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

gabor based kernel pca with fractional power polynomial models for face recognition this paper presents a novel gabor based kernel principal component analysis pca method by integrating the gabor wavelet representation of face images and the kernel pca method for face recognition gabor wavelets first derive desirable facial features characterized by spatial frequency spatial locality and orientation selectivity to cope with the variations due to illumination and facial expression changes the kernel pca method is then extended to include fractional power polynomial models for enhanced face recognition performance a fractional power polynomial however does not necessarily define a kernel function as it might not define a positive semidefinite gram matrix note that the sigmoid kernels one of the three classes of widely used kernel functions polynomial kernels gaussian kernels and sigmoid kernels do not actually define a positive semidefinite gram matrix either nevertheless the sigmoid kernels have been successfully used in practice such as in building support vector machines in order to derive real kernel pca features we apply only those kernel pca eigenvectors that are associated with positive eigenvalues the feasibility of the gabor based kernel pca method with fractional power polynomial models has been successfully tested on both frontal and pose angled face recognition using two data sets from the feret database and the cmu pie database respectively the feret data set contains 600 frontal face images of 200 subjects while the pie data set consists of 680 images across five poses left and right profiles left and right half profiles and frontal view with two different facial expressions neutral and smiling of 68 subjects the effectiveness of the gabor based kernel pca method with fractional power polynomial models is shown in terms of both absolute performance indices and comparative performance against the pca method the kernel pca method with polynomial kernels the kernel pca method with fractional power polynomial models the gabor wavelet based pca method and the gabor wavelet based kernel pca method with polynomial kernels

discrete signal processing on graphs frequency analysis signals and datasets that arise in physical and engineering applications as well as social genetics biomolecular and many other domains are becoming increasingly larger and more complex in contrast to traditional time and image signals data in these domains are supported by arbitrary graphs signal processing on graphs extends concepts and techniques from traditional signal processing to data indexed by generic graphs this paper studies the concepts of low and high frequencies on graphs and low high and band pass graph signals and graph filters in traditional signal processing these concepts are easily defined because of a natural frequency ordering that has a physical interpretation for signals residing on graphs in general there is no obvious frequency ordering we propose a definition of total variation for graph signals that naturally leads to a frequency ordering on graphs and defines low high and band pass graph signals and filters we study the design of graph filters with specified frequency response and illustrate our approach with applications to sensor malfunction detection and data classification

inclusion properties of certain classes of meromorphic functions associated with the generalized hypergeometric function abstract the purpose of the present paper is to introduce several new classes of meromorphic functions defined by using a meromorphic analogue of the choi saigo srivastava operator for the generalized hypergeometric function and investigate various inclusion properties of these classes some interesting applications involving these and other classes of integral operators are also considered

a lower bound for nodal count on discrete and metric graphs we study the number of nodal domains maximal connected regions on which a function has constant sign of the eigenfunctions of schrodinger operators on graphs under a certain genericity condition we show that the number of nodal domains of the nth eigenfunction is bounded below by n l where l is the number of links that distinguish the graph from a tree

shuffling algorithm for boxed plane partitions we introduce discrete time markov chains that preserve uniform measures on boxed plane partitions elementary markov steps change the size of the box from a b c to a 1 b 1 c or a 1 b 1 c algorithmic realization of each step involves o a b c operations one application is an efficient perfect random sampling algorithm for uniformly distributed boxed plane partitions trajectories of our markov chains can be viewed as random point configurations in the three dimensional lattice we compute the bulk limits of the correlation functions of the resulting random point process on suitable two dimensional sections the limiting correlation functions define a two dimensional determinantal point processes with certain gibbs properties

some applications of hadamard convolution to multivalently analytic and multivalently meromorphic functions the aim of the present study is to give several applications of hadamard product or convolution to multivalently analytic and multivalently meromorphic functions

inclusion properties for certain classes of meromorphic functions associated with the choi saigo srivastava operator abstract the purpose of the present paper is to introduce several new classes of meromorphic functions defined by using a meromorphic analogue of the choi saigo srivastava operator for analytic functions and investigate various inclusion properties of these classes some interesting applications involving these and other classes of integral operators are also considered

