covariance regularization by thresholding this paper considers regularizing a covariance matrix of p variables estimated from n observations by hard thresholding we show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is sparse in a suitable sense the variables are gaussian or sub gaussian and log p n 0 and obtain explicit rates the results are uniform over families of covariance matrices which satisfy a fairly natural notion of sparsity we discuss an intuitive resampling scheme for threshold selection and prove a general cross validation result that justifies this approach we also compare thresholding to other covariance estimators in simulations and on an example from climate data 1 introduction estimation of covariance matrices is important in a number of areas of statistical analysis including dimension reduction by principal component analysis pca classification by linear or quadratic discriminant analysis lda and qda establishing independence and conditional independence relations in the context of graphical models and setting confidence intervals on linear functions of the means of the components in recent years many application areas where these tools are used have been dealing with very high dimensional datasets and sample sizes can be very small relative to dimension examples include genetic data brain imaging spectroscopic imaging climate data and many others it is well known by now that the empirical covariance matrix for samples of size n from a p variate gaussian distribution np p is not a good estimator of the population covariance if p is large many results in random matrix theory illustrate this from the classical mary law 29 to the more recent work of johnstone and his students on the theory of the largest eigenvalues 12 23 30 and associated eigenvectors 24 however with the exception of a method for estimating the covariance spectrum 11 these probabilistic results do not offer alternatives to the sample covariance matrix alternative estimators for large covariance matrices have therefore attracted a lot of attention recently two broad classes of covariance estimators have emerged those that rely on a natural ordering among variables and assume that variables

covariance matrix estimation for stationary time series we obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes a precise order of magnitude is derived for spectral radius of sample covariance matrices we also consider thresholded covariance matrix estimator that can better characterize sparsity if the true covariance matrix is sparse as our main tool we implement toeplitz 1911 s idea and relate eigenvalues of covariance matrices to the spectral densities or fourier transforms of the covariances we develop a large deviation result for quadratic forms of stationary processes using m dependence approximation under the framework of causal representation and physical dependence measures

a graduated assignment algorithm for graph matching a graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise by combining graduated nonconvexity two way assignment constraints and sparsity large improvements in accuracy and speed are achieved its low order computational complexity o lm where l and m are the number of links in the two graphs and robustness in the presence of noise offer advantages over traditional combinatorial approaches the algorithm not restricted to any special class of graph is applied to subgraph isomorphism weighted graph matching and attributed relational graph matching to illustrate the performance of the algorithm attributed relational graphs derived from objects are matched then results from twenty five thousand experiments conducted on 100 mode random graphs of varying types graphs with only zero one links weighted graphs and graphs with node attributes and multiple link types are reported no comparable results have been reported by any other graph matching algorithm before in the research literature twenty five hundred control experiments are conducted using a relaxation labeling algorithm and large improvements in accuracy are demonstrated

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

coordination complexity of parallel price directive decomposition the general block angular convex resource sharing problem in k blocks and m nonnegative block separable coupling constraints is considered applications of this model are in combinatorial optimization network flows scheduling communication networks engineering design and finance this paper studies the coordination complexity of approximate price directive decomposition pdd for this problem i e the number of iterations required to solve the problem to a fixed relative accuracy as a function of k and m first a simple pdd method based on the classical logarithmic potential is shown to be optimal up to a logarithmic factor in m in the class of all pdd methods that work with the original unrestricted blocks it is then shown that logarithmic and exponential potentials generate a polylogarithmically optimal algorithm for a wider class of pdd methods which can restrict the blocks by the coupling constraints as an application the fastest currently known deterministic approximation algorithm for minimum cost multicommodity flows is obtained

limit of the smallest eigenvalue of a large dimensional sample covariance matrix in this paper the authors show that the smallest if p leq n or the p n 1 th smallest if p n eigenvalue of a sample covariance matrix of the form 1 n xx tends almost surely to the limit 1 sqrt y 2 as n rightarrow infty and p n rightarrow y in 0 infty where x is a p times n matrix with iid entries with mean zero variance 1 and fourth moment finite also as a by product it is shown that the almost sure limit of the largest eigenvalue is 1 sqrt y 2 a known result obtained by yin bai and krishnaiah the present approach gives a unified treatment for both the extreme eigenvalues of large sample covariance matrices

