Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,su...Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,such as the triple decomposition of motion(TDM)and normal-nilpotent decomposition(NND),have been proposed to analyze the local motions of fluid elements.However,due to the existence of different types and non-uniqueness of Schur forms,as well as various possible definitions of NNDs,confusion has spread widely and is harming the research.This work aims to clean up this confusion.To this end,the complex and real Schur forms are derived constructively from the very basics,with special consideration for their non-uniqueness.Conditions of uniqueness are proposed.After a general discussion of normality and nilpotency,a complex NND and several real NNDs as well as normal-nonnormal decompositions are constructed,with a brief comparison of complex and real decompositions.Based on that,several confusing points are clarified,such as the distinction between NND and TDM,and the intrinsic gap between complex and real NNDs.Besides,the author proposes to extend the real block Schur form and its corresponding NNDs for the complex eigenvalue case to the real eigenvalue case.But their justification is left to further investigations.展开更多
A proof is given that any λ _polynome over real quaternionic sfield can be factorized into produce of some linear factors.By the way,some properties and applications of this factorization in matrix theory are given.
Recently clustering techniques have been used to automatically discover typical user profiles. In general, it is a challenging problem to design effective similarity measure between the session vectors which are usual...Recently clustering techniques have been used to automatically discover typical user profiles. In general, it is a challenging problem to design effective similarity measure between the session vectors which are usually high-dimensional and sparse. Two approaches for mining typical user profiles, based on matrix dimensionality reduction, are presented. In these approaches, non-negative matrix factorization is applied to reduce dimensionality of the session-URL matrix, and the projecting vectors of the user-session vectors are clustered into typical user-session profiles using the spherical k -means algorithm. The results show that two algorithms are successful in mining many typical user profiles in the user sessions.展开更多
Finding solutions of matrix equations in given set SR n×n is an active research field. Lots of investigation have done for these cases, where S are the sets of general or symmetric matrices and symmetric posit...Finding solutions of matrix equations in given set SR n×n is an active research field. Lots of investigation have done for these cases, where S are the sets of general or symmetric matrices and symmetric positive definite or sysmmetric semiposite definite matrices respectively . Recently, however, attentions are been paying to the situation for S to be the set of general(semi) positive definite matrices(called as semipositive subdefinite matrices below) . In this paper the necessary and sufficient conditions for the following two kinds of matrix equations having semipositive, subdefinite solutions are obtained. General solutions and symmetric solutions of the equations (Ⅰ) and (Ⅱ) have been considered in in detail.展开更多
We investigate the realization of 2-qutrit logic gate in a bipartite 3-level system with qusi-Ising interaction. On the basis of Caftan decomposition of matrices, the unitary matrices of 2-qutrit are factorized into p...We investigate the realization of 2-qutrit logic gate in a bipartite 3-level system with qusi-Ising interaction. On the basis of Caftan decomposition of matrices, the unitary matrices of 2-qutrit are factorized into products of a series of realizable matrices. It is equivalent to exerting a certain control field on the system, and the control goal is usually gained by a sequence of control pulses. The general discussion on the realization of 2-qutrit logic gate is made first, and then the realization of the ternary SWAP gate and the ternary √SWAP gate are discussed specifically, and the sequences of control pulses and drift processes implementing these gates are given.展开更多
Abstract： At first one of g-inverses of A （×） In＋Im（×） BT is given out, then the explicit solution to matrix equation AX ＋ XB = C is gained by using the method of matrix decomposition, finally, a nume...Abstract： At first one of g-inverses of A （×） In＋Im（×） BT is given out, then the explicit solution to matrix equation AX ＋ XB = C is gained by using the method of matrix decomposition, finally, a numerical example is obtained.展开更多
In this paper we derive a practical method of solving simultaneously the problem of Schmidt decomposition of quaternion matrix and the orthonormalization of vectors in a generalized unitary space by using elementary c...In this paper we derive a practical method of solving simultaneously the problem of Schmidt decomposition of quaternion matrix and the orthonormalization of vectors in a generalized unitary space by using elementary column operations on matrices over the quaternion field.展开更多
