We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary i...We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary integral equation formulation of the problem, nonnegativity constraints in the form of a penalty term are incorporated conveniently into least-squares iteration schemes for solving the inverse problem. Numerical implementation and examples are presented to illustrate the effectiveness of this strategy in improving recovery results.展开更多
One of the most important properties of M-matrices is element-wise non-negative of its inverse. In this paper, we consider element-wise perturbations of tridiagonal M-matrices and obtain bounds on the perturbations so...One of the most important properties of M-matrices is element-wise non-negative of its inverse. In this paper, we consider element-wise perturbations of tridiagonal M-matrices and obtain bounds on the perturbations so that the non-negative inverse persists. The largest interval is given by which the diagonal entries of the inverse of tridiagonal M-matrices can be perturbed without losing the property of total nonnegativity. A numerical example is given to illustrate our findings.展开更多
In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality...In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.展开更多
High-dimensional and incomplete(HDI)data subject to the nonnegativity constraints are commonly encountered in a big data-related application concerning the interactions among numerous nodes.A nonnegative latent factor...High-dimensional and incomplete(HDI)data subject to the nonnegativity constraints are commonly encountered in a big data-related application concerning the interactions among numerous nodes.A nonnegative latent factor analysis(NLFA)model can perform representation learning to HDI data efficiently.However,existing NLFA models suffer from either slow convergence rate or representation accuracy loss.To address this issue,this paper proposes a proximal alternating-directionmethod-of-multipliers-based nonnegative latent factor analysis(PAN)model with two-fold ideas:(1)adopting the principle of alternating-direction-method-of-multipliers to implement an efficient learning scheme for fast convergence and high computational efficiency;and(2)incorporating the proximal regularization into the learning scheme to suppress the optimization fluctuation for high representation learning accuracy to HDI data.Theoretical studies verify that PAN converges to a Karush-KuhnTucker(KKT)stationary point of its nonnegativity-constrained learning objective with its learning scheme.Experimental results on eight HDI matrices from real applications demonstrate that the proposed PAN model outperforms several state-of-the-art models in both estimation accuracy for missing data of an HDI matrix and computational efficiency.展开更多
Finding crucial vertices is a key problem for improving the reliability and ensuring the effective operation of networks,solved by approaches based on multiple attribute decision that suffer from ignoring the correlat...Finding crucial vertices is a key problem for improving the reliability and ensuring the effective operation of networks,solved by approaches based on multiple attribute decision that suffer from ignoring the correlation among each attribute or the heterogeneity between attribute and structure. To overcome these problems, a novel vertex centrality approach, called VCJG, is proposed based on joint nonnegative matrix factorization and graph embedding. The potential attributes with linearly independent and the structure information are captured automatically in light of nonnegative matrix factorization for factorizing the weighted adjacent matrix and the structure matrix, which is generated by graph embedding. And the smoothness strategy is applied to eliminate the heterogeneity between attributes and structure by joint nonnegative matrix factorization. Then VCJG integrates the above steps to formulate an overall objective function, and obtain the ultimately potential attributes fused the structure information of network through optimizing the objective function. Finally, the attributes are combined with neighborhood rules to evaluate vertex's importance. Through comparative analyses with experiments on nine real-world networks, we demonstrate that the proposed approach outperforms nine state-of-the-art algorithms for identification of vital vertices with respect to correlation, monotonicity and accuracy of top-10 vertices ranking.展开更多
Based on anisotropic total variation regularization(ATVR), a nonnegativity and support constraints recursive inverse filtering(NAS-RIF) blind restoration method is proposed to enhance the quality of optical coherence ...Based on anisotropic total variation regularization(ATVR), a nonnegativity and support constraints recursive inverse filtering(NAS-RIF) blind restoration method is proposed to enhance the quality of optical coherence tomography(OCT) image. First, ATVR is introduced into the cost function of NAS-RIF to improve the noise robustness and retain the details in the image.Since the split Bregman iterative is used to optimize the ATVR based cost function, the ATVR based NAS-RIF blind restoration method is then constructed. Furthermore, combined with the geometric nonlinear diffusion filter and the Poisson-distribution-based minimum error thresholding, the ATVR based NAS-RIF blind restoration method is used to realize the blind OCT image restoration. The experimental results demonstrate that the ATVR based NAS-RIF blind restoration method can successfully retain the details in the OCT images. In addition, the signal-to-noise ratio of the blind restored OCT images can be improved, along with the noise robustness.展开更多
In this paper we investigate the oscillatory property of the solutions of a class or parabonc partial functional differential equations with continuous distrbuted deviating arguments.
