online blind source separation using incremental nonnegative matrix factorization with volume constraint online blind source separation bss is proposed to overcome the high computational cost problem which limits the practical applications of traditional batch bss algorithms however the existing online bss methods are mainly used to separate independent or uncorrelated sources recently nonnegative matrix factorization nmf shows great potential to separate the correlative sources where some constraints are often imposed to overcome the non uniqueness of the factorization in this paper an incremental nmf with volume constraint is derived and utilized for solving online bss the volume constraint to the mixing matrix enhances the identifiability of the sources while the incremental learning mode reduces the computational cost the proposed method takes advantage of the natural gradient based multiplication updating rule and it performs especially well in the recovery of dependent sources simulations in bss for dual energy x ray images online encrypted speech signals and high correlative face images show the validity of the proposed method

nonnegative local coordinate factorization for image representation recently nonnegative matrix factorization nmf has become increasingly popular for feature extraction in computer vision and pattern recognition nmf seeks two nonnegative matrices whose product can best approximate the original matrix the nonnegativity constraints lead to sparse parts based representations that can be more robust than nonsparse global features to obtain more accurate control over the sparseness in this paper we propose a novel method called nonnegative local coordinate factorization nlcf for feature extraction nlcf adds a local coordinate constraint into the standard nmf objective function specifically we require that the learned basis vectors be as close to the original data points as possible in this way each data point can be represented by a linear combination of only a few nearby basis vectors which naturally leads to sparse representation extensive experimental results suggest that the proposed approach provides a better representation and achieves higher accuracy in image clustering

online nonnegative matrix factorization with robust stochastic approximation nonnegative matrix factorization nmf has become a popular dimension reduction method and has been widely applied to image processing and pattern recognition problems however conventional nmf learning methods require the entire dataset to reside in the memory and thus cannot be applied to large scale or streaming datasets in this paper we propose an efficient online rsa nmf algorithm or nmf that learns nmf in an incremental fashion and thus solves this problem in particular or nmf receives one sample or a chunk of samples per step and updates the bases via robust stochastic approximation benefitting from the smartly chosen learning rate and averaging technique or nmf converges at the rate of in each update of the bases furthermore we prove that or nmf almost surely converges to a local optimal solution by using the quasi martingale by using a buffering strategy we keep both the time and space complexities of one step of the or nmf constant and make or nmf suitable for large scale or streaming datasets preliminary experimental results on real world datasets show that or nmf outperforms the existing online nmf onmf algorithms in terms of efficiency experimental results of face recognition and image annotation on public datasets confirm the effectiveness of or nmf compared with the existing onmf algorithms

time domain vector potential technique for the meshless radial point interpolation method summary a time domain meshless algorithm based on vector potentials is introduced for the analysis of transient electromagnetic fields the proposed numerical algorithm is a modification of the radial point interpolation method where radial basis functions are used for local interpolation of the vector potentials and their derivatives in the proposed implementation solving the second order vector potential wave equation intrinsically enforces the divergence free property of the electric and magnetic fields furthermore the computational effort associated with the generation of a dual node distribution as required for solving the first order maxwell s equations is avoided the proposed method is validated with several examples of 2d waveguides and filters and the convergence is empirically demonstrated in terms of node density or size of local support domains it is further shown that inhomogeneous node distributions can provide increased convergence rates that is the same accuracy with smaller number of nodes compared with a solution for homogeneous node distribution a comparison of the magnetic vector potential technique with conventional radial point interpolation method is performed highlighting the superiority of the divergence free formulation copyright 2015 john wiley sons ltd

staggered time integrators for wave equations we consider variations of the adams bashforth backward differentiation and runge kutta families of time integrators to solve systems of linear wave equations on uniform time staggered grids these methods are found to have smaller local truncation errors and to allow larger stable time steps than traditional nonstaggered versions of equivalent orders we investigate the accuracy and stability of these methods analytically experimentally and through the use of a novel root portrait technique

turing patterns in the lengyel epstein system for the cima reaction the first experimental evidence of the turing pattern was observed by de kepper and her associates 1990 on the cima reaction in an open unstirred gel reactor almost 40 years after turing s prediction lengyel and epstein characterized this famous experiment using a system of reaction diffusion equations in this paper we report some fundamental analytic properties of the lengyel epstein system our result also indicates that if either of the initial concentrations of the reactants the size of the reactor or the effective diffusion rate are not large enough then the system does not admit nonconstant steady states a priori estimates are fundamental to our approach for this nonexistence result the degree theory was combined with the a priori estimates to derive existence of nonconstant steady states

variational regularized 2 d nonnegative matrix factorization a novel approach for adaptive regularization of 2 d nonnegative matrix factorization is presented the proposed matrix factorization is developed under the framework of maximum a posteriori probability and is adaptively fine tuned using the variational approach the method enables 1 a generalized criterion for variable sparseness to be imposed onto the solution and 2 prior information to be explicitly incorporated into the basis features the method is computationally efficient and has been demonstrated on two applications that is extracting features from image and separating single channel source mixture in addition it is shown that the basis features of an information bearing matrix can be extracted more efficiently using the proposed regularized priors experimental tests have been rigorously conducted to verify the efficacy of the proposed method