An image fusion method combining complex contourlet transform(CCT) with nonnegative matrix factorization(NMF) is proposed in this paper.After two images are decomposed by CCT,NMF is applied to their highand low-freque...An image fusion method combining complex contourlet transform(CCT) with nonnegative matrix factorization(NMF) is proposed in this paper.After two images are decomposed by CCT,NMF is applied to their highand low-frequency components,respectively,and finally an image is synthesized.Subjective-visual-quality of the image fusion result is compared with those of the image fusion methods based on NMF and the combination of wavelet /contourlet /nonsubsampled contourlet with NMF.The experimental results are evaluated quantitatively,and the running time is also contrasted.It is shown that the proposed image fusion method can gain larger information entropy,standard deviation and mean gradient,which means that it can better integrate featured information from all source images,avoid background noise and promote space clearness in the fusion image effectively.展开更多
Least-squares reverse time migration(LSRTM)can eliminate imaging artifacts in an iterative way based on the concept of inversion,and it can restore imaging amplitude step by step.LSRTM can provide a high-resolution mi...Least-squares reverse time migration(LSRTM)can eliminate imaging artifacts in an iterative way based on the concept of inversion,and it can restore imaging amplitude step by step.LSRTM can provide a high-resolution migration section and can be applied to irregular and poor-quality seismic data and achieve good results.Steeply dipping refl ectors and complex faults are imaged by using wavefi eld extrapolation based on a two-way wave equation.However,the high computational cost limits the method’s application in practice.A fast approach to realize LSRTM in the imaging domain is provided in this paper to reduce the computational cost signifi cantly and enhance its computational effi ciency.The method uses the Kronecker decomposition algorithm to estimate the Hessian matrix.A low-rank matrix can be used to calculate the Kronecker factor,which involves the calculation of Green’s function at the source and receiver point.The approach also avoids the direct construction of the whole Hessian matrix.Factorization-based LSRTM calculates the production of low-rank matrices instead of repeatedly calculating migration and demigration.Unlike traditional LSRTM,factorization-based LSRTM can reduce calculation costs considerably while maintaining comparable imaging quality.While having the same imaging eff ect,factorization-based LSRTM consumes half the running time of conventional LSRTM.In this regard,the application of factorization-based LSRTM has a promising advantage in reducing the computational cost.Ambient noise caused by this method can be removed by applying a commonly used fi ltering method without signifi cantly degrading the imaging quality.展开更多
A new calibration algorithm for multi-camera systems using 1D calibration objects is proposed. The algorithm inte- grates the rank-4 factorization with Zhang (2004)'s method. The intrinsic parameters as well as th...A new calibration algorithm for multi-camera systems using 1D calibration objects is proposed. The algorithm inte- grates the rank-4 factorization with Zhang (2004)'s method. The intrinsic parameters as well as the extrinsic parameters are re- covered by capturing with cameras the 1D object's rotations around a fixed point. The algorithm is based on factorization of the scaled measurement matrix, the projective depth of which is estimated in an analytical equation instead of a recursive form. For more than three points on a 1D object, the approach of our algorithm is to extend the scaled measurement matrix. The obtained parameters are finally refined through the maximum likelihood inference. Simulations and experiments with real images verify that the proposed technique achieves a good trade-off between the intrinsic and extrinsic camera parameters.展开更多
Collaborative f iltering, as one of the most popular techniques, plays an important role in recommendation systems. However,when the user-item rating matrix is sparse,its performance will be degenerate. Recently,domai...Collaborative f iltering, as one of the most popular techniques, plays an important role in recommendation systems. However,when the user-item rating matrix is sparse,its performance will be degenerate. Recently,domain-specific recommendation approaches have been developed to address this problem.The basic idea is to partition the users and items into overlapping domains, and then perform recommendation in each domain independently. Here, a domain means a group of users having similar preference to a group of products. However, these domain-specific methods consisting of two sequential steps ignore the mutual benefi t of domain segmentation and recommendation. Hence, a unified framework is presented to simultaneously realize recommendation and make use of the domain information underlying the rating matrix in this paper. Based on matrix factorization,the proposed model learns both user preferences of multiple domains and preference selection vectors to select relevant features for each group of products. Besides, local context information is utilized from the user-item rating matrix to enhance the new framework.Experimental results on two widely used datasets, e.g., Ciao and Epinions, demonstrate the effectiveness of our proposed model.展开更多