Nonnegative matrix factorization(NMF)has shown good performances on blind audio source separation(BASS).While the NMF analysis is a non-convex optimization problem when both the basis and encoding matrices need to be ...Nonnegative matrix factorization(NMF)has shown good performances on blind audio source separation(BASS).While the NMF analysis is a non-convex optimization problem when both the basis and encoding matrices need to be estimated simultaneously,the source separation step of the NMF-based BASS with a fixed basis matrix has been considered convex.However,because the basis matrix for the BASS is typically constructed by concatenating the basis matrices trained with individual source signals,the subspace spanned by the basis vectors for one source may overlap with that for other sources.In this paper,we have shown that the resulting encoding vector is not unique when the subspaces spanned by basis vectors for the sources overlap,which implies that the initialization of the encoding vector in the source separation stage is not trivial.Furthermore,we propose a novel method to initialize the encoding vector for the separation step based on the prior model of the encoding vector.Experimental results showed that the proposed method outperformed the uniform random initialization by 1.09 and 2.21dB in the source-to-distortion ratio,and 0.20 and 0.23 in PESQ scores for supervised and semi-supervised cases,respectively.展开更多
We consider the following eigenvalue problem: Where f(x, t) is a continuous function with critical growth. We prove the existence of nontrivial solutions.
This paper discusses the existence and stability of steady-states for a three-dimensional system ef parabolic partial differential equations subject to Dirichlet boundary conditions, i.e. the situation in which a pred...This paper discusses the existence and stability of steady-states for a three-dimensional system ef parabolic partial differential equations subject to Dirichlet boundary conditions, i.e. the situation in which a predator feeds on twoprey species. Resultts are obtained by the use of spectral analysis and bifurcation theory.展开更多
The discrimination of neutrons from gamma rays in a mixed radiation field is crucial in neutron detection tasks.Several approaches have been proposed to enhance the performance and accuracy of neutron-gamma discrimina...The discrimination of neutrons from gamma rays in a mixed radiation field is crucial in neutron detection tasks.Several approaches have been proposed to enhance the performance and accuracy of neutron-gamma discrimination.However,their performances are often associated with certain factors,such as experimental requirements and resulting mixed signals.The main purpose of this study is to achieve fast and accurate neutron-gamma discrimination without a priori information on the signal to be analyzed,as well as the experimental setup.Here,a novel method is proposed based on two concepts.The first method exploits the power of nonnegative tensor factorization(NTF)as a blind source separation method to extract the original components from the mixture signals recorded at the output of the stilbene scintillator detector.The second one is based on the principles of support vector machine(SVM)to identify and discriminate these components.In addition to these two main methods,we adopted the Mexican-hat function as a continuous wavelet transform to characterize the components extracted using the NTF model.The resulting scalograms are processed as colored images,which are segmented into two distinct classes using the Otsu thresholding method to extract the features of interest of the neutrons and gamma-ray components from the background noise.We subsequently used principal component analysis to select the most significant of these features wich are used in the training and testing datasets for SVM.Bias-variance analysis is used to optimize the SVM model by finding the optimal level of model complexity with the highest possible generalization performance.In this framework,the obtained results have verified a suitable bias–variance trade-off value.We achieved an operational SVM prediction model for neutron-gamma classification with a high true-positive rate.The accuracy and performance of the SVM based on the NTF was evaluated and validated by comparing it to the charge comparison method via figure of merit.The results indicate that the proposed approach has a superior discrimination quality(figure of merit of 2.20).展开更多
A new inequality on the minimum eigenvalue for the Fan product of nonsingular M-matrices is given. In addition, a new inequality on the spectral radius of the Hadamard product of nonnegative matrices is also obtained....A new inequality on the minimum eigenvalue for the Fan product of nonsingular M-matrices is given. In addition, a new inequality on the spectral radius of the Hadamard product of nonnegative matrices is also obtained. These inequalities can improve considerably some previous results.展开更多
