eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

enhancing bilinear subspace learning by element rearrangement the success of bilinear subspace learning heavily depends on reducing correlations among features along rows and columns of the data matrices in this work we study the problem of rearranging elements within a matrix in order to maximize these correlations so that information redundancy in matrix data can be more extensively removed by existing bilinear subspace learning algorithms an efficient iterative algorithm is proposed to tackle this essentially integer programming problem in each step the matrix structure is refined with a constrained earth mover s distance procedure that incrementally rearranges matrices to become more similar to their low rank approximations which have high correlation among features along rows and columns in addition we present two extensions of the algorithm for conducting supervised bilinear subspace learning experiments in both unsupervised and supervised bilinear subspace learning demonstrate the effectiveness of our proposed algorithms in improving data compression performance and classification accuracy

tensor based aam with continuous variation estimation application to variation robust face recognition the active appearance model aam is a well known model that can represent a non rigid object effectively however the fitting result is often unsatisfactory when an input image deviates from the training images due to its fixed shape and appearance model to obtain more robust aam fitting we propose a tensor based aam that can handle a variety of subjects poses expressions and illuminations in the tensor algebra framework which consists of an image tensor and a model tensor the image tensor estimates image variations such as pose expression and illumination of the input image using two different variation estimation techniques discrete and continuous variation estimation the model tensor generates variation specific aam basis vectors from the estimated image variations which leads to more accurate fitting results to validate the usefulness of the tensor based aam we performed variation robust face recognition using the tensor based aam fitting results to do we propose indirect aam feature transformation experimental results show that tensor based aam with continuous variation estimation outperforms that with discrete variation estimation and conventional aam in terms of the average fitting error and the face recognition rate

ground state solutions of asymptotically linear fractional schrodinger equations this paper is devoted to a time independent fractional schrodinger equation of the form su v x u f x u inrn where n 2 s 0 1 s stands for the fractional laplacian we apply the variational methods to obtain the existence of ground state solutions when f x u is asymptotically linear with respect to u at infinity

sequential algorithm for fast clique percolation in complex network research clique percolation introduced by palla der enyi and vicsek nature london 435 814 2005 is a deterministic community detection method which allows for overlapping communities and is purely based on local topological properties of a network here we present a sequential clique percolation algorithm scp to do fast community detection in weighted and unweighted networks for cliques of a chosen size this method is based on sequentially inserting the constituent links to the network and simultaneously keeping track of the emerging community structure unlike existing algorithms the scp method allows for detecting k clique communities at multiple weight thresholds in a single run and can simultaneously produce a dendrogram representation of hierarchical community structure in sparse weighted networks the scp algorithm can also be used for implementing the weighted clique percolation method recently introduced by farkas et al new j phys 9 180 2007 the computational time of the scp algorithm scales linearly with the number of k cliques in the network as an example the method is applied to a product association network revealing its nested community structure

an integrable system and associated integrable models as well as hamiltonian structures starting from an existed lie algebra introduces a new lie algebra a1 e1 e2 e3 so that two isospectral lax matrices are established by employing the tu scheme an integrable equation hierarchy denoted by ieh is obtained from which a few reduced evolution equations are presented one of them is the mkdv equation the elliptic variable solutions and three kinds of darboux transformations for one coupled equation which is from the ieh are worked out respectively finally we take use of the lie algebra a1 to generate eight higher dimensional lie algebras from which the linear integrable couplings the nonlinear integrable couplings and the bi integrable couplings of the ieh are engendered whose hamiltonian structures are also obtained by the variational identity then further reduce one coupled integrable equation to get a nonlinear generalized mkdv equation

local fractional fokker planck equation we propose a new class of differential equations which we call local fractional differential equations they involve local fractional derivatives and appear to be suitable to deal with phenomena taking place in fractal space and time a local fractional analog of the fokker planck equation has been derived starting from the chapman kolmogorov condition we solve the equation with a specific choice of the transition probability and show how subdiffusive behavior can arise

