label propagation and higher order constraint based segmentation of fluid associated regions in retinal sd oct images the segmentation of the fluid associated region in the retina plays an important role in the treatment of retinal diseases such as diabetic retinopathy dr and age related macular degeneration amd the existing methods for the detection of the fluid region generally suffer from the limitation of the segmentation accuracy and the expensive time costs to overcome these problems in this paper we propose an interactive segmentation method for the fluid associated region in three dimensional 3 d spectral domain optical coherence tomography sd oct retinal imaging in which only a few seeds in one sd oct slice are needed after which the algorithm finishes the segmentation automatically to improve the segmentation accuracy the higher order constraint is introduced into the conventional markov random field mrf framework to impose the superpixel consistency to maintain temporal coherence of the 3 d sd oct slices the labeling information is propagated slice by slice via a proposed motion estimation based algorithm the proposed higher order based energy function can be efficiently solved by the max flow algorithm on a specified graph with several auxiliary nodes experiments on 28 sd oct cubes demonstrate the competitiveness of the proposed method compared with the state of the art methods

cores of nonatomic linear production games cores of games of the form f where is a vector of nonatomic measures and fz max xa z x 0 or equivalently fz min are described in terms of and the data defining f along the way we give a general condition on a game which implies that each measure in its core is a linear combination of a fixed finite set of nonatomic measures

turing instability for a ratio dependent predator prey model with diffusion abstract ratio dependent predator prey models have been increasingly favored by field ecologists where predator prey interactions have to be taken into account the process of predation search in this paper we study the conditions of the existence and stability properties of the equilibrium solutions in a reaction diffusion model in which predator mortality is neither a constant nor an unbounded function but it is increasing with the predator abundance we show that analytically at a certain critical value a diffusion driven turing type instability occurs i e the stationary solution stays stable with respect to the kinetic system the system without diffusion we also show that the stationary solution becomes unstable with respect to the system with diffusion and that turing bifurcation takes place a spatially non homogenous non constant solution structure or pattern arises a numerical scheme that preserve the positivity of the numerical solutions and the boundedness of prey solution will be presented numerical examples are also included

robust nonnegative patch alignment for dimensionality reduction dimensionality reduction is an important method to analyze high dimensional data and has many applications in pattern recognition and computer vision in this paper we propose a robust nonnegative patch alignment for dimensionality reduction which includes a reconstruction error term and a whole alignment term we use correntropy induced metric to measure the reconstruction error in which the weight is learned adaptively for each entry for the whole alignment we propose locality preserving robust nonnegative patch alignment lp rna and sparsity preserviing robust nonnegative patch alignment sp rna which are unsupervised and supervised respectively in the lp rna we propose a locally sparse graph to encode the local geometric structure of the manifold embedded in high dimensional space in particular we select large p nearest neighbors for each sample then obtain the sparse representation with respect to these neighbors the sparse representation is used to build a graph which simultaneously enjoys locality sparseness and robustness in the sp rna we simultaneously use local geometric structure and discriminative information in which the sparse reconstruction coefficient is used to characterize the local geometric structure and weighted distance is used to measure the separability of different classes for the induced nonconvex objective function we formulate it into a weighted nonnegative matrix factorization based on half quadratic optimization we propose a multiplicative update rule to solve this function and show that the objective function converges to a local optimum several experimental results on synthetic and real data sets demonstrate that the learned representation is more discriminative and robust than most existing dimensionality reduction methods

ensemble manifold regularization we propose an automatic approximation of the intrinsic manifold for general semi supervised learning ssl problems unfortunately it is not trivial to define an optimization function to obtain optimal hyperparameters usually cross validation is applied but it does not necessarily scale up other problems derive from the suboptimality incurred by discrete grid search and the overfitting therefore we develop an ensemble manifold regularization emr framework to approximate the intrinsic manifold by combining several initial guesses algorithmically we designed emr carefully so it 1 learns both the composite manifold and the semi supervised learner jointly 2 is fully automatic for learning the intrinsic manifold hyperparameters implicitly 3 is conditionally optimal for intrinsic manifold approximation under a mild and reasonable assumption and 4 is scalable for a large number of candidate manifold hyperparameters from both time and space perspectives furthermore we prove the convergence property of emr to the deterministic matrix at rate root n extensive experiments over both synthetic and real data sets demonstrate the effectiveness of the proposed framework

low rank matrix approximation with manifold regularization this paper proposes a new model of low rank matrix factorization that incorporates manifold regularization to the matrix factorization superior to the graph regularized nonnegative matrix factorization this new regularization model has globally optimal and closed form solutions a direct algorithm for data with small number of points and an alternate iterative algorithm with inexact inner iteration for large scale data are proposed to solve the new model a convergence analysis establishes the global convergence of the iterative algorithm the efficiency and precision of the algorithm are demonstrated numerically through applications to six real world datasets on clustering and classification performance comparison with existing algorithms shows the effectiveness of the proposed method for low rank factorization in general

semantic preserving distance metric learning and applications how do we accurately browse a large set of images or efficiently annotate the images from an image library image clustering methods are invaluable tools for applications such as content based image retrieval and image annotation to perform these tasks it is critical to have proper features to describe the visual and semantic content of images and to define an accurate distance metric to measure the dissimilarity between any two images however existing methods which adopt the features of color histograms edge direction histograms and shape context lack the ability to describe semantic content to solve this problem we propose a new approach that utilizes user provided pairwise constraints to describe the semantic relationship between two images a semantic preserving distance metric learning sp dml algorithm is developed to explore the complementary characteristics of the visual features and pairwise constraints in a unified feature space in this space the learned distance metric can be used to measure the dissimilarity between two images specifically the manifold structure adopted in sp dml is revealed by the image s visual features to integrate semantic contents in distance metric learning sp dml utilizes pairwise constraints to build semantic patches and align these patches to obtain the optimal distance metric for the new feature space experimental results in image clustering demonstrate that the performance of sp dml is appealing

nenmf an optimal gradient method for nonnegative matrix factorization nonnegative matrix factorization nmf is a powerful matrix decomposition technique that approximates a nonnegative matrix by the product of two low rank nonnegative matrix factors it has been widely applied to signal processing computer vision and data mining traditional nmf solvers include the multiplicative update rule mur the projected gradient method pg the projected nonnegative least squares pnls and the active set method as however they suffer from one or some of the following three problems slow convergence rate numerical instability and nonconvergence in this paper we present a new efficient nenmf solver to simultaneously overcome the aforementioned problems it applies nesterov s optimal gradient method to alternatively optimize one factor with another fixed in particular at each iteration round the matrix factor is updated by using the pg method performed on a smartly chosen search point where the step size is determined by the lipschitz constant since nenmf does not use the time consuming line search and converges optimally at rate in optimizing each matrix factor it is superior to mur and pg in terms of efficiency as well as approximation accuracy compared to pnls and as that suffer from numerical instability problem in the worst case nenmf overcomes this deficiency in addition nenmf can be used to solve norm norm and manifold regularized nmf with the optimal convergence rate numerical experiments on both synthetic and real world datasets show the efficiency of nenmf for nmf and its variants comparing to representative nmf solvers extensive experiments on document clustering suggest the effectiveness of nenmf