fast and scalable approximate spectral graph matching for correspondence problems establishing consistent correspondences between two sets of features is a fundamental problem in computer vision this problem can be well formulated as graph matching in which nodes and edges represent feature points and pairwise relationships between feature points respectively spectral matching 19 is the state of the art eigenvector based method for graph matching the spectral matching algorithm has been used successfully for small data but its heavy memory requirement limited the maximum data sizes and contexts it can be used in this paper we propose fasm a fast and scalable approximate spectral matching algorithm the main ideas are twofold first we exploit the redundancy in the data generation process to approximate the affinity matrix with the linear combination of kronecker products between bases and index matrices the bases and index matrices are highly compressed representation of the approximated affinity matrix requiring much smaller memory than in previous works which store the whole affinity matrix second we compute the eigenvector of the approximated affinity matrix using the small bases and index matrices without explicitly materializing the approximated matrix experimental results show that our proposed method is up to 33x faster requiring up to 645x smaller memory than the exact algorithm with little or no loss of accuracy

nonlinear system theory another look at dependence based on the nonlinear system theory we introduce previously undescribed dependence measures for stationary causal processes our physical and predictive dependence measures quantify the degree of dependence of outputs on inputs in physical systems the proposed dependence measures provide a natural framework for a limit theory for stationary processes in particular under conditions with quite simple forms we present limit theorems for partial sums empirical processes and kernel density estimates the conditions are mild and easily verifiable because they are directly related to the data generating mechanisms

a tensor based algorithm for high order graph matching this paper addresses the problem of establishing correspondences between two sets of visual features using higher order constraints instead of the unary or pairwise ones used in classical methods concretely the corresponding hypergraph matching problem is formulated as the maximization of a multilinear objective function over all permutations of the features this function is defined by a tensor representing the affinity between feature tuples it is maximized using a generalization of spectral techniques where a relaxed problem is first solved by a multidimensional power method and the solution is then projected onto the closest assignment matrix the proposed approach has been implemented and it is compared to state of the art algorithms on both synthetic and real data

a novel local surface feature for 3d object recognition under clutter and occlusion this paper presents a highly distinctive local surface feature called the trisi feature for recognizing 3d objects in the presence of clutter and occlusion for a feature point we first construct a unique and repeatable local reference frame lrf using the implicit geometrical information of neighboring triangular faces we then generate three signatures from the three orthogonal coordinate axes of the lrf these signatures are concatenated and then compressed into a trisi feature finally we propose an effective 3d object recognition algorithm based on hierarchical feature matching we tested our trisi feature on two popular datasets rigorous experimental results show that the trisi feature was highly descriptive and outperformed existing algorithms under all levels of gaussian noise laplacian noise shot noise varying mesh resolutions occlusion and clutter moreover we tested our trisi based 3d object recognition algorithm on four standard datasets the experimental results show that our algorithm achieved the best overall recognition results on these datasets

a global solution to sparse correspondence problems we propose a new methodology for reliably solving the correspondence problem between sparse sets of points of two or more images this is a key step inmost problems of computer vision and so far no general method exists to solve it our methodology is able to handle most of the commonly used assumptions in a unique formulation independent of the domain of application and type of features it performs correspondence and outlier rejection in a single step and achieves global optimality with feasible computation feature selection and correspondence are first formulated as an integer optimization problem this is a blunt formulation which considers the whole combinatorial space of possible point selections and correspondences to find its global optimal solution we build a concave objective function and relax the search domain into its convex hull the special structure of this extended problem assures its equivalence to the original one but it can be optimally solved by efficient algorithms that avoid combinatorial search this methodology can use any criterion provided it can be translated into cost functions with continuous second derivatives

faster approximation algorithms for the unit capacity concurrent flow problem with applications to routing and finding sparse cuts this paper describes new algorithms for approximately solving the concurrent multicommodity flow problem with uniform capacities these algorithms are much faster than algorithms discovered previously besides being an important problem in its own right the uniform capacity concurrent flow problem has many interesting applications leighton and rao used uniform capacity concurrent flow to find an approximately sparsest cut in a graph and thereby approximately solve a wide variety of graph problems including minimum feedback arc set minimum cut linear arrangement and minimum area layout however their method appeared to be impractical as it required solving a large linear program this paper shows that their method might be practical by giving an o m 2 log m expected time randomized algorithm for their concurrent flow problem on an m edge graph raghavan and thompson used uniform capacity concurrent flow to solve approximately a channel width minimization problem in very large scale integration an o k 3 2 m n log n expected time randomized algorithm and an o k min n k m n log n log k deterministic algorithm is given for this problem when the channel width is omega log n where k denotes the number of wires to be routed in an n node m edge network