the generalized fractional trace variational identity and fractional integrable couplings of kaup newell hierarchy starting from fractional isospectral problems and general bilinear forms the generalized fractional trace identity is presented then a new explicit lie algebra is introduced for which the fractional integrable couplings of kaup newell hierarchy are derived furthermore we obtained the fractional hamiltonian structures of the fractional integrable couplings of kaup newell hierarchy the methods derived by us can be generalized to other fractional integrable couplings

mechanics with fractional derivatives lagrangian and hamiltonian mechanics can be formulated to include derivatives of fractional order f riewe phys rev 53 1890 1996 lagrangians with fractional derivatives lead directly to equations of motion with nonconservative classical forces such as friction the present work continues the development of fractional derivative mechanics by deriving a modified hamilton s principle introducing two types of canonical transformations and deriving the hamilton jacobi equation using generalized mechanics with fractional and higher order derivatives the method is illustrated with a frictional force proportional to velocity in contrast to conventional mechanics with integer order derivatives quantization of a fractional derivative hamiltonian cannot generally be achieved by the traditional replacement of momenta with coordinate derivatives instead a quantum mechanical wave equation is proposed that follows from the hamilton jacobi equation by application of the correspondence principle

nonlinear continuous integrable hamiltonian couplings based on a kind of special non semisimple lie algebras a scheme is presented for constructing nonlinear continuous integrable couplings variational identities over the corresponding loop algebras are used to furnish hamiltonian structures for the resulting continuous integrable couplings the application of the scheme is illustrated by an example of nonlinear continuous integrable hamiltonian couplings of the akns hierarchy of soliton equations

detection of community overlap according to belief propagation and conflict abstract most existing methods for detection of community overlap cannot balance efficiency and accuracy for large and densely overlapping networks to quickly identify overlapping communities for such networks we propose a new method that uses belief propagation and conflict pcb to occupy communities we first identify triangles with maximal clustering coefficients as seed nodes and sow a new type of belief to the seed nodes then the beliefs explore their territory by occupying nodes with high assent ability the beliefs propagate their strength along the graph to consolidate their territory and conflict with each other when they encounter the same node simultaneously finally the node membership is judged from the belief vectors the pcb time complexity is nearly linear and its space complexity is linear the algorithm was tested in extensive experiments on three real world social networks and three computer generated artificial graphs the experimental results show that pcb is very fast and highly reliable tests on real and artificial networks give excellent results compared with three newly proposed overlapping community detection algorithms

graph embedding and extensions a general framework for dimensionality reduction a large family of algorithms supervised or unsupervised stemming from statistics or geometry theory has been designed to provide different solutions to the problem of dimensionality reduction despite the different motivations of these algorithms we present in this paper a general formulation known as graph embedding to unify them within a common framework in graph embedding each algorithm can be considered as the direct graph embedding or its linear kernel tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided furthermore the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms by utilizing this framework as a tool we propose a new supervised dimensionality reduction algorithm called marginal fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class while the penalty graph connects the marginal points and characterizes the interclass separability we show that mfa effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions real face recognition experiments show the superiority of our proposed mfa in comparison to lda also for corresponding kernel and tensor extensions

the fractional quadratic form identity and hamiltonian structure of an integrable coupling of the fractional ablowitz kaup newell segur hierarchy starting from a general isospectral problem of fractional order we propose a fractional quadratic form identity from which the hamiltonian structure of an integrable coupling of the fractional ablowitz kaup newell segur hierarchy is derived the method can be generalized to other fractional integrable couplings

a physics based analysis of image appearance models linear and multilinear models pca 3dmm aam asm and multilinear tensors of object shape appearance have been very popular in computer vision in this paper we analyze the applicability of these heuristic models from the fundamental physical laws of object motion and image formation we prove that under suitable conditions the image appearance space can be closely approximated to be multilinear with the illumination and texture subspaces being trilinearly combined with the direct sum of the motion and deformation subspaces this result provides a physics based understanding of many of the successes and limitations of the linear and multilinear approaches existing in the computer vision literature and also identifies some of the conditions under which they are valid it provides an analytical representation of the image space in terms of different physical factors that affect the image formation process numerical analysis of the accuracy of the physics based models is performed and tracking results on real data are presented