on the core and dual set of linear programming games we study the relation between the core of a given lp game and the set of payoff vectors generated by optimal dual solutions to the corresponding linear program it is well known that the set of dual payoffs is contained in the core and that cores of games in which players are replicated converge to the set of dual payoffs when the number of replications tends to infinity we give a necessary and sufficient condition for finite convergence as corollaries we strengthen a sufficient condition due to owen and obtain new conditions as well we also study conditions in which the core and the set of dual payoffs coincide even without replication we give a necessary and sufficient condition for this phenomenon and present two classes of lp games with this property which properly subsumes all examples of this type discussed in the literature

secure steganographic communication algorithm based on self organizing patterns a secure steganographic communication algorithm based on patterns evolving in a beddington de angelis type predator prey model with self and cross diffusion is proposed in this paper small perturbations of initial states of the system around the state of equilibrium result in the evolution of self organizing patterns small differences between initial perturbations result in slight differences also in the evolving patterns it is shown that the generation of interpretable target patterns cannot be considered as a secure mean of communication because contours of the secret image can be retrieved from the cover image using statistical techniques if only it represents small perturbations of the initial states of the system an alternative approach when the cover image represents the self organizing pattern that has evolved from initial states perturbed using the dot skeleton representation of the secret image can be considered as a safe visual communication technique protecting both the secret image and communicating parties

low rank matrix factorization with multiple hypergraph regularizer this paper presents a novel low rank matrix factorization method named multihmmf which incorporates multiple hypergraph manifold regularization to the low rank matrix factorization in order to effectively exploit high order information among the data samples the hypergraph is introduced to model the local structure of the intrinsic manifold specifically multiple hypergraph regularization terms are separately constructed to consider the local invariance the optimal intrinsic manifold is constructed by linearly combining multiple hypergraph manifolds then the regularization term is incorporated into a truncated singular value decomposition framework resulting in a unified objective function so that matrix factorization is changed into an optimization problem alternating optimization is used to solve the optimization problem with the result that the low dimensional representation of data space is obtained the experimental results of image clustering demonstrate that the proposed method outperforms state of the art data representation methods we propose a novel low rank matrix factorization method we incorporate multiple hypergraph manifold regularization to the matrix factorization we adopt alternating optimization to solve the optimization problem

pairwise solutions and the core of transportation situations the main aim of this paper is to study the relationship between the so called pairwise solutions and the core of transportation situations or games with this objective in mind we show that every core element of a transportation situation is contained in a pairwise solution with a specific weight system therefore every core element is in fact a particular pairwise distribution furthermore given a core element we outline a procedure in three steps to obtain the corresponding pairwise distribution with weight system

multi label image categorization with sparse factor representation the goal of multilabel classification is to reveal the underlying label correlations to boost the accuracy of classification tasks most of the existing multilabel classifiers attempt to exhaustively explore dependency between correlated labels it increases the risk of involving unnecessary label dependencies which are detrimental to classification performance actually not all the label correlations are indispensable to multilabel model negligible or fragile label correlations cannot be generalized well to the testing data especially if there exists label correlation discrepancy between training and testing sets to minimize such negative effect in the multilabel model we propose to learn a sparse structure of label dependency the underlying philosophy is that as long as the multilabel dependency cannot be well explained the principle of parsimony should be applied to the modeling process of the label correlations the obtained sparse label dependency structure discards the outlying correlations between labels which makes the learned model more generalizable to future samples experiments on real world data sets show the competitive results compared with existing algorithms

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

semi supervised linear discriminant analysis for dimension reduction and classification when facing high dimensional data dimension reduction is necessary before classification among dimension reduction methods linear discriminant analysis lda is a popular one that has been widely used lda aims to maximize the ratio of the between class scatter and total data scatter in projected space and the label of each data is necessary however in real applications the labeled data are scarce and unlabeled data are in large quantity so lda is hard to be used under such case in this paper we propose a novel method named semi supervised linear discriminant analysis slda which can use limited number of labeled data and a quantity of the unlabeled ones for training so that lda can accommodate to the situation of a few labeled data available assuming that f represents the calculated class indicator matrix of the training data and y denotes the true label of the labeled data the objective function contains two parts one is the criterion of lda which is a function of projection w and a class indicator matrix f the other is the difference between the true data label and calculated label of these labeled data as far as we know there is no closed form solution to the objective function to solve such problem we develop an iterative algorithm which calculates the class indicator matrix and the projection alternatively the convergence of the proposed iterative algorithm is proved and confirmed by experiments the experimental results on eight datasets show that the performance of slda is superior to that of traditional lda and some state of the art semi supervised algorithms highlightsa semi supervised variant of lda named semi supervised lda is proposed our method can use limited number of labeled data and a quantity of the unlabeled ones for training we develop an iterative algorithm which calculates the class indicator matrix and the projection alternatively

non negative patch alignment framework in this paper we present a non negative patch alignment framework npaf to unify popular non negative matrix factorization nmf related dimension reduction algorithms it offers a new viewpoint to better understand the common property of different nmf algorithms although multiplicative update rule mur can solve npaf and is easy to implement it converges slowly thus we propose a fast gradient descent fgd to overcome the aforementioned problem fgd uses the newton method to search the optimal step size and thus converges faster than mur experiments on synthetic and real world datasets confirm the efficiency of fgd compared with mur for optimizing npaf based on npaf we develop non negative discriminative locality alignment ndla experiments on face image and handwritten datasets suggest the effectiveness of ndla in classification tasks and its robustness to image occlusions compared with representative nmf related dimension reduction algorithms

principal manifolds and nonlinear dimensionality reduction via tangent space alignment we present a new algorithm for manifold learning and nonlinear dimensionality reduction based on a set of unorganized data points sampled with noise from a parameterized manifold the local geometry of the manifold is learned by constructing an approximation for the tangent space at each data point and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold we also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases we illustrate our algorithm using curves and surfaces both in two dimensional three dimensional 2d 3d euclidean spaces and in higher dimensional euclidean spaces we also address several theoretical and algorithmic issues for further research and improvements

a novel technique for subpixel image classification based on support vector machine this paper presents a novel support vector machine classifier designed for subpixel image classification pixel spectral unmixing the proposed classifier generalizes the properties of svms to the identification and modeling of the abundances of classes in mixed pixels by using fuzzy logic this results in the definition of a fuzzy input fuzzy output support vector machine f2svm classifier that can 1 process fuzzy information given as input to the classification algorithm for modeling the subpixel information in the learning phase of the classifier and 2 provide a fuzzy modeling of the classification results allowing a relation many to one between classes and pixels the presented binary f2svm can address multicategory problems according to two strategies the fuzzy one against all foaa and the fuzzy one against one foao strategies these strategies generalize to the fuzzy case techniques based upon ensembles of binary classifiers used for addressing multicategory problems in crisp classification problems the effectiveness of the proposed f2svm classifier is tested on three problems related to image classification in presence of mixed pixels having different characteristics experimental results confirm the validity of the proposed subpixel classification 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

spatiotemporal saliency detection for video sequences based on random walk with restart a novel saliency detection algorithm for video sequences based on the random walk with restart rwr is proposed in this paper we adopt rwr to detect spatially and temporally salient regions more specifically we first find a temporal saliency distribution using the features of motion distinctiveness temporal consistency and abrupt change among them the motion distinctiveness is derived by comparing the motion profiles of image patches then we employ the temporal saliency distribution as a restarting distribution of the random walker in addition we design the transition probability matrix for the walker using the spatial features of intensity color and compactness finally we estimate the spatiotemporal saliency distribution by finding the steady state distribution of the walker the proposed algorithm detects foreground salient objects faithfully while suppressing cluttered backgrounds effectively by incorporating the spatial transition matrix and the temporal restarting distribution systematically experimental results on various video sequences demonstrate that the proposed algorithm outperforms conventional saliency detection algorithms qualitatively and quantitatively