In this paper,we investigate the properties of strongly coapproximation in normed linear spaces and lo-cally,convex spaces.The relations between strongly coapproximation and strongly unique approximation andof the f-c...In this paper,we investigate the properties of strongly coapproximation in normed linear spaces and lo-cally,convex spaces.The relations between strongly coapproximation and strongly unique approximation andof the f-coapproximation and f-approximation,are also considered.展开更多
Considering the sparsity of hyperspectral images(HSIs),dictionary learning frameworks have been widely used in the field of unsupervised spectral unmixing.However,it is worth mentioning here that existing dictionary l...Considering the sparsity of hyperspectral images(HSIs),dictionary learning frameworks have been widely used in the field of unsupervised spectral unmixing.However,it is worth mentioning here that existing dictionary learning method-based unmixing methods are found to be short of robustness in noisy contexts.To improve the performance,this study specifically puts forward a new unsupervised spectral unmixing solution.For the reason that the solution only functions in a condition that both endmembers and the abundances meet non-negative con-straints,a model is built to solve the unsupervised spectral un-mixing problem on the account of the dictionary learning me-thod.To raise the screening accuracy of final members,a new form of the target function is introduced into dictionary learning practice,which is conducive to the growing robustness of noisy HSI statistics.Then,by introducing the total variation(TV)terms into the proposed spectral unmixing based on robust nonnega-tive dictionary learning(RNDLSU),the context information under HSI space is to be cited as prior knowledge to compute the abundances when performing sparse unmixing operations.Ac-cording to the final results of the experiment,this method makes favorable performance under varying noise conditions,which is especially true under low signal to noise conditions.展开更多
Given a list of real numbers ∧={λ1,…, λn}, we determine the conditions under which ∧will form the spectrum of a dense n × n singular symmetric matrix. Based on a solvability lemma, an algorithm to compute th...Given a list of real numbers ∧={λ1,…, λn}, we determine the conditions under which ∧will form the spectrum of a dense n × n singular symmetric matrix. Based on a solvability lemma, an algorithm to compute the elements of the matrix is derived for a given list ∧ and dependency parameters. Explicit computations are performed for n≤5 and r≤4 to illustrate the result.展开更多
Consider a first-order autoregressive processes , where the innovations are nonnegative random variables with regular variation at both the right endpoint infinity and the unknown left endpoint θ. We propose estimate...Consider a first-order autoregressive processes , where the innovations are nonnegative random variables with regular variation at both the right endpoint infinity and the unknown left endpoint θ. We propose estimates for the autocorrelation parameter f and the unknown location parameter θ by taking the ratio of two sample values chosen with respect to an extreme value criteria for f and by taking the minimum of over the observed series, where represents our estimate for f. The joint limit distribution of the proposed estimators is derived using point process techniques. A simulation study is provided to examine the small sample size behavior of these estimates.展开更多
文摘We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary integral equation formulation of the problem, nonnegativity constraints in the form of a penalty term are incorporated conveniently into least-squares iteration schemes for solving the inverse problem. Numerical implementation and examples are presented to illustrate the effectiveness of this strategy in improving recovery results.
文摘One of the most important properties of M-matrices is element-wise non-negative of its inverse. In this paper, we consider element-wise perturbations of tridiagonal M-matrices and obtain bounds on the perturbations so that the non-negative inverse persists. The largest interval is given by which the diagonal entries of the inverse of tridiagonal M-matrices can be perturbed without losing the property of total nonnegativity. A numerical example is given to illustrate our findings.
基金Supported by the NSFC(11771087,12171091 and 11831005)。
文摘In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.