simultaneous tensor decomposition and completion using factor priors the success of research on matrix completion is evident in a variety of real world applications tensor completion which is a high order extension of matrix completion has also generated a great deal of research interest in recent years given a tensor with incomplete entries existing methods use either factorization or completion schemes to recover the missing parts however as the number of missing entries increases factorization schemes may overfit the model because of incorrectly predefined ranks while completion schemes may fail to interpret the model factors in this paper we introduce a novel concept complete the missing entries and simultaneously capture the underlying model structure to this end we propose a method called simultaneous tensor decomposition and completion stdc that combines a rank minimization technique with tucker model decomposition moreover as the model structure is implicitly included in the tucker model we use factor priors which are usually known a priori in real world tensor objects to characterize the underlying joint manifold drawn from the model factors by exploiting this auxiliary information our method leverages two classic schemes and accurately estimates the model factors and missing entries we conducted experiments to empirically verify the convergence of our algorithm on synthetic data and evaluate its effectiveness on various kinds of real world data the results demonstrate the efficacy of the proposed method and its potential usage in tensor based applications it also outperforms state of the art methods on multilinear model analysis and visual data completion tasks

fractional ginzburg landau equation for fractal media abstract we derive the fractional generalization of the ginzburg landau equation from the variational euler lagrange equation for fractal media to describe fractal media we use the fractional integrals considered as approximations of integrals on fractals some simple solutions of the ginzburg landau equation for fractal media are considered and different forms of the fractional ginzburg landau equation or nonlinear schrodinger equation with fractional derivatives are presented the agrawal variational principle and its generalization have been applied

the trace identity a powerful tool for constructing the hamiltonian structure of integrable systems a new approach to hamiltonian structures of integrable systems is proposed by making use of a trace identity for a variety of isospectral problems that can be unified to one model x u it is shown that both the related hierarchy of evolution equations and the hamiltonian structure can be obtained from the same solution of the equation vx u v

face recognition using laplacianfaces we propose an appearance based face recognition method called the laplacianface approach by using locality preserving projections lpp the face images are mapped into a face subspace for analysis different from principal component analysis pca and linear discriminant analysis lda which effectively see only the euclidean structure of face space lpp finds an embedding that preserves local information and obtains a face subspace that best detects the essential face manifold structure the laplacianfaces are the optimal linear approximations to the eigenfunctions of the laplace beltrami operator on the face manifold in this way the unwanted variations resulting from changes in lighting facial expression and pose may be eliminated or reduced theoretical analysis shows that pca lda and lpp can be obtained from different graph models we compare the proposed laplacianface approach with eigenface and fisherface methods on three different face data sets experimental results suggest that the proposed laplacianface approach provides a better representation and achieves lower error rates in face recognition

multilinear graph embedding representation and regularization for images given a set of images finding a compact and discriminative representation is still a big challenge especially when multiple latent factors are hidden in the way of data generation to represent multifactor images although multilinear models are widely used to parameterize the data most methods are based on high order singular value decomposition hosvd which preserves global statistics but interprets local variations inadequately to this end we propose a novel method called multilinear graph embedding mge as well as its kernelization mkge to leverage the manifold learning techniques into multilinear models our method theoretically links the linear nonlinear and multilinear dimensionality reduction we also show that the supervised mge encodes informative image priors for image regularization provided that an image is represented as a high order tensor from our experiments on face and gait recognition the superior performance demonstrates that mge better represents multifactor images than classic methods including hosvd and its variants in addition the significant improvement in image or tensor completion validates the potential of mge for image regularization

detecting communities in social networks using label propagation with information entropy abstract community detection has become an important and effective methodology to understand the structure and function of real world networks the label propagation algorithm lpa is a near linear time algorithm used to detect non overlapping community however it merely considers the direct neighbor relationship in this paper we propose an algorithm to consider information entropy as the measurement of the relationship between direct neighbors and indirect neighbors in a label update we proposed a new belonging coefficient to describe the weight of the label with the belonging coefficient no less than a threshold each node can keep one or more labels to constitute an overlapping community experimental results on both real world and benchmark networks show that our algorithm also possesses high accuracy on detecting community structure in networks