exponentiated gradient versus gradient descent for linear predictors we consider two algorithm for on line prediction based on a linear model the algorithms are the well known gradient descent gd algorithm and a new algorithm which we call eg they both maintain a weight vector using simple updates for the gd algorithm the update is based on subtracting the gradient of the squared error made on a prediction the eg algorithm uses the components of the gradient in the exponents of factors that are used in updating the weight vector multiplicatively we present worst case loss bounds for eg and compare them to previously known bounds for the gd algorithm the bounds suggest that the losses of the algorithms are in general incomparable but eg has a much smaller loss if only a few components of the input are relevant for the predictions we have performed experiments which show that our worst case upper bounds are quite tight already on simple artificial data

multiplicative update rules for concurrent nonnegative matrix factorization and maximum margin classification the state of the art classification methods which employ nonnegative matrix factorization nmf employ two consecutive independent steps the first one performs data transformation dimensionality reduction and the second one classifies the transformed data using classification methods such as nearest neighbor centroid or support vector machines svms in the following we focus on using nmf factorization followed by svm classification typically the parameters of these two steps e g the nmf bases coefficients and the support vectors are optimized independently thus leading to suboptimal classification performance in this paper we merge these two steps into one by incorporating maximum margin classification constraints into the standard nmf optimization the notion behind the proposed framework is to perform nmf while ensuring that the margin between the projected data of the two classes is maximal the concurrent nmf factorization and support vector optimization are performed through a set of multiplicative update rules in the same context the maximum margin classification constraints are imposed on the nmf problem with additional discriminant constraints and respective multiplicative update rules are extracted the impact of the maximum margin classification constraints on the nmf factorization problem is addressed in section vi experimental results in several databases indicate that the incorporation of the maximum margin classification constraints into the nmf and discriminant nmf objective functions improves the accuracy of the classification

multiple stability switches and hopf bifurcations induced by the delay in a lengyel epstein chemical reaction system abstract this paper examines the dynamical analysis of the lengyel epstein system with a discrete delay in detail under the assumption that the unique positive equilibrium of the model is locally asymptotically stable in the absence of the delay the effect of the increase of delay on the stability of the unique positive equilibrium is analyzed in detail it is found that under suitable conditions on the other parameters the delay doesn t affect the stability of the equilibrium namely the equilibrium is absolutely stable while under the other conditions on the other parameters the equilibrium will become ultimately unstable after passing through multiple stability switches and hopf bifurcations at some certain critical values of delay particularly by means of the normal form method and the center manifold reduction for retarded functional differential equations the explicit formulae determining the direction of hopf bifurcations and the stability of the bifurcating periodic solutions are obtained to verify our theoretical conclusions some numerical simulations for specific examples are also included at the end of this article

local coordinate concept factorization for image representation learning sparse representation of high dimensional data is a state of the art method for modeling data matrix factorization based techniques such as nonnegative matrix factorization and concept factorization cf have shown great advantages in this area especially useful for image representation both of them are linear learning problems and lead to a sparse representation of the images however the sparsity obtained by these methods does not always satisfy locality conditions for example the learned new basis vectors may be relatively far away from the original data thus we may not be able to achieve the optimal performance when using the new representation for other learning tasks such as classification and clustering in this paper we introduce a locality constraint into the traditional cf by requiring the concepts basis vectors to be as close to the original data points as possible each datum can be represented by a linear combination of only a few basis concepts thus our method is able to achieve sparsity and locality simultaneously we analyze the complexity of our novel algorithm and demonstrate the effectiveness in comparison with the state of the art approaches through a set of evaluations based on real world applications

hopf bifurcation analysis of a system of coupled delayed differential equations in this paper we have considered a system of delay differential equations the system without delayed arises in the lengyel epstein model its dynamics are studied in terms of local analysis and hopf bifurcation analysis linear stability is investigated and existence of hopf bifurcation is demonstrated via analyzing the associated characteristic equation for the hopf bifurcation analysis the delay parameter is chosen as a bifurcation parameter the stability of the bifurcating periodic solutions is determined by using the center manifold theorem and the normal form theory introduced by hassard et al 1981 7 furthermore the direction of the bifurcation the stability and the period of periodic solutions are given finally the theoretical results are supported by some numerical simulations

non negative matrix factorization with sparseness constraints non negative matrix factorization nmf is a recently developed technique for finding parts based linear representations of non negative data although it has successfully been applied in several applications it does not always result in parts based representations in this paper we show how explicitly incorporating the notion of sparseness improves the found decompositions additionally we provide complete matlab code both for standard nmf and for our extension our hope is that this will further the application of these methods to solving novel data analysis problems

