extended nearest neighbor chain induced instance weights for svms prior knowledge plays an important role in increasing the performance of support vector machine svm one way to utilize prior knowledge is to assign different weight to each sample which is called weighted support vector machine wsvm in this paper a novel instance weighted method is proposed for support vector machines the weight is determined by the distances between a sequence of the nearest heterogeneous samples named the extended nearest neighbor chain the samples near the decision plane also locate near the heterogeneous samples thus the samples near the decision plane can be found by the extended nearest neighbor chain before svms training and then assigned higher weights meanwhile the samples far away from the decision plane are assigned lower weights this is consistent with the fact that the samples near the decision plane are more important for svms moreover this strategy can also assign lower weights to the samples which locate in the wrong classes the results of the experiments performed on both artificial synthetic datasets and real world benchmark datasets demonstrate that the proposed instance weighted method can further improve the performance of svms a novel instance weighted strategy is proposed for svms the samples near decision plane are assigned higher weights via the proposed method the sample near decision plane can be found by a chain named extended nearest neighbor chain the proposed method makes svm become more robust for noises

subspace learning from image gradient orientations we introduce the notion of subspace learning from image gradient orientations for appearance based object recognition as image data are typically noisy and noise is substantially different from gaussian traditional subspace learning from pixel intensities very often fails to estimate reliably the low dimensional subspace of a given data population we show that replacing pixel intensities with gradient orientations and the l2 norm with a cosine based distance measure offers to some extend a remedy to this problem within this framework which we coin image gradient orientations igo subspace learning we first formulate and study the properties of principal component analysis of image gradient orientations igo pca we then show its connection to previously proposed robust pca techniques both theoretically and experimentally finally we derive a number of other popular subspace learning techniques namely linear discriminant analysis lda locally linear embedding lle and laplacian eigenmaps le experimental results show that our algorithms significantly outperform popular methods such as gabor features and local binary patterns and achieve state of the art performance for difficult problems such as illumination and occlusion robust face recognition in addition to this the proposed igo methods require the eigendecomposition of simple covariance matrices and are as computationally efficient as their corresponding l2 norm intensity based counterparts matlab code for the methods presented in this paper can be found at http ibug doc ic ac uk resources

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

higher rank support tensor machines for visual recognition this work addresses the two class classification problem within the tensor based large margin classification paradigm to this end we formulate the higher rank support tensor machines stms in which the parameters defining the separating hyperplane form a tensor tensorplane that is constrained to be the sum of rank one tensors subsequently we propose two extensions in which the separating tensorplanes take into consideration the spread of the training data along the different tensor modes more specifically we first propose the higher rank s s w stms that use the total or the within class covariance matrix in order to whiten the data and thus provide invariance to affine transformations second we propose the higher rank relative margin support tensor machines rmstms that bound from above the distance of the data samples from the separating tensorplane while maximizing the margin from it the corresponding optimization problem is solved in an iterative manner utilizing the candecomp parafac cp decomposition where at each iteration the parameters corresponding to the projections along a single tensor mode are estimated by solving a typical support vector machine svm type optimization problem the efficiency of the proposed method is illustrated on the problems of gait and action recognition where we report results that improve in some cases considerably the state of the art

constructing descriptive and discriminative nonlinear features rayleigh coefficients in kernel feature spaces we incorporate prior knowledge to construct nonlinear algorithms for invariant feature extraction and discrimination employing a unified framework in terms of a nonlinearized variant of the rayleigh coefficient we propose nonlinear generalizations of fisher s discriminant and oriented pca using support vector kernel functions extensive simulations show the utility of our approach