an introduction to kernel based learning algorithms this paper provides an introduction to support vector machines kernel fisher discriminant analysis and kernel principal component analysis as examples for successful kernel based learning methods we first give a short background about vapnik chervonenkis theory and kernel feature spaces and then proceed to kernel based learning in supervised and unsupervised scenarios including practical and algorithmic considerations we illustrate the usefulness of kernel algorithms by discussing applications such as optical character recognition and dna analysis

a direct method for integrable couplings of td hierarchy a direct method for establishing integrable couplings is proposed in this paper as an example illustration integrable couplings of td hierarchy are obtained by constructing a suitable transformation of lax pairs and a new lie algebra

on the local fractional derivative abstract we present the necessary conditions for the existence of the kolwankar gangal local fractional derivatives kg lfd and introduce more general but weaker notions of lfds by using limits of certain integral averages of the difference quotient by applying classical results due to stein and zygmund 1965 16 we show that the kg lfd is almost everywhere zero in any given intervals we generalize some of our results to higher dimensional cases and use integral approximation formulas obtained to design numerical schemes for detecting fractional dimensional edges in signal processing

integrable systems of derivative nonlinear schrodinger type and their multi hamiltonian structure a spectral problem and the associated hierarchy of schrodinger type equations are proposed it is shown that the hierarchy is integrable in liouville s sense and possesses multi hamiltonian structure it is found that several kinds of important equation such as the kaup newell kn equation the chen lee liu cll equation the gerdjikov ivanov gi equation the modified korteweg de vries equation and the sharma tasso olever equation are members in the hierarchy as its special reductions moreover kn cll and gi equations are described by using a unified generalized derivative schrodinger equation involving a parameter and their hamiltonian structure and lax pairs are also given by unified and explicit formulae

semidirect sums of lie algebras and discrete integrable couplings a relation between semidirect sums of lie algebras and integrable couplings of lattice equations is established and a practicable way to construct integrable couplings is further proposed an application of the resulting general theory to the generalized toda spectral problem yields two classes of integrable couplings for the generalized toda hierarchy of lattice equations the construction of integrable couplings using semidirect sums of lie algebras provides a good source of information on complete classification of integrable lattice equations

the restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics fractional dynamics has experienced a firm upswing during the past few years having been forged into a mature framework in the theory of stochastic processes a large number of research papers developing fractional dynamics further or applying it to various systems have appeared since our first review article on the fractional fokker planck equation metzler r and klafter j 2000a phys rep 339 1 77 it therefore appears timely to put these new works in a cohesive perspective in this review we cover both the theoretical modelling of sub and superdiffusive processes placing emphasis on superdiffusion and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function we also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems

fractional systems and fractional bogoliubov hierarchy equations we consider the fractional generalizations of the phase volume volume element and poisson brackets these generalizations lead us to the fractional analog of the phase space we consider systems on this fractional phase space and fractional analogs of the hamilton equations the fractional generalization of the average value is suggested the fractional analogs of the bogoliubov hierarchy equations are derived from the fractional liouville equation we define the fractional reduced distribution functions the fractional analogs of the vlasov equation and the debye radius are considered

on liouville integrability of zero curvature equations and the yang hierarchy sufficient conditions for a zero curvature equation ut vx u v 0 being liouville integrable are investigated in the case that the equation is integrable an explicit formula of the poisson bracket h lambda h mu for hamiltonians h is proposed the yang hierarchy is derived and shown to be liouville integrable

hamiltonian and quasi hamiltonian structures associated with semi direct sums of lie algebras the trace variational identity is generalized to zero curvature equations associated with non semi simple lie algebras or equivalently lie algebras possessing degenerate killing forms an application of the resulting generalized variational identity to a class of semi direct sums of lie algebras in the akns case furnishes hamiltonian and quasi hamiltonian structures of the associated integrable couplings three examples of integrable couplings for the akns hierarchy are presented one hamiltonian and two quasi hamiltonian