscale nonlinear vibration absorber(NVA)and piezoelectric components.Energy conversion and energy measurement methods are used to evaluate the device performance from multiple perspectives.Research has shown that this device can efficiently transfer transient energy from the main structure and convert a portion of transient energy into electrical energy.Main resonance and higher-order resonance are the main reasons for efficient energy transfer.The device can maintain high vibration reduction performance even when the excitation amplitude changes over a large range.Compared with the single structures with and without precompression,the multiscale NVA-piezoelectric device offers significant vibration reduction advantages.In addition,there are significant differences in the parameter settings of the two substructures for vibration reduction and energy harvesting.展开更多
The concise and informative representation of hyperspectral imagery is achieved via the introduced diffusion geometric coordinates derived from nonlinear dimension reduction maps - diffusion maps. The huge-volume high...The concise and informative representation of hyperspectral imagery is achieved via the introduced diffusion geometric coordinates derived from nonlinear dimension reduction maps - diffusion maps. The huge-volume high- dimensional spectral measurements are organized by the affinity graph where each node in this graph only connects to its local neighbors and each edge in this graph represents local similarity information. By normalizing the affinity graph appropriately, the diffusion operator of the underlying hyperspectral imagery is well-defined, which means that the Markov random walk can be simulated on the hyperspectral imagery. Therefore, the diffusion geometric coordinates, derived from the eigenfunctions and the associated eigenvalues of the diffusion operator, can capture the intrinsic geometric information of the hyperspectral imagery well, which gives more enhanced representation results than traditional linear methods, such as principal component analysis based methods. For large-scale full scene hyperspectral imagery, by exploiting the backbone approach, the computation complexity and the memory requirements are acceptable. Experiments also show that selecting suitable symmetrization normalization techniques while forming the diffusion operator is important to hyperspectral imagery representation.展开更多
A new noise reduction method for nonlinear signal based on maximum variance unfolding(MVU)is proposed.The noisy sig-nal is firstly embedded into a high-dimensional phase space based on phase space reconstruction theor...A new noise reduction method for nonlinear signal based on maximum variance unfolding(MVU)is proposed.The noisy sig-nal is firstly embedded into a high-dimensional phase space based on phase space reconstruction theory,and then the manifold learning algorithm MVU is used to perform nonlinear dimensionality reduction on the data of phase space in order to separate low-dimensional manifold representing the attractor from noise subspace.Finally,the noise-reduced signal is obtained through reconstructing the low-dimensional manifold.The simulation results of Lorenz system show that the proposed MVU-based noise reduction method outperforms the KPCA-based method and has the advantages of simple parameter estimation and low parameter sensitivity.The proposed method is applied to fault detection of a vibration signal from rotor-stator of aero engine with slight rubbing fault.The denoised results show that the slight rubbing features overwhelmed by noise can be effectively extracted by the proposed noise reduction method.展开更多
The complexities of hydrological phenomena, the causes that lead to these complexities, and the essences and defects of reductionism are analyzed. The driving forces for the development of hydrology and the formation ...The complexities of hydrological phenomena, the causes that lead to these complexities, and the essences and defects of reductionism are analyzed. The driving forces for the development of hydrology and the formation of branch subjects of hydrology are discussed. The theoretical basis and limitations of existing hydrology are summarized. Existing misunderstandings in the development of the watershed hydrological model are put forward. Finally, the necessity of the expansion of hydrology from linear to nonlinear is discussed.展开更多
We present our recent work on both linear and nonlinear data reduction methods and algorithms: for the linear case we discuss results on structure analysis of SVD of columnpartitioned matrices and sparse low-rank appr...We present our recent work on both linear and nonlinear data reduction methods and algorithms: for the linear case we discuss results on structure analysis of SVD of columnpartitioned matrices and sparse low-rank approximation; for the nonlinear case we investigate methods for nonlinear dimensionality reduction and manifold learning. The problems we address have attracted great deal of interest in data mining and machine learning.展开更多
Over the past few years,nonlinear manifold learning has been widely exploited in data analysis and machine learning.This paper presents a novel manifold learning algorithm,named atlas compatibility transformation(ACT)...Over the past few years,nonlinear manifold learning has been widely exploited in data analysis and machine learning.This paper presents a novel manifold learning algorithm,named atlas compatibility transformation(ACT),It solves two problems which correspond to two key points in the manifold definition:how to chart a given manifold and how to align the patches to a global coordinate space based on compatibility.For the first problem,we divide the manifold into maximal linear patch(MLP) based on normal vector field of the manifold.For the second problem,we align patches into an optimal global system by solving a generalized eigenvalue problem.Compared with the traditional method,the ACT could deal with noise datasets and fragment datasets.Moreover,the mappings between high dimensional space and low dimensional space are given.Experiments on both synthetic data and real-world data indicate the effection of the proposed algorithm.展开更多