Traditional data driven fault detection methods assume that the process operates in a single mode so that they cannot perform well in processes with multiple operating modes. To monitor multimode processes effectively...Traditional data driven fault detection methods assume that the process operates in a single mode so that they cannot perform well in processes with multiple operating modes. To monitor multimode processes effectively,this paper proposes a novel process monitoring scheme based on orthogonal nonnegative matrix factorization(ONMF) and hidden Markov model(HMM). The new clustering technique ONMF is employed to separate data from different process modes. The multiple HMMs for various operating modes lead to higher modeling accuracy.The proposed approach does not presume the distribution of data in each mode because the process uncertainty and dynamics can be well interpreted through the hidden Markov estimation. The HMM-based monitoring indication named negative log likelihood probability is utilized for fault detection. In order to assess the proposed monitoring strategy, a numerical example and the Tennessee Eastman process are used. The results demonstrate that this method provides efficient fault detection performance.展开更多
This paper considers a problem of unsupervised spectral unmixing of hyperspectral data. Based on the Linear Mixing Model （ LMM）, a new method under the framework of nonnegative matrix fac- torization （NMF） is prop...This paper considers a problem of unsupervised spectral unmixing of hyperspectral data. Based on the Linear Mixing Model （ LMM）, a new method under the framework of nonnegative matrix fac- torization （NMF） is proposed, namely minimum distance constrained nonnegative matrix factoriza- tion （MDC-NMF）. In this paper, firstly, a new regularization term, called endmember distance （ED） is considered, which is defined as the sum of the squared Euclidean distances from each end- member to their geometric center. Compared with the simplex volume, ED has better optimization properties and is conceptually intuitive. Secondly, a projected gradient （PG） scheme is adopted, and by the virtue of ED, in this scheme the optimal step size along the feasible descent direction can be calculated easily at each iteration. Thirdly, a finite step （ no more than the number of endmem- bers） terminated algorithm is used to project a point on the canonical simplex, by which the abun- dance nonnegative constraint and abundance sum-to-one constraint can be accurately satisfied in a light amount of computation. The experimental results, based on a set of synthetic data and real da- ta, demonstrate that, in the same running time, MDC-NMF outperforms several other similar meth- ods proposed recently.展开更多
Let A be an m by n matrix of rank l, and let M and N be m by k and n by q matrices, respectively, where k is not necessarily equal to q or rank(M AN) < min(k, q). In this paper, we provide some necessary and suffic...Let A be an m by n matrix of rank l, and let M and N be m by k and n by q matrices, respectively, where k is not necessarily equal to q or rank(M AN) < min(k, q). In this paper, we provide some necessary and sufficient conditions for the validity of the rank subtractivity formula: rank(A-AN(M AN)-M A) = rank(A)-rank(AN(M AN)-M A)by applying the full rank decomposition of A = F G(F ∈ Rm×l, G ∈ Rl×n, rank(A) =rank(F) = rank(G) = l) and the product singular value decomposition of the matrix pair[F M, GN ]. This rank subtractivity formula along with the condition under which it holds is called the extended Wedderburn-Guttman theorem.展开更多
Most of the existing algorithms for blind sources separation have a limitation that sources are statistically independent. However, in many practical applications, the source signals are non- negative and mutual stati...Most of the existing algorithms for blind sources separation have a limitation that sources are statistically independent. However, in many practical applications, the source signals are non- negative and mutual statistically dependent signals. When the observations are nonnegative linear combinations of nonnegative sources, the correlation coefficients of the observations are larger than these of source signals. In this letter, a novel Nonnegative Matrix Factorization (NMF) algorithm with least correlated component constraints to blind separation of convolutive mixed sources is proposed. The algorithm relaxes the source independence assumption and has low-complexity algebraic com- putations. Simulation results on blind source separation including real face image data indicate that the sources can be successfully recovered with the algorithm.展开更多
The existing collaborative recommendation algorithms have lower robustness against shilling attacks.With this problem in mind,in this paper we propose a robust collaborative recommendation algorithm based on k-distanc...The existing collaborative recommendation algorithms have lower robustness against shilling attacks.With this problem in mind,in this paper we propose a robust collaborative recommendation algorithm based on k-distance and Tukey M-estimator.Firstly,we propose a k-distancebased method to compute user suspicion degree(USD).The reliable neighbor model can be constructed through incorporating the user suspicion degree into user neighbor model.The influence of attack profiles on the recommendation results is reduced through adjusting similarities among users.Then,Tukey M-estimator is introduced to construct robust matrix factorization model,which can realize the robust estimation of user feature matrix and item feature matrix and reduce the influence of attack profiles on item feature matrix.Finally,a robust collaborative recommendation algorithm is devised by combining the reliable neighbor model and robust matrix factorization model.Experimental results show that the proposed algorithm outperforms the existing methods in terms of both recommendation accuracy and robustness.展开更多