unsupervised learning of human action categories using spatial temporal words we present a novel unsupervised learning method for human action categories a video sequence is represented as a collection of spatial temporal words by extracting space time interest points the algorithm automatically learns the probability distributions of the spatial temporal words and the intermediate topics corresponding to human action categories this is achieved by using latent topic models such as the probabilistic latent semantic analysis plsa model and latent dirichlet allocation lda our approach can handle noisy feature points arisen from dynamic background and moving cameras due to the application of the probabilistic models given a novel video sequence the algorithm can categorize and localize the human action s contained in the video we test our algorithm on three challenging datasets the kth human motion dataset the weizmann human action dataset and a recent dataset of figure skating actions our results reflect the promise of such a simple approach in addition our algorithm can recognize and localize multiple actions in long and complex video sequences containing multiple motions

general tensor discriminant analysis and gabor features for gait recognition traditional image representations are not suited to conventional classification methods such as the linear discriminant analysis lda because of the undersample problem usp the dimensionality of the feature space is much higher than the number of training samples motivated by the successes of the two dimensional lda 2dlda for face recognition we develop a general tensor discriminant analysis gtda as a preprocessing step for lda the benefits of gtda compared with existing preprocessing methods such as the principal components analysis pca and 2dlda include the following 1 the usp is reduced in subsequent classification by for example lda 2 the discriminative information in the training tensors is preserved and 3 gtda provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of gtda converges whereas that of 2dlda does not we use human gait recognition to validate the proposed gtda the averaged gait images are utilized for gait representation given the popularity of gabor function based image decompositions for image understanding and object recognition we develop three different gabor function based image representations 1 gabord is the sum of gabor filter responses over directions 2 gabors is the sum of gabor filter responses over scales and 3 gaborsd is the sum of gabor filter responses over scales and directions the gabord gabors and gaborsd representations are applied to the problem of recognizing people from their averaged gait images a large number of experiments were carried out to evaluate the effectiveness recognition rate of gait recognition based on first obtaining a gabor gabord gabors or gaborsd image representation then using gdta to extract features and finally using lda for classification the proposed methods achieved good performance for gait recognition based on image sequences from the university of south florida usf humanid database experimental comparisons are made with nine state of the art classification methods in gait recognition

human action recognition using shape and clg motion flow from multi view image sequences in this paper we present a method for human action recognition from multi view image sequences that uses the combined motion and shape flow information with variability consideration a combined local global clg optic flow is used to extract motion flow feature and invariant moments with flow deviations are used to extract the global shape flow feature from the image sequences in our approach human action is represented as a set of multidimensional clg optic flow and shape flow feature vectors in the spatial temporal action boundary actions are modeled by using a set of multidimensional hmms for multiple views using the combined features which enforce robust view invariant operation we recognize different human actions in daily life successfully in the indoor and outdoor environment using the maximum likelihood estimation approach the results suggest robustness of the proposed method with respect to multiple views action recognition scale and phase variations and invariant analysis of silhouettes

actions as space time shapes human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion we regard human actions as three dimensional shapes induced by the silhouettes in the space time volume we adopt a recent approach 14 for analyzing 2d shapes and generalize it to deal with volumetric space time action shapes our method utilizes properties of the solution to the poisson equation to extract space time features such as local space time saliency action dynamics shape structure and orientation we show that these features are useful for action recognition detection and clustering the method is fast does not require video alignment and is applicable in but not limited to many scenarios where the background is known moreover we demonstrate the robustness of our method to partial occlusions nonrigid deformations significant changes in scale and viewpoint high irregularities in the performance of an action and low quality video

an observational theory for mobile ad hoc networks full version we propose a process calculus to study the behavioural theory of mobile ad hoc networks the operational semantics of our calculus is given both in terms of a reduction semantics and in terms of a labelled transition semantics we prove that the two semantics coincide the labelled transition system is then used to derive the notions of weak simulation and bisimulation for ad hoc networks the labelled bisimilarity completely characterises reduction barbed congruence a standard branching time and contextually defined program equivalence we then use our bi simulation proof method to formally prove a number of non trivial properties of ad hoc networks