基金supported by the National Natural Science Foundation of China(62272078,U21A2019)the Hainan Province Science and Technology Special Fund of China(ZDYF2022SHFZ105)the CAAI-Huawei MindSpore Open Fund(CAAIXSJLJJ-2021-035A)。
文摘High-dimensional and incomplete(HDI)data subject to the nonnegativity constraints are commonly encountered in a big data-related application concerning the interactions among numerous nodes.A nonnegative latent factor analysis(NLFA)model can perform representation learning to HDI data efficiently.However,existing NLFA models suffer from either slow convergence rate or representation accuracy loss.To address this issue,this paper proposes a proximal alternating-directionmethod-of-multipliers-based nonnegative latent factor analysis(PAN)model with two-fold ideas:(1)adopting the principle of alternating-direction-method-of-multipliers to implement an efficient learning scheme for fast convergence and high computational efficiency;and(2)incorporating the proximal regularization into the learning scheme to suppress the optimization fluctuation for high representation learning accuracy to HDI data.Theoretical studies verify that PAN converges to a Karush-KuhnTucker(KKT)stationary point of its nonnegativity-constrained learning objective with its learning scheme.Experimental results on eight HDI matrices from real applications demonstrate that the proposed PAN model outperforms several state-of-the-art models in both estimation accuracy for missing data of an HDI matrix and computational efficiency.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.62162040 and 11861045)。
文摘Finding crucial vertices is a key problem for improving the reliability and ensuring the effective operation of networks,solved by approaches based on multiple attribute decision that suffer from ignoring the correlation among each attribute or the heterogeneity between attribute and structure. To overcome these problems, a novel vertex centrality approach, called VCJG, is proposed based on joint nonnegative matrix factorization and graph embedding. The potential attributes with linearly independent and the structure information are captured automatically in light of nonnegative matrix factorization for factorizing the weighted adjacent matrix and the structure matrix, which is generated by graph embedding. And the smoothness strategy is applied to eliminate the heterogeneity between attributes and structure by joint nonnegative matrix factorization. Then VCJG integrates the above steps to formulate an overall objective function, and obtain the ultimately potential attributes fused the structure information of network through optimizing the objective function. Finally, the attributes are combined with neighborhood rules to evaluate vertex's importance. Through comparative analyses with experiments on nine real-world networks, we demonstrate that the proposed approach outperforms nine state-of-the-art algorithms for identification of vital vertices with respect to correlation, monotonicity and accuracy of top-10 vertices ranking.
基金Supported by National Key Research and Development Program of China(2016YFF0201005)。
文摘Based on anisotropic total variation regularization(ATVR), a nonnegativity and support constraints recursive inverse filtering(NAS-RIF) blind restoration method is proposed to enhance the quality of optical coherence tomography(OCT) image. First, ATVR is introduced into the cost function of NAS-RIF to improve the noise robustness and retain the details in the image.Since the split Bregman iterative is used to optimize the ATVR based cost function, the ATVR based NAS-RIF blind restoration method is then constructed. Furthermore, combined with the geometric nonlinear diffusion filter and the Poisson-distribution-based minimum error thresholding, the ATVR based NAS-RIF blind restoration method is used to realize the blind OCT image restoration. The experimental results demonstrate that the ATVR based NAS-RIF blind restoration method can successfully retain the details in the OCT images. In addition, the signal-to-noise ratio of the blind restored OCT images can be improved, along with the noise robustness.
基金The project supported by the Natural Science Foundation of Shandong Province.
文摘In this paper we investigate the oscillatory property of the solutions of a class or parabonc partial functional differential equations with continuous distrbuted deviating arguments.
基金supported by the research fund of Signal Intelligence Research Center supervised by the Defense Acquisition Program Administration and Agency for Defense Development of Korea
文摘Nonnegative matrix factorization(NMF)has shown good performances on blind audio source separation(BASS).While the NMF analysis is a non-convex optimization problem when both the basis and encoding matrices need to be estimated simultaneously,the source separation step of the NMF-based BASS with a fixed basis matrix has been considered convex.However,because the basis matrix for the BASS is typically constructed by concatenating the basis matrices trained with individual source signals,the subspace spanned by the basis vectors for one source may overlap with that for other sources.In this paper,we have shown that the resulting encoding vector is not unique when the subspaces spanned by basis vectors for the sources overlap,which implies that the initialization of the encoding vector in the source separation stage is not trivial.Furthermore,we propose a novel method to initialize the encoding vector for the separation step based on the prior model of the encoding vector.Experimental results showed that the proposed method outperformed the uniform random initialization by 1.09 and 2.21dB in the source-to-distortion ratio,and 0.20 and 0.23 in PESQ scores for supervised and semi-supervised cases,respectively.
文摘We consider the following eigenvalue problem: Where f(x, t) is a continuous function with critical growth. We prove the existence of nontrivial solutions.