We provide a concise review of the exponentially convergent multiscale finite element method(ExpMsFEM)for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave pr...We provide a concise review of the exponentially convergent multiscale finite element method(ExpMsFEM)for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation.The ExpMsFEM is built on the non-overlapped domain decomposition in the classical MsFEM while enriching the approximation space systematically to achieve a nearly exponential convergence rate regarding the number of basis functions.Unlike most generalizations of the MsFEM in the literature,the ExpMsFEM does not rely on any partition of unity functions.In general,it is necessary to use function representations dependent on the right-hand side to break the algebraic Kolmogorov n-width barrier to achieve exponential convergence.Indeed,there are online and offline parts in the function representation provided by the ExpMsFEM.The online part depends on the right-hand side locally and can be computed in parallel efficiently.The offline part contains basis functions that are used in the Galerkin method to assemble the stiffness matrix;they are all independent of the right-hand side,so the stiffness matrix can be used repeatedly in multi-query scenarios.展开更多
As modern weapons and equipment undergo increasing levels of informatization,intelligence,and networking,the topology and traffic characteristics of battlefield data networks built with tactical data links are becomin...As modern weapons and equipment undergo increasing levels of informatization,intelligence,and networking,the topology and traffic characteristics of battlefield data networks built with tactical data links are becoming progressively complex.In this paper,we employ a traffic matrix to model the tactical data link network.We propose a method that utilizes the Maximum Variance Unfolding(MVU)algorithm to conduct nonlinear dimensionality reduction analysis on high-dimensional open network traffic matrix datasets.This approach introduces novel ideas and methods for future applications,including traffic prediction and anomaly analysis in real battlefield network environments.展开更多
A new manifold learning method, called incremental alignment method （IAM）, is proposed for nonlinear dimensionality reduction of high dimensional data with intrinsic low dimensionality. The main idea is to increment...A new manifold learning method, called incremental alignment method （IAM）, is proposed for nonlinear dimensionality reduction of high dimensional data with intrinsic low dimensionality. The main idea is to incrementally align low-dimensional coordinates of input data patch-by-patch to iteratively generate the representation of the entire data.set. The method consists of two major steps, the incremental step and the alignment step. The incremental step incrementally searches neighborhood patch to be aligned in the next step, and the alignment step iteratively aligns the low-dimensional coordinates of the neighborhood patch searched to generate the embeddings of the entire dataset. Compared with the existing manifold learning methods, the proposed method dominates in several aspects： high efficiency, easy out-of-sample extension, well metric-preserving, and averting of the local minima issue. All these properties are supported by a series of experiments performed on the synthetic and real-life datasets. In addition, the computational complexity of the proposed method is analyzed, and its efficiency is theoretically argued and experimentally demonstrated.展开更多
基金supported by National Natural Science Foundation of China(Grant No.81371299)
文摘Observational studies between magnesium int- ake and risk of type 2 diabetes yielded inconsistent results. We conducted a system literature search of PubMed database through March 2015 for prospective cohort studies of magnesium intake and type 2 diabetes risk. Study-specific results were pooled in a random-effects model. Subgroup and sensitivity analysis were performed to assess the potential sources of heterogeneity and the robustness of the pooled estimation. Generalized least squares trend estimation was used to investigate the dose-response relationship. A total of 15 papers with 19 analyses were identified with 539,735 participants and 25,252 incident diabetes cases. Magnesium intake was associated with a significant lower risk of type 2 diabetes （RR： 0.77; 95% Ch 0.71-0.82） for the highest compared with lowest category. This association was not significantly modified by the pre-specified study characteristics. In the dose-response analysis, a magnesium intake increment of 100 mg/day was associated with a 16% reduction in type 2 diabetes risk （RR： 0.84; 95% Ch 0.80-0.88）. A nonlinear relationship existed between magnesium intake and type 2 diabetes （P-nonlinearity=0.003）. This meta-analysis further verified a protective effect of magnesium intake on type 2 diabetes in a nonlinear dose-response manner.
文摘We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approximation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.