feature guided biased gaussian mixture model for image matching in this article we propose a feature guided biased gaussian mixture model fgbg for image matching we formulate the matching task as a maximum a posteriori map problem by seeing one point set as the centroid of a gaussian mixture model gmm and the other point set as the data a thin plate spline tps transformation between the two point sets is learnt so that the gmm can best fit the data our main contribution is to assign each gaussian mixture component a different weight this is where our model differs from the traditional self governed balanced gaussian mixture model sgbg whose gaussian mixture components have equal coefficients the new weight is defined as a value related to feature similarity which can be computed by simply decomposing a distance matrix in the feature space in this way both feature similarity and spatial arrangement are considered the feature descriptor is introduced as a reasonable prior to guide the matching and the spatial transformation offers a global constraint so that local ambiguity can be alleviated we solve this map problem in a framework similar to 16 in which deterministic annealing and the expectation maximization em algorithms are used we show that our fgbg algorithm is robust to outliers deformation and rotation extensive experiments on self collected and the latest open access data sets show that fgbg can boost the number of correct matches

fast approximation schemes for convex programs with many blocks and coupling constraints this paper presents block coordinate descent algorithms for the approximate solution of large structured convex programming problems the constraints of such problems consist of k disjoint convex compact sets b k called blocks and m nonnegative valued convex block separable inequalities called coupling or resource constraints the algorithms are based on an exponential potential function reduction technique it is shown that feasibility as well as min mix resource sharing problems for such constraints can be solved to a relative accuracy varepsilon in o k ln m varepsilon 2 ln k iterations each of which solves k block problems to a comparable accuracy either sequentially or in parallel the same bound holds for the expected number of iterations of a randomized variant of the algorithm which uniformly selects a random block to process at each iteration an extension to objective and constraint functions of arbitrary sign is also presented the above results yield fast approximatio

on the distribution of the largest eigenvalue in principal components analysis let x 1 denote the square of the largest singular value of an n p matrix x all of whose entries are independent standard gaussian variates equivalently x 1 is the largest principal component variance of the covariance matrix x x or the largest eigenvalue of a p variate wishart distribution on n degrees of freedom with identity covariance consider the limit of large p and n with n p gamma ge 1 when centered by mu p sqrt n 1 sqrt p 2 and scaled by sigma p sqrt n 1 sqrt p 1 sqrt n 1 1 sqrt p 1 3 the distribution of x 1 approaches the tracey widom law of order 1 which is defined in terms of the painleve ii differential equation and can be numerically evaluated and tabulated in software simulations show the approximation to be informative for n and p as small as 5 the limit is derived via a corresponding result for complex wishart matrices using methods from random matrix theory the result suggests that some aspects of large p multivariate distribution theory may be easier to apply in practice than their fixed p counterparts

progressive match expansion via coherent subspace constraint in this paper a quasi dense matching algorithm called progressive match expansion via coherent subspace pecs is proposed our algorithm starts from a set of sparse seeds and iteratively expands potential matches in the region around the seeds until no more matches could be found the main difference from previous methods is that our method computes a coherent non rigid transformation to relate the matching pixels instead of using local planar affine model to approximate the real scene surface within the expanding region the points in the expanding region are treated as a whole and all the matches satisfying the transformation are found at once first dense sift descriptors are extracted and a subspace encoding the feature similarity between two point sets is computed this embedding pulls two points closer if they have similar features and makes the non rigid transformation learning more robust second a coherent non rigid transformation in the subspace is computed to move one point set towards the other and the spatially aligned two points denote a match the proposed model is robust to scenes with non smooth surface and experiment results reveal the good performance in both 2d image matching and 3d reconstruction

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

the maximum concurrent flow problem the maximum concurrent flow problem mcfp is a multicommodity flow problem in which every pair of entities can send and receive flow concurrently the ratio of the flow supplied between a pair of entities to the predefined demand for that pair is called throughput and must be the same for all pairs of entities for a concurrent flow the mcfp objective is to maximize the throughput subject to the capacity constraints we develop a fully polynomial time approximation scheme for the mcfp for the case of arbitrary demands and uniform capacity computational results are presented it is shown that the problem of associating costs distances to the edges so as to maximize the minimum cost of routing the concurrent flow is the dual of the mcfp a path cut type duality theorem to expose the combinatorial structure of the mcfp is also derived our duality theorems are proved constructively for arbitrary demands and uniform capacity using the algorithm applications include packet switched networks 1 4 8 and cluster analysis 16