multiple graph regularized nonnegative matrix factorization non negative matrix factorization nmf has been widely used as a data representation method based on components to overcome the disadvantage of nmf in failing to consider the manifold structure of a data set graph regularized nmf grnmf has been proposed by cai et al by constructing an affinity graph and searching for a matrix factorization that respects graph structure selecting a graph model and its corresponding parameters is critical for this strategy this process is usually carried out by cross validation or discrete grid search which are time consuming and prone to overfitting in this paper we propose a grnmf called multigrnmf in which the intrinsic manifold is approximated by a linear combination of several graphs with different models and parameters inspired by ensemble manifold regularization factorization metrics and linear combination coefficients of graphs are determined simultaneously within a unified object function they are alternately optimized in an iterative algorithm thus resulting in a novel data representation algorithm extensive experiments on a protein subcellular localization task and an alzheimer s disease diagnosis task demonstrate the effectiveness of the proposed algorithm

action recognition based on overcomplete independent components analysis existing works on action recognition rely on two separate stages 1 designing hand designed features or learning features from video data 2 classifying features using a classifier such as svm or adaboost motivated by two observations 1 independent component analysis ica is capable of encoding intrinsic features underlying video data and 2 videos of different actions can be easily distinguished by their intrinsic features we propose a simple but effective action recognition framework based on the recently proposed overcomplete ica model after a set of overcomplete ica basis functions are learned from the densely sampled 3d patches from training videos for each action a test video is classified as the class whose basis functions can reconstruct the sampled 3d patches from the test video with the smallest reconstruction error the experimental results on five benchmark datasets demonstrate that the proposed approach outperforms several state of the art works

low rank matrix factorization with adaptive graph regularizer in this paper we present a novel low rank matrix factorization algorithm with adaptive graph regularizer lmfagr we extend the recently proposed low rank matrix with manifold regularization mmf method with an adaptive regularizer different from mmf which constructs an affinity graph in advance lmfagr can simultaneously seek graph weight matrix and low dimensional representations of data that is graph construction and low rank matrix factorization are incorporated into a unified framework which results in an automatically updated graph rather than a predefined one the experimental results on some data sets demonstrate that the proposed algorithm outperforms the state of the art low rank matrix factorization methods

stability and hopf bifurcation in a delayed competition system abstract in this paper hopf bifurcation for two species lotka volterra competition systems with delay dependence is investigated by choosing the delay as a bifurcation parameter we prove that the system is stable over a range of the delay and beyond that it is unstable in the limit cycle form i e there are periodic solutions bifurcating out from the positive equilibrium our results show that a stable competition system can be destabilized by the introduction of a maturation delay parameter further an explicit algorithm for determining the direction of the hopf bifurcation and the stability of the bifurcating periodic solutions is derived by using the theory of normal forms and center manifolds and numerical simulations supporting the theoretical analysis are also given

exploiting discriminant information in nonnegative matrix factorization with application to frontal face verification in this paper two supervised methods for enhancing the classification accuracy of the nonnegative matrix factorization nmf algorithm are presented the idea is to extend the nmf algorithm in order to extract features that enforce not only the spatial locality but also the separability between classes in a discriminant manner the first method employs discriminant analysis in the features derived from nmf in this way a two phase discriminant feature extraction procedure is implemented namely nmf plus linear discriminant analysis lda the second method incorporates the discriminant constraints inside the nmf decomposition thus a decomposition of a face to its discriminant parts is obtained and new update rules for both the weights and the basis images are derived the introduced methods have been applied to the problem of frontal face verification using the well known xm2vts database both methods greatly enhance the performance of nmf for frontal face verification

shape analysis of elastic curves in euclidean spaces this paper introduces a square root velocity srv representation for analyzing shapes of curves in euclidean spaces under an elastic metric in this srv representation the elastic metric simplifies to the il2 metric the reparameterization group acts by isometries and the space of unit length curves becomes the unit sphere the shape space of closed curves is the quotient space of a submanifold of the unit sphere modulo rotation and reparameterization groups and we find geodesics in that space using a path straightening approach these geodesics and geodesic distances provide a framework for optimally matching deforming and comparing shapes these ideas are demonstrated using 1 shape analysis of cylindrical helices for studying protein structure 2 shape analysis of facial curves for recognizing faces 3 a wrapped probability distribution for capturing shapes of planar closed curves and 4 parallel transport of deformations for predicting shapes from novel poses

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

biologically inspired feature manifold for scene classification biologically inspired feature bif and its variations have been demonstrated to be effective and efficient for scene classification it is unreasonable to measure the dissimilarity between two bifs based on their euclidean distance this is because bifs are extrinsically very high dimensional and intrinsically low dimensional i e bifs are sampled from a low dimensional manifold and embedded in a high dimensional space therefore it is essential to find the intrinsic structure of a set of bifs obtain a suitable mapping to implement the dimensionality reduction and measure the dissimilarity between two bifs in the low dimensional space based on their euclidean distance in this paper we study the manifold constructed by a set of bifs utilized for scene classification form a new dimensionality reduction algorithm by preserving both the geometry of intra bifs and the discriminative information inter bifs termed discriminative and geometry preserving projections dgpp and construct a new framework for scene classification in this framework we represent an image based on a new bif which combines the intensity channel the color channel and the c1 unit of a color image then we project the high dimensional bif to a low dimensional space based on dgpp and finally we conduct the classification based on the multiclass support vector machine svm thorough empirical studies based on the usc scene dataset demonstrate that the proposed framework improves the classification rates around 100 relatively and the training speed 60 times for different sites in comparing with previous gist proposed by siagian and itti in 2007

fuzzy cooperative games arising from linear production programming problems with fuzzy parameters abstract in the present study we consider a production model in which multiple decision makers pool resources to produce finished goods such a production model which is assumed to be linear can be formulated as mathematical programming problems with fuzzy parameters from the viewpoint of experts imprecise or fuzzy understanding of the nature of parameters in a problem formulation process it is shown that a cooperative game with values of coalitions represented by fuzzy numbers arises from the linear production programming problem with fuzzy parameters and such a game is referred to as a fuzzy linear production programming game the values of coalitions of the game can be obtained by employing a parametric approach to solving the linear production programming problem with fuzzy parameters it is proven that the core of the game is not empty and an interval in the core is computed by using the ideas of sensitivity analysis and the duality theory of linear programming problems

cost allocation for a tree network with heterogeneous customers we analyze a cost allocation problem which could naturally arise from a situation wherein a tree networkt n 0 e serving heterogeneous customers has to be constructed the customers located atn require some service from a central supplier located at vertex 0 the customers have heterogeneous preferences for the level or quality of service received from the central supplier we formulate the above cost allocation problem as a cooperative game referred to as anextended tree game the extended tree game is a proper extension of megiddo s 1978 tree game wherein all the customers have identical preferences regarding the level of service received we prove that an extended tree game is convex and we show that its shapley value can be computed in p n time wherep is the number of distinct preference levels we further provide a complete facial description of the core polytope of an extended tree game and demonstrate that even when there are only two classes of customers the number of nonredundant core constraints could be exponential in n nevertheless we are able to construct an p n algorithm to check the core membership of an arbitrary cost allocation which can be used to construct an p n 3 combinatorial algorithm to compute the nucleolus of an extended tree game finally we show that the complements of the facet defining coalitions for the core are all connected in an auxiliary tree graph with node setn