local error estimates for supg solutions of advection dominated elliptic linear quadratic optimal control problems we derive local error estimates for the discretization of optimal control problems governed by linear advection diffusion partial differential equations pdes using the streamline upwind petrov galerkin supg stabilized finite element method we show that if the supg method is used to solve optimization problems governed by an advection dominated pde the convergence properties of the supg method is substantially different from the convergence properties of the supg method applied for the solution of an advection dominated pde the reason is that the solution of the optimal control problem involves another advection dominated pde the so called adjoint equation whose advection field is just the negative of the advection of the governing pdes for the solution of the optimal control problem a coupled system involving both the original governing pde as well as the adjoint pde must be solved we show that in the presence of a boundary layer the local error between the solution of the supg discretized optimal control problem and the solution of the infinite dimensional problem is only of first order even if the error is computed locally in a region away from the boundary layer in the presence of interior layers we prove optimal convergence rates for the local error in a region away from the layer between the solution of the supg discretized optimal control problems and the solution of the infinite dimensional problem numerical examples are presented to illustrate some of the theoretical results

a partial ordering semantics for ccs a new operational semantics for pure ccs is proposed that considers the parallel operator as a first class one and permits a description of the calculus in terms of partial orderings the new semantics also for unguarded agents is given in the sos style via the partial ordering derivation relation ccs agents are decomposed into sets of sequential subagents the new derivations relate sets of subagents and describe their actions and the casual dependencies among them the computations obtained by composing partial ordering derivations are observed either as interleaving or partial orderings of events interleavings coincide with milner s many step derivations and linearizations of partial orderings are all and only interleavings abstract semantics are obtained by introducing two relations of observational equivalence and congruence that preserve concurrency these relations are finer than milner s in that they distinguish interleaving of sequential nondeterministic agents from their concurrent execution

bisimulations for a calculus of broadcasting systems abstract we develop a theory of bisimulation equivalence for the broadcast calculus cbs both the strong and weak versions of bisimulation congruence we study are justified in terms of a characterisation as the largest cbs congruences contained in an appropriate version of barbed bisimulation we then present sound and complete proof systems for both the strong and weak congruences over finite terms the first system we give contains an infinitary proof rule to accommodate input prefixes we improve on this by presenting a unitary proof system where judgements are relative to properties of the data domain

a note on preconditioning for indefinite linear systems preconditioners are often conceived as approximate inverses for nonsingular indefinite matrices of saddle point or kkt form we show how preconditioners incorporating an exact schur complement lead to preconditioned matrices with exactly two or exactly three distinct eigenvalues thus approximations of the schur complement lead to preconditioners which can be very effective even though they are in no sense approximate inverses

behavioral theory for mobile ambients we study a behavioral theory of mobile ambients a process calculus for modelling mobile agents in wide area networks focussing on reduction barbed congruence our contribution is threefold 1 we prove a context lemma which shows that only parallel and nesting contexts need be examined to recover this congruence 2 we characterize this congruence using a labeled bisimilarity this requires novel techniques to deal with asynchronous movements of agents and with the invisibility of migrations of secret locations 3 we develop refined proof methods involving up to proof techniques which allow us to verify a set of algebraic laws and the correctness of more complex examples

adaptive finite element approximation for distributed elliptic optimal control problems in this paper sharp a posteriori error estimators are derived for a class of distributed elliptic optimal control problems these error estimators are shown to be useful in adaptive finite element approximation for the optimal control problems and are implemented in the adaptive approach our numerical results indicate that the sharp error estimators work satisfactorily in guiding the mesh adjustments and can save substantial computational work