regularized estimation of large covariance matrices this paper considers estimating a covariance matrix of p variables from n observations by either banding the sample covariance matrix or estimating a banded version of the inverse of the covariance we show that these estimates are consistent in the operator norm as long as logp 2 n 0 and obtain explicit rates the results are uniform over some fairly natural well conditioned families of covariance matrices we also introduce an analogue of the gaussian white noise model and show that if the population covariance is embeddable in that model and well conditioned then the banded approximations produce consistent estimates of the eigenvalues and associated eigenvectors of the covariance matrix the results can be extended to smooth versions of banding and to non gaussian distributions with su ciently short tails a resampling approach is proposed for choosing the banding parameter in practice this approach is illustrated numerically on both simulated and real data

convex banding of the covariance matrix abstractwe introduce a new sparse estimator of the covariance matrix for high dimensional models in which the variables have a known ordering our estimator which is the solution to a convex optimization problem is equivalently expressed as an estimator that tapers the sample covariance matrix by a toeplitz sparsely banded data adaptive matrix as a result of this adaptivity the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators in particular our convex banding estimator is minimax rate adaptive in frobenius and operator norms up to log factors over commonly studied classes of covariance matrices and over more general classes furthermore it correctly recovers the bandwidth when the true covariance is exactly banded our convex formulation admits a simple and efficient algorithm empirical studies demonstrate its practical effectiveness and illustrate that our exactly banded estimator works well even when the true covariance

fast approximation algorithms for fractional packing and covering problems this paper presents fast algorithms that find approximate solutions for a general class of problems which we call fractional packing and covering problems the only previously known algorithms for solving these problems are based on general linear programming techniques the techniques developed in this paper greatly outperform the general methods in many applications and are extensions of a method previously applied to find approximate solutions to multicommodity flow problems our algorithm is a lagrangian relaxation technique an important aspect of our results is that we obtain a theoretical analysis of the running time of a lagrangian relaxation based algorithm we give several applications of our algorithms the new approach yields several orders of magnitude of improvement over the best previously known running times for algorithms for the scheduling of unrelated parallel machines in both the preemptive and the nonpreemptive models for the job shop problem for the held and karp bound for the tr

an exact rate of convergence in the functional central limit theorem for special martingale difference arrays since the topology of weak convergence of probability distributions on the borel field of the space c c 0 1 is metrizable it is natural to describe the speed of convergence in weak functional limit theorems by means of an appropriate metric using the metric proposed by prokhorov it is shown that under suitable conditions the rate of convergence in the functional central limit theorem for c valued partial sum processes based on martingale difference arrays is the same as in the special case of row wise independent random variables where this rate is known to be an optimal one

a three domain covariance framework for eeg meg data in this paper we introduce a covariance framework for the analysis of single subject eeg and meg data that takes into account observed temporal stationarity on small time scales and trial to trial variations we formulate a model for the covariance matrix which is a kronecker product of three components that correspond to space time and epochs trials and consider maximum likelihood estimation of the unknown parameter values an iterative algorithm that finds approximations of the maximum likelihood estimates is proposed our covariance model is applicable in a variety of cases where spontaneous eeg or meg acts as source of noise and realistic noise covariance estimates are needed such as in evoked activity studies or where the properties of spontaneous eeg or meg are themselves the topic of interest like in combined eeg fmri experiments in which the correlation between eeg and fmri signals is investigated we use a simulation study to assess the performance of the estimator and investigate the influence of different assumptions about the covariance factors on the estimated covariance matrix and on its components we apply our method to real eeg and meg data sets

operator norm consistent estimation of large dimensional sparse covariance matrices estimating covariance matrices is a problem of fundamental importance in multivariate statistics in practice it is increasingly frequent to work with data matrices x of dimension n x p where p and n are both large results from random matrix theory show very clearly that in this setting standard estimators like the sample covariance matrix perform in general very poorly in this large n large p setting it is sometimes the case that practitioners are willing to assume that many elements of the population covariance matrix are equal to 0 and hence this matrix is sparse we develop an estimator to handle this situation the estimator is shown to be consistent in operator norm when for instance we have p n as n oo in other words the largest singular value of the difference between the estimator and the population covariance matrix goes to zero this implies consistency of all the eigenvalues and consistency of eigenspaces associated to isolated eigenvalues we also propose a notion of sparsity for matrices that is compatible with spectral analysis and is independent of the ordering of the variables