some subclasses of meromorphically multivalent functions associated with a linear operator abstract let p denote the class of functions normalized by f z z p n 1 a n z n p p n 1 2 3 which are analytic and p valent in 0 z 1 making use of a linear operator which is defined here by means of the hadamard product or convolution we introduce some new subclasses of the meromorphically p valent function class p and investigate their inclusion relationships and convolution properties some integral preserving properties are also considered

a unified framework for semi supervised dimensionality reduction in practice many applications require a dimensionality reduction method to deal with the partially labeled problem in this paper we propose a semi supervised dimensionality reduction framework which can efficiently handle the unlabeled data under the framework several classical methods such as principal component analysis pca linear discriminant analysis lda maximum margin criterion mmc locality preserving projections lpp and their corresponding kernel versions can be seen as special cases for high dimensional data we can give a low dimensional embedding result for both discriminating multi class sub manifolds and preserving local manifold structure experiments show that our algorithms can significantly improve the accuracy rates of the corresponding supervised and unsupervised approaches

self organization as an iterative kernel smoothing process kohonen s self organizing map when described in a batch processing mode can be interpreted as a statistical kernel smoothing problem the batch som algorithm consists of two steps first the training data are partitioned according to the voronoi regions of the map unit locations second the units are updated by taking weighted centroids of the data falling into the voronoi regions with the weighing function given by the neighborhood then the neighborhood width is decreased and steps 1 2 are repeated the second step can be interpreted as a statistical kernel smoothing problem where the neighborhood function corresponds to the kernel and neighborhood width corresponds to kernel span to determine the new unit locations kernel smoothing is applied to the centroids of the voronoi regions in the topological space this interpretation leads to some new insights concerning the role of the neighborhood and dimensionality reduction it also strengthens the algorithm s connection with the principal curve algorithm a generalized self organizing algorithm is proposed where the kernel smoothing step is replaced with an arbitrary nonparametric regression method

some criteria for meromorphic multivalent starlike functions abstract the main purpose of the present paper is to derive some new criteria for meromorphic multivalent starlike functions

some inclusion relationships and integral preserving properties of certain subclasses of meromorphic functions associated with a family of integral operators the object of the present paper is to investigate a family of integral operators defined on the space of normalized meromorphic functions by making use of these novel integral operators we introduce and investigate several new subclasses of starlike convex close to convex and quasi convex meromorphic functions in particular we establish some inclusion relationships associated with the aforementioned integral operators several interesting integral preserving properties are also considered

a linear operator and associated families of meromorphically multivalent functions making use of a linear operator which is defined here by means of the hadamard product or convolution the authors introduce and investigate the various properties and characteristics of two novel families of meromorphically multivalent functions they also extend the familiar concept of neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions

some properties of certain meromorphically multivalent functions the main object of the present paper is to investigate some interesting properties of certain meromorphically multivalent functions associated with a linear operator l p a c

some properties of certain subclasses of meromorphically multivalent functions in this paper the author investigates interesting properties of certain subclasses of meromorphically multivalent functions which are defined here by means of certain linear operator

quasiconformal kernel common locality discriminant analysis with application to breast cancer diagnosis dimensionality reduction dr is a popular method in recognition and classification in many areas such as facial and medical imaging in this paper we propose a novel supervised dr method namely quasiconformal kernel common locality discriminant analysis qkclda qkclda preserves the local and discriminative relationships of the data moreover it adjusts the kernel structure according to the distribution of the input data and thus possesses a classification advantage over traditional kernel based methods in qkclda the parameter of the quasiconformal kernel is automatically calculated through optimizing an objective function of maximizing the class discriminative ability qkclda is employed in breast cancer diagnoses and some experiments using wisconsin diagnostic breast cancer wdbc and mini mias databases have tested its feasibility and performance in assigning these diagnoses