spatiotemporal localization and categorization of human actions in unsegmented image sequences in this paper we address the problem of localization and recognition of human activities in unsegmented image sequences the main contribution of the proposed method is the use of an implicit representation of the spatiotemporal shape of the activity which relies on the spatiotemporal localization of characteristic ensembles of feature descriptors evidence for the spatiotemporal localization of the activity is accumulated in a probabilistic spatiotemporal voting scheme the local nature of the proposed voting framework allows us to deal with multiple activities taking place in the same scene as well as with activities in the presence of clutter and occlusion we use boosting in order to select characteristic ensembles per class this leads to a set of class specific codebooks where each codeword is an ensemble of features during training we store the spatial positions of the codeword ensembles with respect to a set of reference points as well as their temporal positions with respect to the start and end of the action instance during testing each activated codeword ensemble casts votes concerning the spatiotemporal position and extend of the action using the information that was stored during training mean shift mode estimation in the voting space provides the most probable hypotheses concerning the localization of the subjects at each frame as well as the extend of the activities depicted in the image sequences we present classification and localization results for a number of publicly available datasets and for a number of sequences where there is a significant amount of clutter and occlusion

reduced order optimal control of the convective fitzhugh nagumo equations abstract in this paper we compare three model order reduction methods the proper orthogonal decomposition pod discrete empirical interpolation method deim and dynamic mode decomposition dmd for the optimal control of the convective fitzhugh nagumo fhn equations the convective fhn equations consist of the semi linear activator and the linear inhibitor equations modeling blood coagulation in moving excitable media the semilinear activator equation leads to a non convex optimal control problem ocp the most commonly used method in reduced optimal control is pod we use deim and dmd to approximate efficiently the nonlinear terms in reduced order models we compare the accuracy and computational times of three reduced order optimal control solutions with the full order discontinuous galerkin finite element solution of the convection dominated fhn equations with terminal controls numerical results show that pod is the most accurate whereas pod dmd is the fastest

tensor decompositions and applications this survey provides an overview of higher order tensor decompositions their applications and available software a tensor is a multidimensional or n way array decompositions of higher order tensors i e n way arrays with n geq 3 have applications in psycho metrics chemometrics signal processing numerical linear algebra computer vision numerical analysis data mining neuroscience graph analysis and elsewhere two particular tensor decompositions can be considered to be higher order extensions of the matrix singular value decomposition candecomp parafac cp decomposes a tensor as a sum of rank one tensors and the tucker decomposition is a higher order form of principal component analysis there are many other tensor decompositions including indscal parafac2 candelinc dedicom and paratuck2 as well as nonnegative variants of all of the above the n way toolbox tensor toolbox and multilinear engine are examples of software packages for working with tensors

a one dimensional reaction diffusion system with a fast reaction abstract we consider a system of second order ordinary differential equations describing steady state for a three component chemical system with diffusion in the case when one of the reactions is fast we discuss the existence of solutions and the existence uniqueness and characterization of a limit as the rate of the fast reaction approaches infinity

fast iterative solution of reaction diffusion control problems arising from chemical processes pde constrained optimization problems and the development of preconditioned iterative methods for the efficient solution of the arising matrix systems is a field of numerical analysis that has recently been attracting much attention in this paper we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction diffusion equations which themselves result from chemical processes important aspects of our solvers are saddle point theory mass matrix representation and effective schur complement approximation as well as the incorporation of control constraints and application of the outer newton iteration to take into account the nonlinearity of the underlying pdes

human action recognition in videos using kinematic features and multiple instance learning we propose a set of kinematic features that are derived from the optical flow for human action recognition in videos the set of kinematic features includes divergence vorticity symmetric and antisymmetric flow fields second and third principal invariants of flow gradient and rate of strain tensor and third principal invariant of rate of rotation tensor each kinematic feature when computed from the optical flow of a sequence of images gives rise to a spatiotemporal pattern it is then assumed that the representative dynamics of the optical flow are captured by these spatiotemporal patterns in the form of dominant kinematic trends or kinematic modes these kinematic modes are computed by performing principal component analysis pca on the spatiotemporal volumes of the kinematic features for classification we propose the use of multiple instance learning mil in which each action video is represented by a bag of kinematic modes each video is then embedded into a kinematic mode based feature space and the coordinates of the video in that space are used for classification using the nearest neighbor algorithm the qualitative and quantitative results are reported on the benchmark data sets