an interactive fuzzy satisficing method for generalized multiobjective linear programming problems with fuzzy parameters abstract a new interactive fuzzy satisficing method for multiobjective linear programming problems with fuzzy parameters is proposed in general two types of fuzziness of human judgements should be incorporated in multiobjective programming problems one is the experts ambiguous understanding of the nature of the parameters in the problem formulation process and the other is the fuzzy goals of the decision maker for each of the objective functions in order to cope with both types of fuzziness multiobjective linear programming problems with fuzzy parameters which reflect the experts ambiguous understanding in the problem formulation are formulated and the concept of generalized multiobjective linear programming and m pareto optimality is introduced in our interactive fuzzy satisficing method the satisficing solution of the decision maker is derived efficiently from among m pareto optimal solutions on the basis of the proposed method an interactive computer program is written to implement man machine interactive procedures finally an illustrative numerical example for multiobjective linear programming problems with fuzzy parameters is demonstrated along with the corresponding computer outputs

multi manifold matrix decomposition for data co clustering we propose a novel multi manifold matrix decomposition for co clustering m3dc algorithm that considers the geometric structures of both the sample manifold and the feature manifold simultaneously specifically multiple candidate manifolds are constructed separately to take local invariance into account then we employ multi manifold learning to approximate the optimal intrinsic manifold which better reflects the local geometrical structure by linearly combining these candidate manifolds in m3dc the candidate manifolds are obtained using various manifold based dimensionality reduction methods these methods are based on different rationales and use different metrics for data distances experimental results on several real data sets demonstrate the effectiveness of our proposed m3dc highlightswe consider the geometric structures of both sample and feature manifolds to reduces the complexity we use two low dimensional intermediate matrices we employ multi manifold learning to approximate the intrinsic manifold the intrinsic manifold is constructed by linearly combining multiple manifolds the candidate manifolds are constructed using six dimensionality reduction methods

a generalized linear production model a unifying model we introduce a generalized linear production model whose attractive feature being that the resources held by any subset of producerss is not restricted to be the vector sum of the resources held by the members ofs we provide sufficient conditions for the non emptiness of the core of the associated generalized linear production game and show that if the core of the game is not empty then a solution in it can be produced from a dual optimal solution to the associated linear programming problem our generalized linear production model is a proper generalization of the linear production model introduced by owen and it can be used to analyze cooperative games which cannot be studied in the ordinary linear production model framework we use the generalized model to show that the cooperative game induced by a network optimization problem in which players are the nodes of the network has a non empty core we further employ our model to prove the non emptiness of the core of two other classes of cooperative games which were not previously studied in the literature and we also use our generalized model to provide an alternative proof for the non emptiness of the core of the class of minimum cost spanning tree games thus it appears that the generalized linear production model is a unifying model which can be used to explain the non emptiness of the core of cooperative games generated by various seemingly different optimization models

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

existence of spatial patterns in a predator prey model with self and cross diffusion in this work we investigate the spatiotemporal dynamics of reaction diffusion equations subject to cross diffusion in the frame of a two dimensional ratio dependent predator prey model the conditions for diffusion driven instability are obtained and the turing space in the parameters space is achieved moreover the criteria for local and global asymptotic stability of the unique positive homogeneous steady state without diffusion are discussed numerical simulations are carried out in order to validate the feasibility of the obtained analytical findings different types of spatial patterns through diffusion driven instability of the proposed model are portrayed and analysed lastly the paper finishes with an external discussion of biological relevance of the analysis regarding cross diffusion and pattern issues

matrixized learning machine with modified pairwise constraints matrix pattern oriented classifier design matcd has been demonstrated to be effective in terms of the classification performance since it utilizes two sided weight vectors to constrain the matrix based patterns however the existing matcd might not be able to acquire the prior distribution knowledge such as the relationship between two patterns inspired by the pairwise constraints pc method i e must links and cannot links between the patterns this paper introduces a new regularization term named rp with a modified pc method into matcd the new classifier design strategy is expected to not only learn the structural information of each pattern itself but also acquire the prior distribution knowledge about each constrained pair with both the discrimination metric from the traditional pc and the spatial distance measure from the heat kernel method in practice this paper selects one typical matrixized classifier named matmhks as the basic building block and introduces the term rp into it the newly proposed classifier is named mlmmpc and the subsequent experiments validate the effectiveness of it two major contributions of this paper can be concluded as 1 improving the existing matrix pattern oriented classifier design techniques and 2 modifying the traditional pc method by combining the discrimination metric and the distance measure together highlightsa novel matrix oriented classification algorithm named mlmmpc is proposed to improve the original matrix learning framework by a new regularization term r p to combine pairwise constraints and spatial measure together in r p implementability is demonstrated on both image and vector based datasets

totally balanced games and games of flow a class of characteristic function games arising from maximum flow problems is introduced and is shown to coincide with the class of totally balanced games the proof relies on the max flow min cut theorem of ford and fulkerson and on the observation that the class of totally balanced games is the span of the additive games with the minimum operation

unsupervised image categorization by hypergraph partition we present a framework for unsupervised image categorization in which images containing specific objects are taken as vertices in a hypergraph and the task of image clustering is formulated as the problem of hypergraph partition first a novel method is proposed to select the region of interest roi of each image and then hyperedges are constructed based on shape and appearance features extracted from the rois each vertex image and its k nearest neighbors based on shape or appearance descriptors form two kinds of hyperedges the weight of a hyperedge is computed as the sum of the pairwise affinities within the hyperedge through all of the hyperedges not only the local grouping relationships among the images are described but also the merits of the shape and appearance characteristics are integrated together to enhance the clustering performance finally a generalized spectral clustering technique is used to solve the hypergraph partition problem we compare the proposed method to several methods and its effectiveness is demonstrated by extensive experiments on three image databases

on some network flow games we analyze three subclasses of cooperative games arising from network optimization problems in which the resources such as arcs or nodes in the network are controlled by individuals who have conflicting objectives the first subclass of cooperative games is induced by network optimization problems over directed augmented trees we show that for this subclass of games the kernel coincides with the nucleolus and that the nucleolus can be characterized as the unique revenue allocation vector in which every pair of arc owners who are adjacent in the tree are located symmetrically with respect to their bargaining range we further give a linear characterization of the core of this subclass of games which is then used to provide a more explicit representation of the nucleolus and to construct a strongly polynomial algorithm for generating it the second subclass of cooperative games is induced by maximum flow problems in simple undirected networks we provide a useful parametric representation of the core of this subclass of games which is used to characterize the nucleolus and the intersection of the core and the kernel explicitly we show that the intersection of the core and the kernel consists of all revenue allocations in the core which assign equal payoffs to any pair of unseparated arc owners we further demonstrate that among the core vectors the nucleolus is the unique revenue allocation vector in which the smallest allocations are maximized in a lexicographical sense the third cooperative game that we study is the assignment game introduced by shapley and shubik 1972 this game is induced by the assignment problem which can be cast as a network optimization problem we investigate the relationship between the kernel and the core of the assignment game and provide a necessary and sufficient condition for the core to be contained in the kernel we further show that in general the intersection of the kernel and the core is not a convex set we also exhibit that under certain conditions the nucleolus has a simple characterization as the unique vector in the core in which the smallest revenue allocations are maximized in a lexicographical sense finally we consider the horse market example of bohm bawerk 1923 for which it is shown that the core is contained in the kernel and that the nucleolus is the midpoint of the core