graph regularized nonnegative matrix factorization for data representation matrix factorization techniques have been frequently applied in information retrieval computer vision and pattern recognition among them nonnegative matrix factorization nmf has received considerable attention due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts based in the human brain on the other hand from the geometric perspective the data is usually sampled from a low dimensional manifold embedded in a high dimensional ambient space one then hopes to find a compact representation which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure in this paper we propose a novel algorithm called graph regularized nonnegative matrix factorization gnmf for this purpose in gnmf an affinity graph is constructed to encode the geometrical information and we seek a matrix factorization which respects the graph structure our empirical study shows encouraging results of the proposed algorithm in comparison to the state of the art algorithms on real world problems

geometric mean for subspace selection subspace selection approaches are powerful tools in pattern classification and data visualization one of the most important subspace approaches is the linear dimensionality reduction step in the fisher s linear discriminant analysis flda which has been successfully employed in many fields such as biometrics bioinformatics and multimedia information management however the linear dimensionality reduction step in flda has a critical drawback for a classification task with c classes if the dimension of the projected subspace is strictly lower than c 1 the projection to a subspace tends to merge those classes which are close together in the original feature space if separate classes are sampled from gaussian distributions all with identical covariance matrices then the linear dimensionality reduction step in flda maximizes the mean value of the kullback leibler kl divergences between different classes based on this viewpoint the geometric mean for subspace selection is studied in this paper three criteria are analyzed 1 maximization of the geometric mean of the kl divergences 2 maximization of the geometric mean of the normalized kl divergences and 3 the combination of 1 and 2 preliminary experimental results based on synthetic data uci machine learning repository and handwriting digits show that the third criterion is a potential discriminative subspace selection method which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in flda and its several representative extensions

a point interpolation meshless method based on radial basis functions a point interpolation meshless method is proposed based on combining radial and polynomial basis functions involvement of radial basis functions overcomes possible singularity associated with the meshless methods based on only the polynomial basis this non singularity is useful in constructing well performed shape functions furthermore the interpolation function obtained passes through all scattered points in an influence domain and thus shape functions are of delta function property this makes the implementation of essential boundary conditions much easier than the meshless methods based on the moving least squares approximation in addition the partial derivatives of shape functions are easily obtained thus improving computational efficiency examples on curve surface fittings and solid mechanics problems show that the accuracy and convergence rate of the present method is high copyright 2002 john wiley sons ltd

multiplicative updates for nonnegative quadratic programming many problems in neural computation and statistical learning involve optimizations with nonnegativity constraints in this article we study convex problems in quadratic programming where the optimization is confined to an axis aligned region in the nonnegative orthant for these problems we derive multiplicative updates that improve the value of the objective function at each iteration and converge monotonically to the global minimum the updates have a simple closed form and do not involve any heuristics or free parameters that must be tuned to ensure convergence despite their simplicity they differ strikingly in form from other multiplicative updates used in machine learning we provide complete proofs of convergence for these updates and describe their application to problems in signal processing and pattern recognition

the meshless local petrov galerkin method in two dimensional electromagnetic wave analysis this paper deals with one member of the class of meshless methods namely the meshless local petrov galerkin mlpg method and explores its application to boundary value problems arising in the analysis of two dimensional electromagnetic wave propagation and scattering this method shows some similitude with the widespread finite element method fem like the discretization of weak forms and sparse global matrices mlpg and fem differ in what regards the construction of an unstructured mesh in mlpg there is no mesh just a cloud of nodes without connection to each other spread throughout the domain the suppression of the mesh is counterbalanced by the use of special shape functions constructed numerically this paper illustrates how to apply mlpg to wave scattering problems through a number of cases in which the results are compared either to analytical solutions or to those provided by other numerical methods

application and optimization of pml abc for the 3 d wave equation in the time domain a three dimensional algorithm with the perfectly matched layer pml absorbing boundary condition abc for the scalar wave equation in the time domain is presented for general inhomogeneous lossy or loss free problems the proposed pml abc is applicable to practical finite difference schemes treating the time domain wave equation such as the time domain wave potential tdwp technique and the time domain scalar wave equation approaches to the analysis of optical structures the time domain wave equation for lossy media is expressed in terms of stretched coordinate variables the algorithm is tested for homogeneous and inhomogeneous media we demonstrate applications to open radiation problems and to port terminations in high frequency circuit problems new pml conductivity profiles are developed for use with the second order wave equation which offer lower reflections in a wider frequency band in comparison with the commonly used in finite difference time domain fdtd algorithms profiles the effect of the termination walls on the overall pml performance is studied and the best choices are singled out

projected gradient methods for nonnegative matrix factorization nonnegative matrix factorization nmf can be formulated as a minimization problem with bound constraints although bound constrained optimization has been studied extensively in both theory and practice so far no study has formally applied its techniques to nmf in this letter we propose two projected gradient methods for nmf both of which exhibit strong optimization properties we discuss efficient implementations and demonstrate that one of the proposed methods converges faster than the popular multiplicative update approach a simple matlab code is also provided