analysis of stabilized higher order finite element approximation of nonstationary and nonlinear convection diffusion reaction equations abstract in this work the numerical approximation of unsteady and nonlinear convection diffusion reaction models with small diffusion by higher order finite element methods is studied streamline upwind petrov galerkin supg stabilization together with anisotropic shock capturing as an additional stabilization in crosswind direction are used error analyses and the parameter design given in the literature are generalized to the case of nonlinear reaction rates by numerical studies it is illustrated that the combination of these approximation techniques reduce spurious oscillations in crosswind direction and improve the accuracy of simulations

a discontinuous galerkin method for optimal control problems governed by a system of convection diffusion pdes with nonlinear reaction terms in this paper we study the numerical solution of optimal control problems governed by a system of convection diffusion pdes with nonlinear reaction terms arising from chemical processes the symmetric interior penalty galerkin sipg method with upwinding for the convection term is used as a discretization method we use a residual based error estimator for the state and the adjoint variables an adaptive mesh refinement indicated by a posteriori error estimates is applied the arising saddle point system is solved using a suitable preconditioner numerical results are presented to illustrate the performance of the proposed error estimator

an hdg method for distributed control of convection diffusion pdes abstract we propose a hybridizable discontinuous galerkin hdg method to approximate the solution of a distributed optimal control problem governed by an elliptic linear convection diffusion pde we use degree k polynomials to approximate the state adjoint state their fluxes and the optimal control and we show the approximations converge with order k 1 in the l 2 norm finally we use a simple element by element postprocessing scheme to obtain new superconvergent approximations of the state dual state and the control we show the postprocessed variables converge with order k 2 in the l 2 norm we present 2d and 3d numerical experiments to illustrate our theoretical results

on finite element methods for 3d time dependent convection diffusion reaction equations with small diffusion the paper studies finite element methods for the simulation of time dependent convection diffusion reaction equations with small diffusion the supg method a sold method and two types of fem fct methods the methods are assessed in particular with respect to the size of the spurious oscillations in the computed solutions at a 3d example with nonhomogeneous dirichlet boundary conditions and homogeneous neumann boundary conditions

petri nets event structures and domains part i abstract the general aim of this paper is to find a theory of concurrency combining the approaches of petri and scott and others in part i we introduce our formalisms to connect the abstract ideas of events and domains of information we show how casual nets induce certain kinds of domains where the information points are certain sets of events this allows translations between the languages of net theory and domain theory following the idea that events of causal nets are occurrences we generalise causal nets to occurrence nets by adding forwards conflict just as infinite flow charts unfold finite ones so transition nets can be unfolded into occurrence nets next we extend the above connections between nets and domains to these new nets event structures which are intermediate between nets and domains play an important part in all our work finally as an example of how concepts translate from one formalism to the other we show how petri s notion of confusion ties up with kahn and plotkin s concrete domains in part ii we shall continue the job of connecting up notions within net theory and the theory of domains in particular we shall examine the idea of states of computations

a posteriori error estimates for a discontinuous galerkin approximation of second order elliptic problems several a posteriori error estimators are introduced and analyzed for a discontinuous galerkin formulation of a model second order elliptic problem in addition to residual type estimators we introduce some estimators that are couched in the ideas and techniques of domain decomposition results of numerical experiments are presented

low rank tensor train coefficient array estimation for tensor on tensor regression the tensor on tensor regression can predict a tensor from a tensor which generalizes most previous multilinear regression approaches including methods to predict a scalar from a tensor and a tensor from a scalar however the coefficient array could be much higher dimensional due to both high order predictors and responses in this generalized way compared with the current low candecomp parafac cp rank approximation based method the low tensor train tt approximation can further improve the stability and efficiency of the high or even ultrahigh dimensional coefficient array estimation in the proposed low tt rank coefficient array estimation for tensor on tensor regression we adopt a tt rounding procedure to obtain adaptive ranks instead of selecting ranks by experience besides an ell 2 constraint is imposed to avoid overfitting the hierarchical alternating least square is used to solve the optimization problem numerical experiments on a synthetic data set and two real life data sets demonstrate that the proposed method outperforms the state of the art methods in terms of prediction accuracy with comparable computational complexity and the proposed method is more computationally efficient when the data are high dimensional with small size in each mode