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

approaching criticality via the zero dissipation limit in the abelian avalanche model the discrete height abelian sandpile model was introduced by bak tang wiesenfeld and dhar as an example for the concept of self organized criticality when the model is modified to allow grains to disappear on each toppling it is called bulk dissipative we provide a detailed study of a continuous height version of the abelian sandpile model called the abelian avalanche model which allows an arbitrarily small amount of dissipation to take place on every toppling we prove that for non zero dissipation the infinite volume limit of the stationary measure of the abelian avalanche model exists and can be obtained via a weighted spanning tree measure we show that in the whole non zero dissipation regime the model is not critical i e spatial covariances of local observables decay exponentially we then study the zero dissipation limit and prove that the self organized critical model is recovered both for the stationary measure and for the dynamics we obtain rigorous bounds on toppling probabilities and introduce an exponent describing their scaling at criticality we rigorously establish the mean field value of this exponent for d 4

a certain family of meromorphically multivalent functions abstract by making use of a familiar analogue of the ruscheweyh derivative as well as of the principle of subordination between two analytic functions the authors introduce and study rather systematically a certain family of meromorphically multivalent functions in the open unit disk u z z c and 0 several inclusion properties of this family are associated with an integral operator of the bernardi libera livingston type

subclasses of meromorphic functions associated with the cho kwon srivastava operator abstract we consider a multiplier transformation and some subclasses of the class of meromorphic functions which was defined by means of the hadamard product by n e cho o s kwon and h m srivastava in n e cho o s kwon h m srivastava inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations j math anal appl 300 2004 505 520

random forests and networks analysis wilson proceedings of the twenty eight annual acm symposium on the theory of computing pp 296 303 1996 in the 1990s described a simple and efficient algorithm based on loop erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph this algorithm provides a powerful tool in analyzing structures on networks and along this line of thinking in recent works avena and gaudilliere in a proof of the transfer current theorem in absence of reversibility in stat probab lett 142 17 22 2018 avena and gaudilliere in j theor probab 2017 https doi org 10 1007 s10959 017 0771 3 avena et al in approximate and exact solutions of intertwining equations though random spanning forests 2017 arxiv 1702 05992v1 avena et al in intertwining wavelets or multiresolution analysis on graphs through random forests 2017 arxiv 1707 04616 to appear in acha 2018 we focused on applications of spanning rooted forests on finite graphs the resulting main conclusions are reviewed in this paper by collecting related theorems algorithms heuristics and numerical experiments a first foundational part on determinantal structures and efficient sampling procedures is followed by four main applications 1 a random walk based notion of well distributed points in a graph 2 a framework to describe metastable like dynamics in finite settings by means of markov intertwining dualities 3 coarse graining schemes for networks and associated processes 4 wavelets like pyramidal algorithms for graph signals

a high performance edge detector based on fuzzy inference rules edge detection is an important topic in computer vision and image processing in this paper a novel edge detector based on fuzzy if then inference rules and edge continuity is proposed the fuzzy if then rule system is designed to model edge continuity criteria the maximum entropy principle is used in the parameter adjusting process we also discuss the related issues in designing fuzzy edge detectors we compare it with the popular edge detectors sobel and canny edge detectors the proposed fuzzy edge detector does not need parameter setting as canny edge detector does and it can preserve an appropriate detection in details it is very robust to noise and can work well under high level noise situations while other edge detectors cannot the detector efficiently extracts edges in images corrupted by noise without requiring the filtering process the experimental results demonstrate the superiority of the proposed method to existing ones

independent component analysis of gabor features for face recognition we present an independent gabor features igfs method and its application to face recognition the novelty of the igf method comes from 1 the derivation of independent gabor features in the feature extraction stage and 2 the development of an igf features based probabilistic reasoning model prm classification method in the pattern recognition stage in particular the igf method first derives a gabor feature vector from a set of downsampled gabor wavelet representations of face images then reduces the dimensionality of the vector by means of principal component analysis and finally defines the independent gabor features based on the independent component analysis ica the independence property of these gabor features facilitates the application of the prm method for classification the rationale behind integrating the gabor wavelets and the ica is twofold on the one hand the gabor transformed face images exhibit strong characteristics of spatial locality scale and orientation selectivity these images can thus produce salient local features that are most suitable for face recognition on the other hand ica would further reduce redundancy and represent independent features explicitly these independent features are most useful for subsequent pattern discrimination and associative recall experiments on face recognition using the face recognition technology feret and the orl datasets where the images vary in illumination expression pose and scale show the feasibility of the igf method in particular the igf method achieves 98 5 correct face recognition accuracy when using 180 features for the feret dataset and 100 accuracy for the orl dataset using 88 features