A novel framework is proposed to obtain physiologically meaningful features for Alzheimer's disease(AD)classification based on sparse functional connectivity and non-negative matrix factorization.Specifically,the ...A novel framework is proposed to obtain physiologically meaningful features for Alzheimer's disease(AD)classification based on sparse functional connectivity and non-negative matrix factorization.Specifically,the non-negative adaptive sparse representation(NASR)method is applied to compute the sparse functional connectivity among brain regions based on functional magnetic resonance imaging(fMRI)data for feature extraction.Afterwards,the sparse non-negative matrix factorization(sNMF)method is adopted for dimensionality reduction to obtain low-dimensional features with straightforward physical meaning.The experimental results show that the proposed framework outperforms the competing frameworks in terms of classification accuracy,sensitivity and specificity.Furthermore,three sub-networks,including the default mode network,the basal ganglia-thalamus-limbic network and the temporal-insular network,are found to have notable differences between the AD patients and the healthy subjects.The proposed framework can effectively identify AD patients and has potentials for extending the understanding of the pathological changes of AD.展开更多
This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the prop...This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the propeller and intermediate shafts, under the influence of propeller-induced static and variable hydrodynamic excitations are also studied. The transfer matrix method related to the constant coefficients of differential equation solutions is used. The advantage of the latter as compared with a well-known method of transfer matrix associated with state vector is the possibility of reducing the number of multiplied matrices when adjacent shaft segments have the same material properties and diameters. The results show that there is no risk of buckling and confirm that the strength of the shaft line depends on the value of the static tangential stresses which is the most important component of the stress tensor.展开更多
For classical transformation （q1,q2） → （Aq1 ＋ Bq2, Cq1 ＋ Dq2）, where AD - CB ≠ 1, we find its quantum mechanical image by using LDU decomposition of the matrix （A B C D ）. The explicit operators L, D, and U ...For classical transformation （q1,q2） → （Aq1 ＋ Bq2, Cq1 ＋ Dq2）, where AD - CB ≠ 1, we find its quantum mechanical image by using LDU decomposition of the matrix （A B C D ）. The explicit operators L, D, and U axe derived and their physical meaning is revealed, this also provides a new way for disentangling some exponential operators.展开更多
文摘Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,such as the triple decomposition of motion(TDM)and normal-nilpotent decomposition(NND),have been proposed to analyze the local motions of fluid elements.However,due to the existence of different types and non-uniqueness of Schur forms,as well as various possible definitions of NNDs,confusion has spread widely and is harming the research.This work aims to clean up this confusion.To this end,the complex and real Schur forms are derived constructively from the very basics,with special consideration for their non-uniqueness.Conditions of uniqueness are proposed.After a general discussion of normality and nilpotency,a complex NND and several real NNDs as well as normal-nonnormal decompositions are constructed,with a brief comparison of complex and real decompositions.Based on that,several confusing points are clarified,such as the distinction between NND and TDM,and the intrinsic gap between complex and real NNDs.Besides,the author proposes to extend the real block Schur form and its corresponding NNDs for the complex eigenvalue case to the real eigenvalue case.But their justification is left to further investigations.
文摘A proof is given that any λ _polynome over real quaternionic sfield can be factorized into produce of some linear factors.By the way,some properties and applications of this factorization in matrix theory are given.
文摘Recently clustering techniques have been used to automatically discover typical user profiles. In general, it is a challenging problem to design effective similarity measure between the session vectors which are usually high-dimensional and sparse. Two approaches for mining typical user profiles, based on matrix dimensionality reduction, are presented. In these approaches, non-negative matrix factorization is applied to reduce dimensionality of the session-URL matrix, and the projecting vectors of the user-session vectors are clustered into typical user-session profiles using the spherical k -means algorithm. The results show that two algorithms are successful in mining many typical user profiles in the user sessions.