manifold regularized discriminative nonnegative matrix factorization with fast gradient descent nonnegative matrix factorization nmf has become a popular data representation method and has been widely used in image processing and pattern recognition problems this is because the learned bases can be interpreted as a natural parts based representation of data and this interpretation is consistent with the psychological intuition of combining parts to form a whole for practical classification tasks however nmf ignores both the local geometry of data and the discriminative information of different classes in addition existing research results show that the learned basis is unnecessarily parts based because there is neither explicit nor implicit constraint to ensure the representation parts based in this paper we introduce the manifold regularization and the margin maximization to nmf and obtain the manifold regularized discriminative nmf md nmf to overcome the aforementioned problems the multiplicative update rule mur can be applied to optimizing md nmf but it converges slowly in this paper we propose a fast gradient descent fgd to optimize md nmf fgd contains a newton method that searches the optimal step length and thus fgd converges much faster than mur in addition fgd includes mur as a special case and can be applied to optimizing nmf and its variants for a problem with 165 samples in r1600 fgd converges in 28 s while mur requires 282 s we also apply fgd in a variant of md nmf and experimental results confirm its efficiency experimental results on several face image datasets suggest the effectiveness of md nmf

graph based semisupervised learning graph based learning provides a useful approach for modeling data in classification problems in this modeling scenario the relationship between labeled and unlabeled data impacts the construction and performance of classifiers and therefore a semisupervised learning framework is adopted we propose a graph classifier based on kernel smoothing a regularization framework is also introduced and it is shown that the proposed classifier optimizes certain loss functions its performance is assessed on several synthetic and real benchmark data sets with good results especially in settings where only a small fraction of the data are labeled

hypergraph modelling for geometric model fitting in this paper we propose a novel hypergraph based method called hf to fit and segment multi structural data the proposed hf formulates the geometric model fitting problem as a hypergraph partition problem based on a novel hypergraph model in the hypergraph model vertices represent data points and hyperedges denote model hypotheses the hypergraph with large and data determined degrees of hyperedges can express the complex relationships between model hypotheses and data points in addition we develop a robust hypergraph partition algorithm to detect sub hypergraphs for model fitting hf can effectively and efficiently estimate the number of and the parameters of model instances in multi structural data heavily corrupted with outliers simultaneously experimental results show the advantages of the proposed method over previous methods on both synthetic data and real images highlightswe propose a novel hypergraph based method to fit and segment multi structural data the proposed method includes a hypergraph model with large degrees of hyperedges the proposed method includes a robust hypergraph partition algorithm experimental results show that the proposed method is superior to some state of the art fitting methods

orthogonal optimal reverse prediction for semi supervised learning optimal reverse prediction orp has recently been proposed as a semi supervised framework to unify supervised and unsupervised training methods such as supervised least square principal component analysis pca k means clustering and normalized graph cut orp has an ability to deal with classification tasks in which the labeled data are insufficient but the performance of orp and its kernelized version is still not satisfactory for classification applications to further improve performance of orp motivated by recently proposed orthogonal k means clustering in this paper we propose an orthogonal optimal reverse prediction oorp together with its kernelized and laplacian regularized extensions with only limited additional computations our algorithms can greatly enhance the classification performance compared to the original orp extensive experiments on synthetic and benchmark data collections consistently prove the effectiveness and efficiency of our oorp in comparison with several competing approaches highlightswe imposed the column orthogonal constraints to the mapping operator and propose the orthogonal optimal reverse prediction algorithm which shows a better performance than the original algorithm we imposed the orthogonal constraints method to the kernelized optimal reverse prediction algorithm and proposed the kernelized orthogonal optimal reverse prediction an optimization algorithm is designed to solve the problem and the model s classification performance is encouraging we also extend the idea to the laplacian orthogonal optimal reverse prediction and get a better classification performance

spatio temporal dynamics near the steady state of a planktonic system abstract the study of spatio temporal behaviour of ecological systems is fundamentally important as it can provide deep understanding of species interaction and predict the effects of environmental changes in this paper we first propose a spatial model with prey taxis for planktonic systems in which we also consider the herb behaviour in prey and effect of the hyperbolic mortality rate applying the homogeneous neumann boundary condition to the model and using prey tactic sensitivity coefficient as bifurcation parameter we then detailedly analyse the stability and bifurcation of the steady state of the system firstly we carry out a study of the equilibrium bifurcation showing the occurrence of fold bifurcation hopf bifurcation and the bt bifurcation then by using an abstract bifurcation theory and taking prey tactic sensitivity coefficient as the bifurcation parameter we investigate the turing hopf bifurcation obtaining a branch of stable non constant solutions bifurcating from the positive equilibrium and our results show that prey taxis can yield the occurrence of spatio temporal patterns finally numerical simulations are carried out to illustrate our theoretical results showing the existence of a periodic solution when the prey tactic sensitivity coefficient is away from the critical value

robust bilinear factorization with missing and grossly corrupted observations recovering low rank and sparse matrices from incomplete or corrupted observations is an important problem in statistics machine learning computer vision as well as signal and image processing in theory this problem can be solved by the natural convex joint mixed relaxations i e l 1 norm and trace norm under certain conditions however all current provable algorithms suffer from superlinear per iteration cost which severely limits their applicability to large scale problems in this paper we propose a scalable provable and structured robust bilinear factorization rbf method to recover low rank and sparse matrices from missing and grossly corrupted data i e robust matrix completion rmc or incomplete and grossly corrupted measurements i e compressive principal component pursuit cpcp specifically we first present two small scale matrix trace norm regularized bilinear factorization models for rmc and cpcp problems in which repetitively calculating svd of a large scale matrix is replaced by updating two much smaller factor matrices then we apply the alternating direction method of multipliers admm to efficiently solve the rmc problems finally we provide the convergence analysis of our algorithm and extend it to address general cpcp problems experimental results verified both the efficiency and effectiveness of our method compared with the state of the art methods

semisupervised multiview distance metric learning for cartoon synthesis in image processing cartoon character classification retrieval and synthesis are critical so that cartoonists can effectively and efficiently make cartoons by reusing existing cartoon data to successfully achieve these tasks it is essential to extract visual features that comprehensively represent cartoon characters and to construct an accurate distance metric to precisely measure the dissimilarities between cartoon characters in this paper we introduce three visual features color histogram shape context and skeleton to characterize the color shape and action respectively of a cartoon character these three features are complementary to each other and each feature set is regarded as a single view however it is improper to concatenate these three features into a long vector because they have different physical properties and simply concatenating them into a high dimensional feature vector will suffer from the so called curse of dimensionality hence we propose a semisupervised multiview distance metric learning ssm dml ssm dml learns the multiview distance metrics from multiple feature sets and from the labels of unlabeled cartoon characters simultaneously under the umbrella of graph based semisupervised learning ssm dml discovers complementary characteristics of different feature sets through an alternating optimization based iterative algorithm therefore ssm dml can simultaneously accomplish cartoon character classification and dissimilarity measurement on the basis of ssm dml we develop a novel system that composes the modules of multiview cartoon character classification multiview graph based cartoon synthesis and multiview retrieval based cartoon synthesis experimental evaluations based on the three modules suggest the effectiveness of ssm dml in cartoon applications