non well founded sets modeled as ideal fixed points abstract motivated by ideas from the study of abstract data types we show how to interpret non well founded sets as fixed points of continuous transformations of an initial continuous algebra we conisder a preordered structure closely related to the set hf of well founded hereditarily finite sets by taking its ideal completion we obtain an initial continuous algebra in which we are able to solve all of the usual systems of equations that characterize hereditarily finite non well founded sets in this way we are able to obtain a structure which is isomorphic to hf 1 the non well founded analog of hf

discriminant nonnegative tensor factorization algorithms nonnegative matrix factorization nmf has proven to be very successful for image analysis especially for object representation and recognition nmf requires the object tensor with valence more than one to be vectorized this procedure may result in information loss since the local object structure is lost due to vectorization recently in order to remedy this disadvantage of nmf methods nonnegative tensor factorizations ntf algorithms that can be applied directly to the tensor representation of object collections have been introduced in this paper we propose a series of unsupervised and supervised ntf methods that is we extend several nmf methods using arbitrary valence tensors moreover by incorporating discriminant constraints inside the ntf decompositions we present a series of discriminant ntf methods the proposed approaches are tested for face verification and facial expression recognition where it is shown that they outperform other popular subspace approaches

maximum relative margin and data dependent regularization leading classification methods such as support vector machines svms and their counterparts achieve strong generalization performance by maximizing the margin of separation between data classes while the maximum margin approach has achieved promising performance this article identifies its sensitivity to affine transformations of the data and to directions with large data spread maximum margin solutions may be misled by the spread of data and preferentially separate classes along large spread directions this article corrects these weaknesses by measuring margin not in the absolute sense but rather only relative to the spread of data in any projection direction maximum relative margin corresponds to a data dependent regularization on the classification function while maximum absolute margin corresponds to an l2 norm constraint on the classification function interestingly the proposed improvements only require simple extensions to existing maximum margin formulations and preserve the computational efficiency of svms through the maximization of relative margin surprising performance gains are achieved on real world problems such as digit text classification and on several other benchmark data sets in addition risk bounds are derived for the new formulation based on rademacher averages

a primal dual active set strategy for optimal boundary control of a nonlinear reaction diffusion system this paper is concerned with optimal boundary control of an instationary reaction diffusion system in three spatial dimensions this problem involves a coupled nonlinear system of parabolic differential equations with bilateral as well as integral control constraints we include the integral constraint in the cost by a penalty term whereas the bilateral control constraints are handled explicitly first and second order conditions for the optimization problem are analyzed a primal dual active set strategy is utilized to compute optimal solutions numerically the algorithm is compared to a semismooth newton method

on meije and sccs infinite sum operators vs non guarded definitions une des principales differences actuellement entre meije et sccs se trouve dans les limites que le calcul precedent etablit a l interieur de sa syntaxe sur la creation de choix de comportement inifini a chaque point du processus

optimal control of convective fitzhughnagumo equation we investigate smooth and sparse optimal control problems for convective fitzhughnagumo equation with traveling wave solutions in moving excitable media the cost function includes distributed spacetime and terminal observations or targets the state and adjoint equations are discretized in space by symmetric interior point galerkin sipg method and by backward euler method in time several numerical results are presented for the control of the traveling waves we also show numerically the validity of the second order optimality conditions for the local solutions of the sparse optimal control problem for vanishing tikhonov regularization parameter further we estimate the distance between the discrete control and associated local optima numerically by the help of the perturbation method and the smallest eigenvalue of the reduced hessian