文摘Finding solutions of matrix equations in given set SR n×n is an active research field. Lots of investigation have done for these cases, where S are the sets of general or symmetric matrices and symmetric positive definite or sysmmetric semiposite definite matrices respectively . Recently, however, attentions are been paying to the situation for S to be the set of general(semi) positive definite matrices(called as semipositive subdefinite matrices below) . In this paper the necessary and sufficient conditions for the following two kinds of matrix equations having semipositive, subdefinite solutions are obtained. General solutions and symmetric solutions of the equations (Ⅰ) and (Ⅱ) have been considered in in detail.
基金supported by the National Natural Science Foundation of China under Grant No. 60433050the Science Foundation of Xuzhou Normal University under Grant No. 06XLA05
文摘We investigate the realization of 2-qutrit logic gate in a bipartite 3-level system with qusi-Ising interaction. On the basis of Caftan decomposition of matrices, the unitary matrices of 2-qutrit are factorized into products of a series of realizable matrices. It is equivalent to exerting a certain control field on the system, and the control goal is usually gained by a sequence of control pulses. The general discussion on the realization of 2-qutrit logic gate is made first, and then the realization of the ternary SWAP gate and the ternary √SWAP gate are discussed specifically, and the sequences of control pulses and drift processes implementing these gates are given.
文摘Abstract： At first one of g-inverses of A （×） In＋Im（×） BT is given out, then the explicit solution to matrix equation AX ＋ XB = C is gained by using the method of matrix decomposition, finally, a numerical example is obtained.
文摘In this paper we derive a practical method of solving simultaneously the problem of Schmidt decomposition of quaternion matrix and the orthonormalization of vectors in a generalized unitary space by using elementary column operations on matrices over the quaternion field.
基金Supported by National Natural Science Foundation of China (No. 60872065)
文摘An image fusion method combining complex contourlet transform(CCT) with nonnegative matrix factorization(NMF) is proposed in this paper.After two images are decomposed by CCT,NMF is applied to their highand low-frequency components,respectively,and finally an image is synthesized.Subjective-visual-quality of the image fusion result is compared with those of the image fusion methods based on NMF and the combination of wavelet /contourlet /nonsubsampled contourlet with NMF.The experimental results are evaluated quantitatively,and the running time is also contrasted.It is shown that the proposed image fusion method can gain larger information entropy,standard deviation and mean gradient,which means that it can better integrate featured information from all source images,avoid background noise and promote space clearness in the fusion image effectively.
基金funded by the National Natural Science Foundation of China (No.41574098&41630964)the Fundamental Research Funds for the Central Universities (No.18CX02059A)+3 种基金the Development Fund of Key Laboratory of Deep Oil&Gas (No. 20CX02111A)SINOPEC Key Laboratory of Geophysics open fund (No. wtyjy-wx2018-01-07)Shandong Natural Science Foundation of China(No. ZR2020MD048)the Major Scientific and Technological Projects of CNPC (No. ZD2019-183-003)
文摘Least-squares reverse time migration(LSRTM)can eliminate imaging artifacts in an iterative way based on the concept of inversion,and it can restore imaging amplitude step by step.LSRTM can provide a high-resolution migration section and can be applied to irregular and poor-quality seismic data and achieve good results.Steeply dipping refl ectors and complex faults are imaged by using wavefi eld extrapolation based on a two-way wave equation.However,the high computational cost limits the method’s application in practice.A fast approach to realize LSRTM in the imaging domain is provided in this paper to reduce the computational cost signifi cantly and enhance its computational effi ciency.The method uses the Kronecker decomposition algorithm to estimate the Hessian matrix.A low-rank matrix can be used to calculate the Kronecker factor,which involves the calculation of Green’s function at the source and receiver point.The approach also avoids the direct construction of the whole Hessian matrix.Factorization-based LSRTM calculates the production of low-rank matrices instead of repeatedly calculating migration and demigration.Unlike traditional LSRTM,factorization-based LSRTM can reduce calculation costs considerably while maintaining comparable imaging quality.While having the same imaging eff ect,factorization-based LSRTM consumes half the running time of conventional LSRTM.In this regard,the application of factorization-based LSRTM has a promising advantage in reducing the computational cost.Ambient noise caused by this method can be removed by applying a commonly used fi ltering method without signifi cantly degrading the imaging quality.