on market prices in linear production games consider a game in which resources may be combined to produce products of known values for linear production processes the game may be characterized by a family of linear programs it is shown that appropriately defined market prices for the resources coincide with the set of optimal dual solutions to one of these linear programs this result generalizes and unifies the known cases in game theory in which the core of a game coincides with the set of dual optimal solutions to a corresponding master linear programming problem

fusing mathcal r r features and local features with context aware kernels for action recognition the performance of action recognition in video sequences depends significantly on the representation of actions and the similarity measurement between the representations in this paper we combine two kinds of features extracted from the spatio temporal interest points with context aware kernels for action recognition for the action representation local cuboid features extracted around interest points are very popular using a bag of visual words bovw model such representations however ignore potentially valuable information about the global spatio temporal distribution of interest points we propose a new global feature to capture the detailed geometrical distribution of interest points it is calculated by using the 3d mathcal r r transform which is defined as an extended 3d discrete radon transform followed by the application of a two directional two dimensional principal component analysis for the similarity measurement we model a video set as an optimized probabilistic hypergraph and propose a context aware kernel to measure high order relationships among videos the context aware kernel is more robust to the noise and outliers in the data than the traditional context free kernel which just considers the pairwise relationships between videos the hyperedges of the hypergraph are constructed based on a learnt mahalanobis distance metric any disturbing information from other classes is excluded from each hyperedge finally a multiple kernel learning algorithm is designed by integrating the l 2 l2 norm regularization into a linear svm classifier to fuse the mathcal r r feature and the bovw representation for action recognition experimental results on several datasets demonstrate the effectiveness of the proposed approach for action recognition

linear programming with multiple fuzzy goals abstract this paper describes the use of fuzzy set theory in goal programming gp problems in particular it is demonstrated how fuzzy or imprecise aspirations of the decision maker dm can be quantified through the use of piecewise linear and continuous functions models are then presented for the use of fuzzy goal programming with preemptive priorities with archimedean weights and with the maximization of the membership function corresponding to the minimum goal examples are also provided

nonnegative matrix factorization with earth mover s distance metric for image analysis nonnegative matrix factorization nmf approximates a given data matrix as a product of two low rank nonnegative matrices usually by minimizing the l2 or the kl distance between the data matrix and the matrix product this factorization was shown to be useful for several important computer vision applications we propose here two new nmf algorithms that minimize the earth mover s distance emd error between the data and the matrix product the algorithms emd nmf and bilateral emd nmf are iterative and based on linear programming methods we prove their convergence discuss their numerical difficulties and propose efficient approximations naturally the matrices obtained with emd nmf are different from those obtained with l2 nmf we discuss these differences in the context of two challenging computer vision tasks texture classification and face recognition perform actual nmf based image segmentation for the first time and demonstrate the advantages of the new methods with common benchmarks

constrained nonnegative matrix factorization for image representation nonnegative matrix factorization nmf is a popular technique for finding parts based linear representations of nonnegative data it has been successfully applied in a wide range of applications such as pattern recognition information retrieval and computer vision however nmf is essentially an unsupervised method and cannot make use of label information in this paper we propose a novel semi supervised matrix decomposition method called constrained nonnegative matrix factorization cnmf which incorporates the label information as additional constraints specifically we show how explicitly combining label information improves the discriminating power of the resulting matrix decomposition we explore the proposed cnmf method with two cost function formulations and provide the corresponding update solutions for the optimization problems empirical experiments demonstrate the effectiveness of our novel algorithm in comparison to the state of the art approaches through a set of evaluations based on real world applications

delay induced turing instability in reaction diffusion equations time delays have been commonly used in modeling biological systems and can significantly change the dynamics of these systems quite a few works have been focused on analyzing the effect of small delays on the pattern formation of biological systems in this paper we investigate the effect of any delay on the formation of turing patterns of reaction diffusion equations first for a delay system in a general form we propose a technique calculating the critical value of the time delay above which a turing instability occurs then we apply the technique to a predator prey model and study the pattern formation of the model due to the delay for the model in question we find that when the time delay is small it has a uniform steady state or irregular patterns which are not of turing type however in the presence of a large delay we find spiral patterns of turing type for such a model we also find that the critical delay is a decreasing function of the ratio of carrying capacity to half saturation of the prey density

using underapproximations for sparse nonnegative matrix factorization nonnegative matrix factorization consists in approximately factorizing a nonnegative data matrix by the product of two low rank nonnegative matrices it has been successfully applied as a data analysis technique in numerous domains e g text mining image processing microarray data analysis collaborative filtering etc we introduce a novel approach to solve nmf problems based on the use of an underapproximation technique and show its effectiveness to obtain sparse solutions this approach based on lagrangian relaxation allows the resolution of nmf problems in a recursive fashion we also prove that the underapproximation problem is np hard for any fixed factorization rank using a reduction of the maximum edge biclique problem in bipartite graphs we test two variants of our underapproximation approach on several standard image datasets and show that they provide sparse part based representations with low reconstruction error our results are comparable and sometimes superior to those obtained by two standard sparse nonnegative matrix factorization techniques

image clustering based on sparse patch alignment framework image clustering methods are efficient tools for applications such as content based image retrieval and image annotation recently graph based manifold learning methods have shown promising performance in extracting features for image clustering typical manifold learning methods adopt appropriate neighborhood size to construct the neighborhood graph which captures local geometry of data distribution because the density of data points distribution may be different in different regions of the manifold a fixed neighborhood size may be inappropriate in building the manifold in this paper we propose a novel algorithm named sparse patch alignment framework for the embedding of data lying in multiple manifolds specifically we assume that for each data point there exists a small neighborhood in which only the points that come from the same manifold lie approximately in a low dimensional affine subspace based on the patch alignment framework we propose an optimization strategy for constructing local patches which adopt sparse representation to select a few neighbors of each data point that span a low dimensional affine subspace passing near that point after that the whole alignment strategy is utilized to build the manifold experiments are conducted on four real world datasets and the results demonstrate the effectiveness of the proposed method

convergence of optimal solutions about approximation scheme for fuzzy programming with minimum risk criteria this paper presents a class of two stage fuzzy programming with minimum risk criteria in the sense of value at risk var since the proposed two stage fuzzy minimum risk problem fmrp often includes fuzzy variable coefficients defined through possibility distributions with infinite supports it is inherently an infinite dimensional optimization problem that can rarely be solved directly thus algorithm procedures for solving such an optimization problem must rely on soft computing and approximation schemes which result in a finite dimensional optimization problem in this paper we develop an approximation method to compute the objective function of the two stage fmrp and discuss the convergent results about the use of the approximation method in fmrp including the convergence of the objective value optimal value and the optimal solutions to apply the convergent results about the approximation method we consider a two stage fuzzy facility location allocation fla problem with var objective and solve the problem indirectly by solving its approximating problem since the approximating fuzzy fla problem is neither linear nor convex conventional optimization algorithms cannot be used to solve it in this paper we design a hybrid particle swarm optimization pso algorithm to solve the approximating fuzzy fla problem one numerical example with five facilities and ten customers is also presented to demonstrate the effectiveness of the designed algorithm