local error analysis of discontinuous galerkin methods for advection dominated elliptic linear quadratic optimal control problems this paper analyzes the local properties of the symmetric interior penalty upwind discontinuous galerkin sipg method for the numerical solution of optimal control problems governed by linear reaction advection diffusion equations with distributed controls the theoretical and numerical results presented in this paper show that for advection dominated problems the convergence properties of the sipg discretization can be superior to the convergence properties of stabilized finite element discretizations such as the streamline upwind petrov galerkin supg method for example we show that for a small diffusion parameter the sipg method is optimal in the interior of the domain this is in sharp contrast to supg discretizations for which it is known that the existence of boundary layers can pollute the numerical solution of optimal control problems everywhere even into domains where the solution is smooth and as a consequence in general reduces the convergence rates to only first order in order to prove

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

multilinear discriminant analysis for face recognition there is a growing interest in subspace learning techniques for face recognition however the excessive dimension of the data space often brings the algorithms into the curse of dimensionality dilemma in this paper we present a novel approach to solve the supervised dimensionality reduction problem by encoding an image object as a general tensor of second or even higher order first we propose a discriminant tensor criterion whereby multiple interrelated lower dimensional discriminative subspaces are derived for feature extraction then a novel approach called k mode optimization is presented to iteratively learn these subspaces by unfolding the tensor along different tensor directions we call this algorithm multilinear discriminant analysis mda which has the following characteristics 1 multiple interrelated subspaces can collaborate to discriminate different classes 2 for classification problems involving higher order tensors the mda algorithm can avoid the curse of dimensionality dilemma and alleviate the small sample size problem and 3 the computational cost in the learning stage is reduced to a large extent owing to the reduced data dimensions in k mode optimization we provide extensive experiments on orl cmu pie and feret databases by encoding face images as second or third order tensors to demonstrate that the proposed mda algorithm based on higher order tensors has the potential to outperform the traditional vector based subspace learning algorithms especially in the cases with small sample sizes

a convergent adaptive algorithm for poisson s equation we construct a converging adaptive algorithm for linear elements applied to poisson s equation in two space dimensions starting from a macro triangulation we describe how to construct an initial triangulation from a priori information then we use a posteriors error estimators to get a sequence of refined triangulation and approximate solutions it is proved that the error measured in the energy norm decreases at a constant rate in each step until a prescribed error bound is reached extension to higher order elements in two space dimension and numerical results are included

minimum class variance support vector machines in this paper a modified class of support vector machines svms inspired from the optimization of fisher s discriminant ratio is presented the so called minimum class variance svms mcvsvms the mcvsvms optimization problem is solved in cases in which the training set contains less samples that the dimensionality of the training vectors using dimensionality reduction through principal component analysis pca afterward the mcvsvms are extended in order to find nonlinear decision surfaces by solving the optimization problem in arbitrary hilbert spaces defined by mercer s kernels in that case it is shown that under kernel pca the nonlinear optimization problem is transformed into an equivalent linear mcvsvms problem the effectiveness of the proposed approach is demonstrated by comparing it with the standard svms and other classifiers like kernel fisher discriminant analysis in facial image characterization problems like gender determination eyeglass and neutral facial expression detection

calculi for synchrony and asynchrony abstract a calculus for distributed computation is studied based upon four combinators a central idea is an abelian group of actions which models the interfaces between components of a distributed computing agent using a notion of bisimulation congruence relations are defined over computing agents and thence an algebraic theory is derived the calculus models both synchronous and asynchronous computation in particular it is shown that the author s calculus of communicating systems 1980 which is an asynchronous model is derivable from the calculus presented here

a synchronous π calculus the sl synchronous programming model is a relaxation of the esterel synchronous model where the reaction to the absence of a signal within an instant can only happen at the next instant in previous work we have revisited the sl synchronous programming model in particular we have discussed an alternative design of the model introduced a cps translation to a tail recursive form and proposed a notion of bisimulation equivalence in the present work we extend the tail recursive model with first order data types obtaining a non deterministic synchronous model whose complexity is comparable to the one of the calculus we show that our approach to bisimulation equivalence can cope with this extension and in particular that labelled bisimulation can be characterised as a contextual bisimulation