a class of integral operators preserving subordination and superordination for meromorphic functions the purpose of the present paper is to investigate several subordination and superordination preserving properties of a certain class of integral operators which are defined on the space of meromorphic functions in the punctured open unit disk the sandwich type theorem for these integral operators is also presented moreover we consider an application of the subordination and superordination theorem to the gauss hypergeometric function

hadamard product of certain meromorphic starlike and convex functions in this paper the authors establish certain results concerning the hadamard product for two classes related to starlike and convex univalent meromorphic functions of order a and type b with positive coefficients

local characteristics entropy and limit theorems for spanning trees and domino tilings via transfer impedances let g be a finite graph or an infinite graph on which mathbb z d acts with finite fundamental domain if g is finite let mathbf t be a random spanning tree chosen uniformly from all spanning trees of g if g is infinite methods from pemantle show that this still makes sense producing a random essential spanning forest of g a method for calculating local characteristics i e finite dimensional marginals of mathbf t from the transfer impedance matrix is presented this differs from the classical matrix tree theorem in that only small pieces of the matrix n dimensional minors are needed to compute small n dimensional marginals calculation of the matrix entries relies on the calculation of the green s function for g which is not a local calculation however it is shown how the calculation of the green s function may be reduced to a finite computation in the case when g is an infinite graph admitting a z d action with finite quotient the same computation also gives the entropy of the law of mathbf t these results are applied to the problem of tiling certain lattices by dominos the so called dimer problem another application of these results is to prove modified versions of conjectures of aldous on the limiting distribution of degrees of a vertex and on the local structure near a vertex of a uniform random spanning tree in a lattice whose dimension is going to infinity included is a generalization of moments to tree valued random variables and criteria for these generalized moments to determine a distribution

wulff droplets and the metastable relaxation of kinetic ising models we consider the kinetic ising models glauber dynamics corresponding to the infinite volume ising model in dimension 2 with nearest neighbor ferromagnetic interaction and under a positive external magnetic field h minimal conditions on the flip rates are assumed so that all the common choices are being considered we study the relaxation towards equilibrium when the system is at an arbitrary subcritical temperature t and the evolution is started from a distribution which is stochastically lower than the phase we show that as h 0 the relaxation time blows up as exp c t h with lgr c t w t 2 12 t m t here m t is the spontaneous magnetization and w t is the integrated surface tension of the wulff body of unit volume moreover for 0 c the state of the process at time exp h is shown to be close when h is small to the phase the difference between this state and the phase can be described in terms of an asymptotic expansion in powers of the external field this expansion can be interpreted as describing a set of continuations in h of the family of gibbs distributions with the negative magnetic fields into the region of positive fields

a unified presentation of some classes of meromorphically multivalent functions the authors introduce and investigate various properties of a general class uk p a a b p k n 1 2 3 0 p 0 1 a b 1 0 b 1 which unifies and extends several known or new subclasses of meromorphically multivalent functions the properties and characteristics of this general class which are presented here include growth and distortion theorems they also involve hadamard products or convolution of functions belonging to the class uk p a b

renormalization group for markov chains and application to metastability in this paper we introduce a new renormalization group method for the study of the long time behavior of markov chains with finite state space and with transition probabilities exponentially small in an external parameter a general approach of metastability problems emerges from this analysis and is discussed in detail in the case of a two dimensional ising system at low temperature