基金the National Natural Science Foundation of China (No. 60675017) the National Basic Research Program of China (No. 2006CB303103)
文摘A new calibration algorithm for multi-camera systems using 1D calibration objects is proposed. The algorithm inte- grates the rank-4 factorization with Zhang (2004)'s method. The intrinsic parameters as well as the extrinsic parameters are re- covered by capturing with cameras the 1D object's rotations around a fixed point. The algorithm is based on factorization of the scaled measurement matrix, the projective depth of which is estimated in an analytical equation instead of a recursive form. For more than three points on a 1D object, the approach of our algorithm is to extend the scaled measurement matrix. The obtained parameters are finally refined through the maximum likelihood inference. Simulations and experiments with real images verify that the proposed technique achieves a good trade-off between the intrinsic and extrinsic camera parameters.
基金supported in part by the Humanity&Social Science general project of Ministry of Education under Grants No.14YJAZH046National Science Foundation of China under Grants No.61402304the Beijing Educational Committee Science and Technology Development Planned under Grants No.KM201610028015
文摘Collaborative f iltering, as one of the most popular techniques, plays an important role in recommendation systems. However,when the user-item rating matrix is sparse,its performance will be degenerate. Recently,domain-specific recommendation approaches have been developed to address this problem.The basic idea is to partition the users and items into overlapping domains, and then perform recommendation in each domain independently. Here, a domain means a group of users having similar preference to a group of products. However, these domain-specific methods consisting of two sequential steps ignore the mutual benefi t of domain segmentation and recommendation. Hence, a unified framework is presented to simultaneously realize recommendation and make use of the domain information underlying the rating matrix in this paper. Based on matrix factorization,the proposed model learns both user preferences of multiple domains and preference selection vectors to select relevant features for each group of products. Besides, local context information is utilized from the user-item rating matrix to enhance the new framework.Experimental results on two widely used datasets, e.g., Ciao and Epinions, demonstrate the effectiveness of our proposed model.
基金Supported by the National Natural Science Foundation of China(61374140,61403072)
文摘Traditional data driven fault detection methods assume that the process operates in a single mode so that they cannot perform well in processes with multiple operating modes. To monitor multimode processes effectively,this paper proposes a novel process monitoring scheme based on orthogonal nonnegative matrix factorization(ONMF) and hidden Markov model(HMM). The new clustering technique ONMF is employed to separate data from different process modes. The multiple HMMs for various operating modes lead to higher modeling accuracy.The proposed approach does not presume the distribution of data in each mode because the process uncertainty and dynamics can be well interpreted through the hidden Markov estimation. The HMM-based monitoring indication named negative log likelihood probability is utilized for fault detection. In order to assess the proposed monitoring strategy, a numerical example and the Tennessee Eastman process are used. The results demonstrate that this method provides efficient fault detection performance.
基金Supported by the National Natural Science Foundation of China （ No. 60872083 ） and the National High Technology Research and Development Program of China （No. 2007AA12Z149）.
文摘This paper considers a problem of unsupervised spectral unmixing of hyperspectral data. Based on the Linear Mixing Model （ LMM）, a new method under the framework of nonnegative matrix fac- torization （NMF） is proposed, namely minimum distance constrained nonnegative matrix factoriza- tion （MDC-NMF）. In this paper, firstly, a new regularization term, called endmember distance （ED） is considered, which is defined as the sum of the squared Euclidean distances from each end- member to their geometric center. Compared with the simplex volume, ED has better optimization properties and is conceptually intuitive. Secondly, a projected gradient （PG） scheme is adopted, and by the virtue of ED, in this scheme the optimal step size along the feasible descent direction can be calculated easily at each iteration. Thirdly, a finite step （ no more than the number of endmem- bers） terminated algorithm is used to project a point on the canonical simplex, by which the abun- dance nonnegative constraint and abundance sum-to-one constraint can be accurately satisfied in a light amount of computation. The experimental results, based on a set of synthetic data and real da- ta, demonstrate that, in the same running time, MDC-NMF outperforms several other similar meth- ods proposed recently.