基金Project (No 2008AA01Z132) supported by the National High-Tech Research and Development Program of China
文摘Image feature optimization is an important means to deal with high-dimensional image data in image semantic understanding and its applications. We formulate image feature optimization as the establishment of a mapping between highand low-dimensional space via a five-tuple model. Nonlinear dimensionality reduction based on manifold learning provides a feasible way for solving such a problem. We propose a novel globular neighborhood based locally linear embedding (GNLLE) algorithm using neighborhood update and an incremental neighbor search scheme, which not only can handle sparse datasets but also has strong anti-noise capability and good topological stability. Given that the distance measure adopted in nonlinear dimensionality reduction is usually based on pairwise similarity calculation, we also present a globular neighborhood and path clustering based locally linear embedding (GNPCLLE) algorithm based on path-based clustering. Due to its full consideration of correlations between image data, GNPCLLE can eliminate the distortion of the overall topological structure within the dataset on the manifold. Experimental results on two image sets show the effectiveness and efficiency of the proposed algorithms.
基金supported by the National Key R&D Program of China(No.2018YFA0702504)the National Natural Science Foundation of China(No.42174152 and No.41974140)the Strategic Cooperation Technology Projects of CNPC and CUPB(No.ZLZX2020-03).
文摘In this study,a k-nearest neighbor(kNN)method based on nonlinear directional dimension reduction is applied to gas-bearing reservoir prediction.The kNN method can select the most relevant training samples to establish a local model according to feature similarities.However,the kNN method cannot extract gas-sensitive attributes and faces dimension problems.The features important to gas-bearing reservoir prediction could not be the main features of the samples.Thus,linear dimension reduction methods,such as principal component analysis,fail to extract relevant features.We thus implemented dimension reduction using a fully connected artifi cial neural network(ANN)with proper architecture.This not only increased the separability of the samples but also maintained the samples’inherent distribution characteristics.Moreover,using the kNN to classify samples after the ANN dimension reduction is also equivalent to replacing the deep structure of the ANN,which is considered to have a linear classifi cation function.When applied to actual data,our method extracted gas-bearing sensitive features from seismic data to a certain extent.The prediction results can characterize gas-bearing reservoirs accurately in a limited scope.
基金Project supported by the National Natural Science Foundation of China(Nos.11972050 and 12332001)。
文摘A multi-degree-of-freedom device is proposed,which can achieve efficient vibration reduction as the main objective and energy harvesting as the secondary purpose.The device comprises a multiscale nonlinear vibration absorber(NVA)and piezoelectric components.Energy conversion and energy measurement methods are used to evaluate the device performance from multiple perspectives.Research has shown that this device can efficiently transfer transient energy from the main structure and convert a portion of transient energy into electrical energy.Main resonance and higher-order resonance are the main reasons for efficient energy transfer.The device can maintain high vibration reduction performance even when the excitation amplitude changes over a large range.Compared with the single structures with and without precompression,the multiscale NVA-piezoelectric device offers significant vibration reduction advantages.In addition,there are significant differences in the parameter settings of the two substructures for vibration reduction and energy harvesting.
基金The National Key Technologies R & D Program during the 11th Five-Year Plan Period (No.2006BAB15B01)
文摘The concise and informative representation of hyperspectral imagery is achieved via the introduced diffusion geometric coordinates derived from nonlinear dimension reduction maps - diffusion maps. The huge-volume high- dimensional spectral measurements are organized by the affinity graph where each node in this graph only connects to its local neighbors and each edge in this graph represents local similarity information. By normalizing the affinity graph appropriately, the diffusion operator of the underlying hyperspectral imagery is well-defined, which means that the Markov random walk can be simulated on the hyperspectral imagery. Therefore, the diffusion geometric coordinates, derived from the eigenfunctions and the associated eigenvalues of the diffusion operator, can capture the intrinsic geometric information of the hyperspectral imagery well, which gives more enhanced representation results than traditional linear methods, such as principal component analysis based methods. For large-scale full scene hyperspectral imagery, by exploiting the backbone approach, the computation complexity and the memory requirements are acceptable. Experiments also show that selecting suitable symmetrization normalization techniques while forming the diffusion operator is important to hyperspectral imagery representation.
文摘A new noise reduction method for nonlinear signal based on maximum variance unfolding(MVU)is proposed.The noisy sig-nal is firstly embedded into a high-dimensional phase space based on phase space reconstruction theory,and then the manifold learning algorithm MVU is used to perform nonlinear dimensionality reduction on the data of phase space in order to separate low-dimensional manifold representing the attractor from noise subspace.Finally,the noise-reduced signal is obtained through reconstructing the low-dimensional manifold.The simulation results of Lorenz system show that the proposed MVU-based noise reduction method outperforms the KPCA-based method and has the advantages of simple parameter estimation and low parameter sensitivity.The proposed method is applied to fault detection of a vibration signal from rotor-stator of aero engine with slight rubbing fault.The denoised results show that the slight rubbing features overwhelmed by noise can be effectively extracted by the proposed noise reduction method.