kpca plus lda a complete kernel fisher discriminant framework for feature extraction and recognition this paper examines the theory of kernel fisher discriminant analysis kfd in a hilbert space and develops a two phase kfd framework i e kernel principal component analysis kpca plus fisher linear discriminant analysis lda this framework provides novel insights into the nature of kfd based on this framework the authors propose a complete kernel fisher discriminant analysis ckfd algorithm ckfd can be used to carry out discriminant analysis in double discriminant subspaces the fact that it can make full use of two kinds of discriminant information regular and irregular makes ckfd a more powerful discriminator the proposed algorithm was tested and evaluated using the feret face database and the cenparmi handwritten numeral database the experimental results show that ckfd outperforms other kfd algorithms

structural multiple empirical kernel learning multiple kernel learning mkl can boost classification performance through using multiple kernels rather than a single fixed one unlike the traditional mkl with the implicit kernels multiple empirical kernel learning mekl explicitly maps input data into multiple feature spaces this paper focuses on mekl and proposes an effective threefold structural mekl tsmekl the first fold structure is the space structural information between different mapped feature spaces the second one is the class discriminant information within each mapped feature space the third one is the cluster structural information of samples in each mapped feature space the classical mekl mainly pays attention to the first two structures but neglects the last one the proposed tsmekl introduces the cluster structural information into mekl doing so can simultaneously utilize the space the class and the cluster information in the way from globality to locality therefore tsmekl utilizes threefold structural information to result in the improvement of classification performance to the best of our knowledge it is the first time to introduce the cluster information into the mekl framework the main advantage of the developed tsmekl is considering different folds of data information to improve classification performance the experimental results validate the feasibility and effectiveness of tsmekl moreover we discuss the theoretical and experimental generalization risk bound of the proposed algorithm in terms of the rademacher complexity

inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations making use of a multiplier transformation which is defined here by means of the hadamard product or convolution the authors introduce some new subclasses of meromorphic functions and investigate their inclusion relationships and argument properties some integral preserving properties in a given sector are also considered

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

a multiscale pyramid transform for graph signals multiscale transforms designed to process analog and discrete time signals and images cannot be directly applied to analyze high dimensional data residing on the vertices of a weighted graph as they do not capture the intrinsic topology of the graph data domain in this paper we adapt the laplacian pyramid transform for signals on euclidean domains so that it can be used to analyze high dimensional data residing on the vertices of a weighted graph our approach is to study existing methods and develop new methods for the four fundamental operations of graph downsampling graph reduction and filtering and interpolation of signals on graphs equipped with appropriate notions of these operations we leverage the basic multiscale constructs and intuitions from classical signal processing to generate a transform that yields both a multiresolution of graphs and an associated multiresolution of a graph signal on the underlying sequence of graphs

certain subclasses of meromorphically multivalent functions associated with generalized hypergeometric function in this paper we introduce and study two subclasses s p q s a 1 a b l and s p q s a 1 a b l of meromorphic p valent functions of order l email protected email protected

certain classes of meromorphic multivalent functions in this paper we introduce and investigate two new classes of meromorphic multivalent functions such results as subordination properties coefficient inequalities convolution properties and integral representations are proved several sufficient conditions for meromorphic multivalent starlikeness and convexity are also derived

uniform spanning forests we study uniform spanning forest measures on infinite graphs which are weak limits of uniform spanning tree measures from finite subgraphs these limits can be taken with free fsf or wired wsf boundary conditions pemantle proved that the free and wired spanning forests coincide in z d and that they give a single tree iff d 4 in the present work we extend pemantle s alternative to general graphs and exhibit further connections of uniform spanning forests to random walks potential theory invariant percolation and amenability the uniform spanning forest model is related to random cluster models in statistical physics but because of the preceding connections its analysis can be carried further among our results are the following the fsf and wsf in a graph g coincide iff all harmonic dirichlet functions on g are constant the tail fields of the wsf and the fsf are trivial on any graph on any cayley graph that is not a finite extension of z all component trees of the wsf have one end this is new in z d for d 5 on any tree as well as on any graph with spectral radius less than 1 a s all components of the wsf are recurrent the basic topology of the free and the wired uniform spanning forest measures on lattices in hyperbolic space h d is analyzed a cayley graph is amenable iff for all e 0 the union of the wsf and bernoulli percolation with parameter e is connected harmonic measure from infinity is shown to exist on any recurrent proper planar graph with finite codegrees we also present numerous open problems and conjectures