a priori and a posteriori error analysis of edge stabilization galerkin method for the optimal control problem governed by convection dominated diffusion equation in this paper we study an edge stabilization galerkin approximation scheme for the constrained optimal control problem governed by convection dominated diffusion equation the method uses least square stabilization of the gradient jumps across element edges a priori and a posteriori error estimates are derived for both the state co state and the control the theoretical results are illustrated by two numerical experiments

canonical correlation analysis of video volume tensors for action categorization and detection this paper addresses a spatiotemporal pattern recognition problem the main purpose of this study is to find a right representation and matching of action video volumes for categorization a novel method is proposed to measure video to video volume similarity by extending canonical correlation analysis cca a principled tool to inspect linear relations between two sets of vectors to that of two multiway data arrays or tensors the proposed method analyzes video volumes as inputs avoiding the difficult problem of explicit motion estimation required in traditional methods and provides a way of spatiotemporal pattern matching that is robust to intraclass variations of actions the proposed matching is demonstrated for action classification by a simple nearest neighbor classifier we moreover propose an automatic action detection method which performs 3d window search over an input video with action exemplars the search is speeded up by dynamic learning of subspaces in the proposed cca experiments on a public action data set kth and a self recorded hand gesture data showed that the proposed method is significantly better than various state of the art methods with respect to accuracy our method has low time complexity and does not require any major tuning parameters

discontinuous hp finite element methods for advection diffusion reaction problems we consider the hp version of the discontinuous galerkin finite element method dgfem for second order partial differential equations with nonnegative characteristic form this class of equations includes second order elliptic and parabolic equations advection reaction equations as well as problems of mixed hyperbolic elliptic parabolic type our main concern is the error analysis of the method in the absence of streamline diffusion stabilization in the hyperbolic case an hp optimal error bound is derived here we consider only advection reaction problems which satisfy a certain standard positivity condition in the self adjoint elliptic case an error bound that is h optimal and p suboptimal by frac 1 2 a power of p is obtained these estimates are then combined to deduce an error bound in the general case for elementwise analytic solutions the method exhibits exponential rates of convergence under p refinement the theoretical results are illustrated by numerical experiments

robust a posteriori error estimates for stationary convection diffusion equations we analyze a posteriori error estimators for finite element discretizations of convection dominated stationary convection diffusion equations using locally refined isotropic meshes the estimators are based on either the evaluation of local residuals or the solution of discrete local problems with dirichlet or neumann boundary conditions all estimators yield global upper and lower bounds for the error measured in a norm that incorporates the standard energy norm and a dual norm of the convective derivative they are fully robust in the sense that the ratio of the upper and lower bounds is uniformly bounded with respect to the size of the convection the estimates are also uniform with respect to the size of the zero order reaction term and also hold for the limit case of vanishing reaction

mpca multilinear principal component analysis of tensor objects this paper introduces a multilinear principal component analysis mpca framework for tensor object feature extraction objects of interest in many computer vision and pattern recognition applications such as 2d 3d images and video sequences are naturally described as tensors or multilinear arrays the proposed framework performs feature extraction by determining a multilinear projection that captures most of the original tensorial input variation the solution is iterative in nature and it proceeds by decomposing the original problem to a series of multiple projection subproblems as part of this work methods for subspace dimensionality determination are proposed and analyzed it is shown that the mpca framework discussed in this work supplants existing heterogeneous solutions such as the classical principal component analysis pca and its 2d variant 2d pca finally a tensor object recognition system is proposed with the introduction of a discriminative tensor feature selection mechanism and a novel classification strategy and applied to the problem of gait recognition results presented here indicate mpca s utility as a feature extraction tool it is shown that even without a fully optimized design an mpca based gait recognition module achieves highly competitive performance and compares favorably to the state of the art gait recognizers