solutions based on fuzzy goals in fuzzy linear programming games abstract in this paper we deal with linear programming problems with fuzzy parameters from the viewpoint of experts imprecise or fuzzy understanding of the nature of parameters in a problem formulation process and consider fuzzy linear programming games arising from the linear programming problems constructing fuzzy goals of coalitions with respect to payoff in order to suitably reflect fuzzy environments in which the linear programming games are formulated we define solutions maximizing minimal fuzzy goal and solutions maximizing the sum of fuzzy goals and develop computational methods for obtaining the solutions finally we give a numerical example to illustrate construction of a fuzzy linear programming game and derivation of the solutions

a new iterative method for solving multiobjective linear programming problem in the paper we present a new iterative method for solving multiobjective linear programming problems with an arbitrary number of decision makers the method is based on the principles of game theory each step of the method yields a unique solution which respects the aspirations of decision makers within the frame of given possibilities each decision maker is assigned an objective indicator which shows the reality of his aspiration and which may be used to define the strategy for the next step the method can be easily extended to general nonlinear multiobjective programming problems but the numerical application would require further research on computational methods

on computational methods for solutions of multiobjective linear production programming games abstract in this paper we consider a production model in which multiple decision makers pool resources to produce finished goods such a production model which is assumed to be linear can be formulated as a multiobjective linear programming problem it is shown that a multi commodity game arises from the multiobjective linear production programming problem with multiple decision makers and such a game is referred to as a multiobjective linear production programming game the characteristic sets in the game can be obtained by finding the set of all the pareto extreme points of the multiobjective programming problem it is proven that the core of the game is not empty and points in the core are computed by using the duality theory of multiobjective linear programming problems moreover the least core and the nucleolus of the game are examined finally we consider a situation that decision makers first optimize their multiobjective linear production programming problem and then they examine allocation of profits and or costs computational methods are developed and illustrative numerical examples are given

multi criteria minimum cost spanning tree games abstract the minimum cost spanning tree game mcst game is a well known model within operations research games that has been widely studied in the literature in this paper we introduce the multi criteria version of the mcst game as a set valued tu game we prove that the extension of bird s cost allocation rule provides dominance core elements in this game we also give a family of core solutions that are different from the previous one these solutions are based on proportional allocations obtained using scalar solutions of the multi criteria spanning tree problem besides we prove necessary and sufficient conditions ensuring that the preference core of this game is not empty

on the core of network synthesis games we use polynomial formulations to show that several rational and discrete network synthesis games including the minimum cost spanning tree game satisfy the assumptions of owen s linear production game model we also discuss computational issues related to finding and recognizing core points for these classes of games

3 2 type criteria for global attractivity of lotka volterra competition system without instantaneous negative feedbacks this paper deals with a two species lotka volterra competition model with discrete delays but without instantaneous negative feedbacks motivated by wright s 3 2 global attractivity result for the delayed scalar logistic equation we establish some new 3 type criteria for global attractivity of the positive equilibrium of the system these criteria provide convenient and better than some existing estimates for the diagonal delays

dynamic linear programming games with risk averse players motivated by situations in which independent agents wish to cooperate in some uncertain endeavor over time we study dynamic linear programming games which generalize classical linear production games to multi period settings under uncertainty we specifically consider that players may have risk averse attitudes towards uncertainty and model this risk aversion using coherent conditional risk measures for this setting we study the strong sequential core a natural extension of the core to dynamic settings we characterize the strong sequential core as the set of allocations that satisfy a particular finite set of inequalities that depend on an auxiliary optimization model and then leverage this characterization to establish sufficient conditions for emptiness and non emptiness qualitatively whereas the strong sequential core is always non empty when players are risk neutral our results indicate that cooperation in the presence of risk aversion is much more difficult we illustrate this with an application to cooperative newsvendor games where we find that cooperation is possible when it least benefits players and may be impossible when it offers more benefit

efficient algorithms for game theoretic betweenness centrality betweenness centrality measures the ability of different nodes to control the flow of information in a network in this article we extend the standard definition of betweenness centrality using semivalues a family of solution concepts from cooperative game theory that includes among others the shapley value and the banzhaf power index any semivalue based betweenness centrality measure such as for example the shapley value based betweenness centrality measure has the advantage of evaluating the importance of individual nodes by considering the roles they each play in different groups of nodes our key result is the development of a general polynomial time algorithm to compute the semivalue based betweenness centrality measure and an even faster algorithm to compute the shapley value based betweenness centrality measure both for weighted and unweighted networks interestingly for the unweighted case our algorithm for computing the shapley value based centrality has the same complexity as the best known algorithm for computing the standard betweenness centrality due to brandes 15 we empirically evaluate our measures in a simulated scenario where nodes fail simultaneously we show that compared to the standard measure the ranking obtained by our measures reflects more accurately the influence that different nodes have on the functionality of the network we propose a betweenness centrality based on the shapley value and semivalue we develop polynomial algorithms for our game theoretic metrics we evaluate our measures in scenarios where simultaneous node failures occur our measures obtain better results than standard betweenness centrality we provide an empirical evaluation of algorithms on real life and random graphs

fuzzy goal programming complementary slackness conditions and computational schemes abstract goal programming gp is an important category in linear programming and multiobjective versions which minimize the deviation among value of each objective function and its goal with satisfying other constraints of problem in this paper we deal with fuzzy goal programming fgp which is a generalized problem in vague nature where parameters relations and goals are given as fuzzy quantities with respect to imprecise data recently inuiguchi et al m inuiguchi j ramik t tanio m vlach satisficing solutions and duality in interval and fuzzy linear programming fuzzy sets and systems 135 2003 151 177 have proved some important dual theorems on fgp which are very close to the same crisp versions in continuation to their works based on fuzzy extensions of relations we get complementary slackness conditions for fgp which have an essential role in many optimization techniques moreover we obtain the most optimistic and pessimistic satisficing solutions employing these conditions and present a convex combination of them which covers the satisficing solutions for a fixed level of certainty our practical schemes implement an efficient interior point algorithm as sub procedure so they are polynomial time algorithms

manifold regularization a geometric framework for learning from labeled and unlabeled examples we propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution we focus on a semi supervised framework that incorporates labeled and unlabeled data in a general purpose learner some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases we use properties of reproducing kernel hilbert spaces to prove new representer theorems that provide theoretical basis for the algorithms as a result in contrast to purely graph based approaches we obtain a natural out of sample extension to novel examples and so are able to handle both transductive and truly semi supervised settings we present experimental evidence suggesting that our semi supervised algorithms are able to use unlabeled data effectively finally we have a brief discussion of unsupervised and fully supervised learning within our general framework

on the concavity of delivery games abstract delivery games introduced by hamers borm van de leensel and tijs in 1994 are combinatorial optimization games that arise from delivery problems closely related to the chinese postman problem cpp they showed that delivery games are not necessarily balanced for delivery problems corresponding to the class of bridge connected euler graphs they showed that the related games are balanced this paper focuses on the concavity property for delivery games a delivery game arising from a delivery model corresponding to a bridge connected euler graph need not be concave the main result will be that for delivery problems corresponding to the class of bridge connected cyclic graphs which is a subclass of the class of bridge connected euler graphs the related delivery games are concave further we discuss some extreme points of the core and the value for this class of concave delivery games