基金supported by the National Natural Science Foundation of China (Grant No. 41130639)
文摘The complexities of hydrological phenomena, the causes that lead to these complexities, and the essences and defects of reductionism are analyzed. The driving forces for the development of hydrology and the formation of branch subjects of hydrology are discussed. The theoretical basis and limitations of existing hydrology are summarized. Existing misunderstandings in the development of the watershed hydrological model are put forward. Finally, the necessity of the expansion of hydrology from linear to nonlinear is discussed.
基金This work was supported in part by the Special Funds for Major State Basic Research Projectsthe National Natural Science Foundation of China(Grants No.60372033 and 9901936)NSF CCR9901986,DMS 0311800.
文摘We present our recent work on both linear and nonlinear data reduction methods and algorithms: for the linear case we discuss results on structure analysis of SVD of columnpartitioned matrices and sparse low-rank approximation; for the nonlinear case we investigate methods for nonlinear dimensionality reduction and manifold learning. The problems we address have attracted great deal of interest in data mining and machine learning.
基金supported by National Natural Science Foundation of China(No.61171145)Shanghai Educational Development Fundation(No.12ZZ083)
文摘Over the past few years,nonlinear manifold learning has been widely exploited in data analysis and machine learning.This paper presents a novel manifold learning algorithm,named atlas compatibility transformation(ACT),It solves two problems which correspond to two key points in the manifold definition:how to chart a given manifold and how to align the patches to a global coordinate space based on compatibility.For the first problem,we divide the manifold into maximal linear patch(MLP) based on normal vector field of the manifold.For the second problem,we align patches into an optimal global system by solving a generalized eigenvalue problem.Compared with the traditional method,the ACT could deal with noise datasets and fragment datasets.Moreover,the mappings between high dimensional space and low dimensional space are given.Experiments on both synthetic data and real-world data indicate the effection of the proposed algorithm.
基金part supported by the NSF Grants DMS-1912654 and DMS 2205590。
文摘We provide a concise review of the exponentially convergent multiscale finite element method(ExpMsFEM)for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation.The ExpMsFEM is built on the non-overlapped domain decomposition in the classical MsFEM while enriching the approximation space systematically to achieve a nearly exponential convergence rate regarding the number of basis functions.Unlike most generalizations of the MsFEM in the literature,the ExpMsFEM does not rely on any partition of unity functions.In general,it is necessary to use function representations dependent on the right-hand side to break the algebraic Kolmogorov n-width barrier to achieve exponential convergence.Indeed,there are online and offline parts in the function representation provided by the ExpMsFEM.The online part depends on the right-hand side locally and can be computed in parallel efficiently.The offline part contains basis functions that are used in the Galerkin method to assemble the stiffness matrix;they are all independent of the right-hand side,so the stiffness matrix can be used repeatedly in multi-query scenarios.
文摘As modern weapons and equipment undergo increasing levels of informatization,intelligence,and networking,the topology and traffic characteristics of battlefield data networks built with tactical data links are becoming progressively complex.In this paper,we employ a traffic matrix to model the tactical data link network.We propose a method that utilizes the Maximum Variance Unfolding(MVU)algorithm to conduct nonlinear dimensionality reduction analysis on high-dimensional open network traffic matrix datasets.This approach introduces novel ideas and methods for future applications,including traffic prediction and anomaly analysis in real battlefield network environments.
基金supported by the National Basic Research 973 Program of China under Grant No.2007CB311002the National Natural Science Foundation of China under Grant No.60905003
文摘A new manifold learning method, called incremental alignment method （IAM）, is proposed for nonlinear dimensionality reduction of high dimensional data with intrinsic low dimensionality. The main idea is to incrementally align low-dimensional coordinates of input data patch-by-patch to iteratively generate the representation of the entire data.set. The method consists of two major steps, the incremental step and the alignment step. The incremental step incrementally searches neighborhood patch to be aligned in the next step, and the alignment step iteratively aligns the low-dimensional coordinates of the neighborhood patch searched to generate the embeddings of the entire dataset. Compared with the existing manifold learning methods, the proposed method dominates in several aspects： high efficiency, easy out-of-sample extension, well metric-preserving, and averting of the local minima issue. All these properties are supported by a series of experiments performed on the synthetic and real-life datasets. In addition, the computational complexity of the proposed method is analyzed, and its efficiency is theoretically argued and experimentally demonstrated.