文摘Let A be an m by n matrix of rank l, and let M and N be m by k and n by q matrices, respectively, where k is not necessarily equal to q or rank(M AN) < min(k, q). In this paper, we provide some necessary and sufficient conditions for the validity of the rank subtractivity formula: rank(A-AN(M AN)-M A) = rank(A)-rank(AN(M AN)-M A)by applying the full rank decomposition of A = F G(F ∈ Rm×l, G ∈ Rl×n, rank(A) =rank(F) = rank(G) = l) and the product singular value decomposition of the matrix pair[F M, GN ]. This rank subtractivity formula along with the condition under which it holds is called the extended Wedderburn-Guttman theorem.
基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (No.20060280003)Shanghai Leading Academic Dis-cipline Project (T0102)
文摘Most of the existing algorithms for blind sources separation have a limitation that sources are statistically independent. However, in many practical applications, the source signals are non- negative and mutual statistically dependent signals. When the observations are nonnegative linear combinations of nonnegative sources, the correlation coefficients of the observations are larger than these of source signals. In this letter, a novel Nonnegative Matrix Factorization (NMF) algorithm with least correlated component constraints to blind separation of convolutive mixed sources is proposed. The algorithm relaxes the source independence assumption and has low-complexity algebraic com- putations. Simulation results on blind source separation including real face image data indicate that the sources can be successfully recovered with the algorithm.
基金National Natural Science Foundation of China under Grant No.61379116，Natural Science Foundation of Hebei Province under Grant No.F2015203046 and No.F2013203124，Key Program of Research on Science and Technology of Higher Education Institutions of Hebei Province under Grant No.ZH2012028
文摘The existing collaborative recommendation algorithms have lower robustness against shilling attacks.With this problem in mind,in this paper we propose a robust collaborative recommendation algorithm based on k-distance and Tukey M-estimator.Firstly,we propose a k-distancebased method to compute user suspicion degree(USD).The reliable neighbor model can be constructed through incorporating the user suspicion degree into user neighbor model.The influence of attack profiles on the recommendation results is reduced through adjusting similarities among users.Then,Tukey M-estimator is introduced to construct robust matrix factorization model,which can realize the robust estimation of user feature matrix and item feature matrix and reduce the influence of attack profiles on item feature matrix.Finally,a robust collaborative recommendation algorithm is devised by combining the reliable neighbor model and robust matrix factorization model.Experimental results show that the proposed algorithm outperforms the existing methods in terms of both recommendation accuracy and robustness.
基金The Foundation of Hygiene and Health of Jiangsu Province(No.H2018042)the National Natural Science Foundation of China(No.61773114)the Key Research and Development Plan(Industry Foresight and Common Key Technology)of Jiangsu Province(No.BE2017007-3)
文摘A novel framework is proposed to obtain physiologically meaningful features for Alzheimer's disease(AD)classification based on sparse functional connectivity and non-negative matrix factorization.Specifically,the non-negative adaptive sparse representation(NASR)method is applied to compute the sparse functional connectivity among brain regions based on functional magnetic resonance imaging(fMRI)data for feature extraction.Afterwards,the sparse non-negative matrix factorization(sNMF)method is adopted for dimensionality reduction to obtain low-dimensional features with straightforward physical meaning.The experimental results show that the proposed framework outperforms the competing frameworks in terms of classification accuracy,sensitivity and specificity.Furthermore,three sub-networks,including the default mode network,the basal ganglia-thalamus-limbic network and the temporal-insular network,are found to have notable differences between the AD patients and the healthy subjects.The proposed framework can effectively identify AD patients and has potentials for extending the understanding of the pathological changes of AD.
文摘This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the propeller and intermediate shafts, under the influence of propeller-induced static and variable hydrodynamic excitations are also studied. The transfer matrix method related to the constant coefficients of differential equation solutions is used. The advantage of the latter as compared with a well-known method of transfer matrix associated with state vector is the possibility of reducing the number of multiplied matrices when adjacent shaft segments have the same material properties and diameters. The results show that there is no risk of buckling and confirm that the strength of the shaft line depends on the value of the static tangential stresses which is the most important component of the stress tensor.
基金Supported by the President Foundation of Chinese Academy of Science and Specialized Research Fund for the Doctorial Progress of Higher Education under Grant No.20070358009
文摘For classical transformation （q1,q2） → （Aq1 ＋ Bq2, Cq1 ＋ Dq2）, where AD - CB ≠ 1, we find its quantum mechanical image by using LDU decomposition of the matrix （A B C D ）. The explicit operators L, D, and U axe derived and their physical meaning is revealed, this also provides a new way for disentangling some exponential operators.