a unified model for probabilistic principal surfaces principal curves and surfaces are nonlinear generalizations of principal components and subspaces respectively they can provide insightful summary of high dimensional data not typically attainable by classical linear methods solutions to several problems such as proof of existence and convergence faced by the original principal curve formulation have been proposed in the past few years nevertheless these solutions are not generally extensible to principal surfaces the mere computation of which presents a formidable obstacle consequently relatively few studies of principal surfaces are available we previously 2000 proposed the probabilistic principal surface pps to address a number of issues associated with current principal surface algorithms pps uses a manifold oriented covariance noise model based on the generative topographical mapping gtm which can be viewed as a parametric formulation of kohonen s self organizing map building on the pps we introduce a unified covariance model that implements pps 0 1 by varying the clamping parameter spl alpha then we comprehensively evaluate the empirical performance of pps gtm and the manifold aligned gtm on three popular benchmark data sets it is shown in two different comparisons that the pps outperforms the gtm under identical parameter settings convergence of the pps is found to be identical to that of the gtm and the computational overhead incurred by the pps decreases to 40 percent or less for more complex manifolds these results show that the generalized pps provides a flexible and effective way of obtaining principal surfaces

argument estimates of certain meromorphically multivalent functions associated with generalized hypergeometric function the object of this paper is to obtain some argument properties of meromorphically multivalent functions associated with generalized hypergeometric function we also derive the integral preserving properties in a sector

on certain subclasses of meromorphically multivalent convex functions abstract making use of certain differential operators defined by hadamard product the author studies among other things the subclasses j n p 0 p p n 1 2 of meromorphically multivalent convex functions in the open unit disk u where n is any integer greater than p the author shows in particular that j n 1 p j n p and considers the integrals of functions in j n p

transfer current and pattern fields in spanning trees when a simply connected domain d subset mathbb r d d ge 2 is approximated in a good way by embedded connected weighted graphs we prove that the transfer current matrix defined on the edges of the graph viewed as an electrical network converges up to a local weight factor to the differential of green s function on d this observation implies that properly rescaled correlations of the spanning tree model and correlations of minimal subconfigurations in the abelian sandpile model have a universal and conformally covariant limit we further show that on a periodic approximation of the domain all pattern fields of the spanning tree model as well as the minimal pattern e g zero height fields of the sandpile converge weakly in distribution to gaussian white noise

graph sparsification by effective resistances we present a nearly linear time algorithm that produces high quality spectral sparsifiers of weighted graphs given as input a weighted graph g v e w and a parameter epsilon 0 we produce a weighted subgraph h v tilde e tilde w of g such that tilde e o n log n epsilon 2 and all x in mathbb r v satisfy 1 epsilon sum uv in e x u x v 2w uv leq sum uv in tilde e x u x v 2 tilde w uv leq 1 epsilon sum uv in e x u x v 2w uv this improves upon the spectral sparsifiers constructed by spielman and teng which had o n log c n edges for some large constant c and upon the cut sparsifiers of benczur and karger which only satisfied these inequalities for x in 0 1 v a key ingredient in our algorithm is a subroutine of independent interest a nearly linear time algorithm that builds a data structure from which we can query the approximate effective resistance between any two vertices in a graph in o log n time

on certain subclass of meromorphic close to convex functions in the present paper we introduce and investigate a certain new subclass mk s l a b of meromorphic close to convex functions such results as inclusion relationships coefficient inequalities and convolution property are derived relevant connections of the results presented here with those obtained in earlier works are also pointed out

a class of meromorphically multivalent functions defined by means of a linear operator abstract let p denote the class of functions of the form f z z p n 1 a n z n p n n 1 2 3 which are analytic in the punctured open unit disk u 0 z 0 z 1 making use of a linear operator which is defined here by means of the hadamard product or convolution we introduce a new subclass m p a c h of p and investigate some properties for the class m p a c h