totally balanced combinatorial optimization games combinatorial optimization games deal with cooperative games for which the value of every subset of players is obtained by solving a combinatorial optimization problem on the resources collectively owned by this subset a solution of the game is in the core if no subset of players is able to gain advantage by breaking away from this collective decision of all players the game is totally balanced if and only if the core is non empty for every induced subgame of it we study the total balancedness of several combinatorial optimization games in this paper for a class of the partition game 5 we have a complete characterization for the total balancedness for the packing and covering games 3 we completely clarify the relationship between the related primal dual linear programs for the corresponding games to be totally balanced our work opens up the question of fully characterizing the combinatorial structures of totally balanced packing and covering games for which we present some interesting examples the totally balanced matching vertex cover and minimum coloring games

an application of the aumann shapley prices for cost allocation in transportation problems the aumann shapley a s prices are axiomatically determined on certain classes of piecewise continuously differentiable cost functions one of these classes consists of all cost functions derived from the transportation problems and some of their generalizations these prices are used here to allocate costs among destinations in a way that each destination will pay its real part in the total transportation costs an economic transportation model is presented in which the a s prices are compatible with consumer demands finally an algorithm is provided to calculate both the optimal solution and the associated a s prices for transportation problems

generalized network problems yielding totally balanced games a class of multiperson mathematical optimization problems is considered and is shown to generate cooperative games with nonempty cores the class includes but is not restricted to numerous versions of network flow problems it was shown by owen that for games generated by linear programming optimization problems optimal dual solutions correspond to points in the core we identify a special class of network flow problems for which the converse is true i e every point in the core corresponds to an optimal dual solution

multiple graph regularized graph transduction via greedy gradient max cut abstract graph transduction methods have been widely adopted for label prediction under semi supervised settings to alleviate the relevant sensitivity to initial labels and graph construction processes recent studies have been aiming at developing robust graph transduction techniques in particular the graph transduction method via greedy gradient max cut ggmc that minimizes a cost function over a continuous classification function and a binary label variable has been successfully applied to a wide range of applications however this method predominately relies on the choice of a high quality single graph representation often leading to unstable performance due to selection bias to tackle this major drawback we leverage an ensemble learning framework into the ggmc method for exploiting the advantage of constructing and combining multiple graphs as opposed to performing constrained max cut on a single graph the proposed multiple graph greedy gradient max cut method mg ggmc simultaneously solves the label prediction and the true graph estimation problems specifically the true graph is approximated by a linear combination of a set of constructed graphs the coefficients of the linear combination are learned automatically by alternately minimizing a unified objective function in an iterative manner comparison studies with representative methods across various real world benchmarks conspicuously demonstrate the efficaciousness and the superiority of the proposed algorithm in standard evaluation metrics

adaptive hypergraph learning and its application in image classification recent years have witnessed a surge of interest in graph based transductive image classification existing simple graph based transductive learning methods only model the pairwise relationship of images however and they are sensitive to the radius parameter used in similarity calculation hypergraph learning has been investigated to solve both difficulties it models the high order relationship of samples by using a hyperedge to link multiple samples nevertheless the existing hypergraph learning methods face two problems i e how to generate hyperedges and how to handle a large set of hyperedges this paper proposes an adaptive hypergraph learning method for transductive image classification in our method we generate hyperedges by linking images and their nearest neighbors by varying the size of the neighborhood we are able to generate a set of hyperedges for each image and its visual neighbors our method simultaneously learns the labels of unlabeled images and the weights of hyperedges in this way we can automatically modulate the effects of different hyperedges thorough empirical studies show the effectiveness of our approach when compared with representative baselines

on the core and f nucleolus of flow games using the ellipsoid method both deng et al deng x q fang x sun 2006 finding nucleolus of flow game proc 17th acm siam sympos discrete algorithms acm press new york 124 131 and potters et al potters j h reijnierse a biswas 2006 the nucleolus of balanced simple flow networks games econom behav 54 205 225 show that the nucleolus of simple flow games where all edge capacities are equal to one can be computed in polynomial time our main result is a combinatorial method based on eliminating redundant s t path constraints such that only a polynomial number of constraints remains this leads to efficient algorithms for computing the core nucleolus and nucleon of simple flow games deng et al also prove that computing the nucleolus for general flow games is np hard we generalize this by proving that computing the f nucleolus of flow games is np hard for all priority functions f that satisfy f a 0 for all coalitions a with worth v a 0 so including the priority functions corresponding to the nucleolus nucleon and per capita nucleolus

turing instability and pattern induced by cross diffusion in a predator prey system with allee effect to have spatial patterns form small allee effect admits relatively large range of predator mortality rate found cross diffusion is the key mechanism of spatial pattern formation obtained amplitude equations suggest both supercritical and subcritical bifurcation may occur weak allee effect admits supercritical bifurcation while strong one allows subcritical bifurcation in this paper we first propose a mathematical model for a spatial predator prey system with allee effect and then by using the proposed model we investigate the turing instability and the phenomena of pattern formation we show how cross diffusion destabilizes the spatially uniform steady state the method of multiple time scales is employed to derive the amplitude equations which is the cubic stuart landau equation in the supercritical case and the quintic in the subcritical case based on the amplitude equations we obtain the asymptotic solutions of the model close to the onset of instability

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

totally balanced games arising from controlled programming problems a cooperative game in characteristic function form is obtained by allowing a number of individuals to esercise partial control over the constraints of a generally nonlinear mathematical programming problem either directly or through committee voting conditions are imposed on the functions defining the programming problem and the control system which suffice to make the game totally balanced this assures a nonempty core and hence a stable allocation of the full value of the programming problem among the controlling palyers in the linear case the core is closely related to the solutions of the dual problem applications are made to a variety of economic models including the transferable utility trading economies of shapley and shubik and a multishipper one commodity transshipment model with convex cost functions and concave revenue functions dropping the assumption of transferable utility leads to a class of controlled multiobjective or pareto programming problems which again yield totally balanced games

stability of steady state solutions to a prey predator system with cross diffusion abstract this paper is concerned with a cross diffusion system arising in a prey predator population model the main purpose is to discuss the stability analysis for coexistence steady state solutions obtained by kuto and yamada j differential equations to appear we will give some criteria on the stability of these coexistence steady states furthermore we show that the hopf bifurcation phenomenon occurs on the steady state solution branch under some conditions

cross diffusion induced turing instability for a competition model with saturation effect abstract competitive behavior like predation widely exists in the world which has influences on the dynamics of ecosystems though a good knowledge for the patten formation and selection of predator prey models with diffusion is known in the literature little is known for that of a diffused competition model as a result a competition model with saturation effect and self and cross diffusion is proposed and analyzed in this paper firstly by making use of nullcline analysis we derive the condition of existence and stability of positive equilibrium and prove global stability then using the linear stability analysis the turing bifurcation critical value and the condition of the occurrence of turing pattern are obtained when control parameter is selected finally we deduce the amplitude equations around the turing bifurcation point by using the standard multiple scale analysis meanwhile a series of numerical simulations are given to expand our theoretical analysis this work shows that cross diffusion plays a key role in the formation of spatial patterns for competitive model with saturation effect

flow control using the theory of zero sum markov games considers the problem of dynamic flow control of arriving packets into an infinite buffer the service rate may depend on the state of the system may change in time and is unknown to the controller the goal of the controller is to design an efficient policy which guarantees the best performance under the worst service conditions the cost is composed of a holding cost a cost of rejecting customers packets and a cost that depends on the quality of the service the problem is studied in the framework of zero sum markov games and a value iteration algorithm is used to solve it it is shown that there exists an optimal stationary policy such that the decisions depend only on the actual number of customers in the queue it is of a threshold type and it uses randomization in at most one state