文摘This paper discusses the existence and stability of steady-states for a three-dimensional system ef parabolic partial differential equations subject to Dirichlet boundary conditions, i.e. the situation in which a predator feeds on twoprey species. Resultts are obtained by the use of spectral analysis and bifurcation theory.
基金L’Ore´al-UNESCO for the Women in Science Maghreb Program Grant Agreement No.4500410340.
文摘The discrimination of neutrons from gamma rays in a mixed radiation field is crucial in neutron detection tasks.Several approaches have been proposed to enhance the performance and accuracy of neutron-gamma discrimination.However,their performances are often associated with certain factors,such as experimental requirements and resulting mixed signals.The main purpose of this study is to achieve fast and accurate neutron-gamma discrimination without a priori information on the signal to be analyzed,as well as the experimental setup.Here,a novel method is proposed based on two concepts.The first method exploits the power of nonnegative tensor factorization(NTF)as a blind source separation method to extract the original components from the mixture signals recorded at the output of the stilbene scintillator detector.The second one is based on the principles of support vector machine(SVM)to identify and discriminate these components.In addition to these two main methods,we adopted the Mexican-hat function as a continuous wavelet transform to characterize the components extracted using the NTF model.The resulting scalograms are processed as colored images,which are segmented into two distinct classes using the Otsu thresholding method to extract the features of interest of the neutrons and gamma-ray components from the background noise.We subsequently used principal component analysis to select the most significant of these features wich are used in the training and testing datasets for SVM.Bias-variance analysis is used to optimize the SVM model by finding the optimal level of model complexity with the highest possible generalization performance.In this framework,the obtained results have verified a suitable bias–variance trade-off value.We achieved an operational SVM prediction model for neutron-gamma classification with a high true-positive rate.The accuracy and performance of the SVM based on the NTF was evaluated and validated by comparing it to the charge comparison method via figure of merit.The results indicate that the proposed approach has a superior discrimination quality(figure of merit of 2.20).
文摘A new inequality on the minimum eigenvalue for the Fan product of nonsingular M-matrices is given. In addition, a new inequality on the spectral radius of the Hadamard product of nonnegative matrices is also obtained. These inequalities can improve considerably some previous results.
文摘In this paper,we investigate the properties of strongly coapproximation in normed linear spaces and lo-cally,convex spaces.The relations between strongly coapproximation and strongly unique approximation andof the f-coapproximation and f-approximation,are also considered.
基金supported by the National Natural Science Foundation of China(61801513).
文摘Considering the sparsity of hyperspectral images(HSIs),dictionary learning frameworks have been widely used in the field of unsupervised spectral unmixing.However,it is worth mentioning here that existing dictionary learning method-based unmixing methods are found to be short of robustness in noisy contexts.To improve the performance,this study specifically puts forward a new unsupervised spectral unmixing solution.For the reason that the solution only functions in a condition that both endmembers and the abundances meet non-negative con-straints,a model is built to solve the unsupervised spectral un-mixing problem on the account of the dictionary learning me-thod.To raise the screening accuracy of final members,a new form of the target function is introduced into dictionary learning practice,which is conducive to the growing robustness of noisy HSI statistics.Then,by introducing the total variation(TV)terms into the proposed spectral unmixing based on robust nonnega-tive dictionary learning(RNDLSU),the context information under HSI space is to be cited as prior knowledge to compute the abundances when performing sparse unmixing operations.Ac-cording to the final results of the experiment,this method makes favorable performance under varying noise conditions,which is especially true under low signal to noise conditions.
文摘Given a list of real numbers ∧={λ1,…, λn}, we determine the conditions under which ∧will form the spectrum of a dense n × n singular symmetric matrix. Based on a solvability lemma, an algorithm to compute the elements of the matrix is derived for a given list ∧ and dependency parameters. Explicit computations are performed for n≤5 and r≤4 to illustrate the result.
文摘Consider a first-order autoregressive processes , where the innovations are nonnegative random variables with regular variation at both the right endpoint infinity and the unknown left endpoint θ. We propose estimates for the autocorrelation parameter f and the unknown location parameter θ by taking the ratio of two sample values chosen with respect to an extreme value criteria for f and by taking the minimum of over the observed series, where represents our estimate for f. The joint limit distribution of the proposed estimators is derived using point process techniques. A simulation study is provided to examine the small sample size behavior of these estimates.