kernel class wise locality preserving projection in the recent years the pattern recognition community paid more attention to a new kind of feature extraction method the manifold learning methods which attempt to project the original data into a lower dimensional feature space by preserving the local neighborhood structure among them locality preserving projection lpp is one of the most promising feature extraction techniques however when lpp is applied to the classification tasks it shows some limitations such as the ignorance of the label information in this paper we propose a novel local structure based feature extraction method called class wise locality preserving projection clpp clpp utilizes class information to guide the procedure of feature extraction in clpp the local structure of the original data is constructed according to a certain kind of similarity between data points which takes special consideration of both the local information and the class information the kernelized nonlinear counterpart of this linear feature extractor is also established in the paper moreover a kernel version of clpp namely kernel clpp kclpp is developed through applying the kernel trick to clpp to increase its performance on nonlinear feature extraction experiments on orl face database and yale face database are performed to test and evaluate the proposed algorithm

some subclasses of meromorphically multivalent functions associated with the generalized hypergeometric function in the present paper we introduce and investigate each of the following new subclasses f p k q s a a 1 f g p q s a a 1 f andh p q s a a 1 f as well as f p k q s a a 1 f g p q s a a 1 f andh p q s a a 1 f of meromorphically p valent functions which is defined by means of a certain meromorphically p modified version of the familiar dziok srivastava linear operator involving the generalized hypergeometric function such results as inclusion relationships integral representations and convolution properties for these function classes are proved the results presented here provide extensions of those given in some earlier works several other new results are also obtained

perfect reconstruction two channel wavelet filter banks for graph structured data in this work we propose the construction of two channel wavelet filter banks for analyzing functions defined on the vertices of any arbitrary finite weighted undirected graph these graph based functions are referred to as graph signals as we build a framework in which many concepts from the classical signal processing domain such as fourier decomposition signal filtering and downsampling can be extended to graph domain especially we observe a spectral folding phenomenon in bipartite graphs which occurs during downsampling of these graphs and produces aliasing in graph signals this property of bipartite graphs allows us to design critically sampled two channel filter banks and we propose quadrature mirror filters referred to as graph qmf for bipartite graph which cancel aliasing and lead to perfect reconstruction for arbitrary graphs we present a bipartite subgraph decomposition which produces an edge disjoint collection of bipartite subgraphs graph qmfs are then constructed on each bipartite subgraph leading to multi dimensional separable wavelet filter banks on graphs our proposed filter banks are critically sampled and we state necessary and sufficient conditions for orthogonality aliasing cancellation and perfect reconstruction the filter banks are realized by chebychev polynomial approximations

on certain classes of meromorphically multivalent functions associated with the generalized hypergeometric function making use of a linear operator which is defined here by means of the hadamard product or convolution involving the generalized hypergeometric function we introduce two novel subclasses w p q s a 1 a b l and w p q s a 1 a b l of meromorphically multivalent functions of order l email protected email protected

gabor feature based classification using the enhanced fisher linear discriminant model for face recognition this paper introduces a novel gabor fisher 1936 classifier gfc for face recognition the gfc method which is robust to changes in illumination and facial expression applies the enhanced fisher linear discriminant model efm to an augmented gabor feature vector derived from the gabor wavelet representation of face images the novelty of this paper comes from 1 the derivation of an augmented gabor feature vector whose dimensionality is further reduced using the efm by considering both data compression and recognition generalization performance 2 the development of a gabor fisher classifier for multi class problems and 3 extensive performance evaluation studies in particular we performed comparative studies of different similarity measures applied to various classifiers we also performed comparative experimental studies of various face recognition schemes including our novel gfc method the gabor wavelet method the eigenfaces method the fisherfaces method the efm method the combination of gabor and the eigenfaces method and the combination of gabor and the fisherfaces method the feasibility of the new gfc method has been successfully tested on face recognition using 600 feret frontal face images corresponding to 200 subjects which were acquired under variable illumination and facial expressions the novel gfc method achieves 100 accuracy on face recognition using only 62 features