asymptotic spectral theory for nonlinear time series we consider asymptotic problems in spectral analysis of stationary causal processes limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given instead of the commonly used strong mixing conditions in our asymptotic spectral theory we impose conditions only involving conditional moments which are easily verifiable for a variety of nonlinear time series

iterative point matching for registration of free form curves and surfaces a heuristic method has been developed for registering two sets of 3 d curves obtained by using an edge based stereo system or two dense 3 d maps obtained by using a correlation based stereo system geometric matching in general is a difficult unsolved problem in computer vision fortunately in many practical applications some a priori knowledge exists which considerably simplifies the problem in visual navigation for example the motion between successive positions is usually approximately known from this initial estimate our algorithm computes observer motion with very good precision which is required for environment modeling e g building a digital elevation map objects are represented by a set of 3 d points which are considered as the samples of a surface no constraint is imposed on the form of the objects the proposed algorithm is based on iteratively matching points in one set to the closest points in the other a statistical method based on the distance distribution is used to deal with outliers occlusion appearance and disappearance which allows us to do subset subset matching a least squares technique is used to estimate 3 d motion from the point correspondences which reduces the average distance between points in the two sets both synthetic and real data have been used to test the algorithm and the results show that it is efficient and robust and yields an accurate motion estimate

improving an interior point approach for large block angular problems by hybrid preconditioners abstract the computational time required by interior point methods is often dominated by the solution of linear systems of equations an efficient specialized interior point algorithm for primal block angular problems has been used to solve these systems by combining cholesky factorizations for the block constraints and a conjugate gradient based on a power series preconditioner for the linking constraints in some problems this power series preconditioner resulted to be inefficient on the last interior point iterations when the systems became ill conditioned in this work this approach is combined with a splitting preconditioner based on lu factorization which works well for the last interior point iterations computational results are provided for three classes of problems multicommodity flows oriented and nonoriented minimum distance controlled tabular adjustment for statistical data protection and the minimum congestion problem the results show that in most cases the hybrid preconditioner improves the performance and robustness of the interior point solver in particular for some block angular problems the solution time is reduced by a factor of 10

optimal rates of convergence for covariance matrix estimation covariance matrix plays a central role in multivariate statistical analysis significant advances have been made recently on developing both theory and methodology for estimating large covariance matrices however a minimax theory has yet been developed in this paper we establish the optimal rates of convergence for estimating the covariance matrix under both the operator norm and frobenius norm it is shown that optimal procedures under the two norms are different and consequently matrix estimation under the operator norm is fundamentally different from vector estimation the minimax upper bound is obtained by constructing a special class of tapering estimators and by studying their risk properties a key step in obtaining the optimal rate of convergence is the derivation of the minimax lower bound the technical analysis requires new ideas that are quite different from those used in the more conventional function sequence estimation problems

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

on the limit of the largest eigenvalue of the large dimensional sample covariance matrix in this paper the authors show that the largest eigenvalue of the sample covariance matrix tends to a limit under certain conditions when both the number of variables and the sample size tend to infinity the above result is proved under the mild restriction that the fourth moment of the elements of the sample sums of squares and cross products sp matrix exist

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

central limit theorem for fourier transforms of stationary processes we consider asymptotic behavior of fourier transforms of stationary ergodic sequences with finite second moments we establish a central limit theorem clt for almost all frequencies and also an annealed clt the theorems hold for all regular sequences our results shed new light on the foundation of spectral analysis and on the asymptotic distribution of periodogram and it provides a nice blend of harmonic analysis theory of stationary processes and theory of martingales

quadratic regularizations in an interior point method for primal block angular problems one of the most efficient interior point methods for some classes of primal block angular problems solves the normal equations by a combination of cholesky factorizations and preconditioned conjugate gradient for respectively the block and linking constraints its efficiency depends on the spectral radius in 0 1 of a certain matrix in the definition of the preconditioner spectral radius close to 1 degrade the performance of the approach the purpose of this work is twofold first to show that a separable quadratic regularization term in the objective reduces the spectral radius significantly improving the overall performance in some classes of instances second to consider a regularization term which decreases with the barrier function thus with no need for an extra parameter computational experience with some primal block angular problems confirms the efficiency of the regularized approach in particular for some difficult problems the solution time is reduced by a factor of two to ten by the regularization term outperforming state of the art commercial solvers

fast and scalable approximate spectral matching for higher order graph matching this paper presents a fast and efficient computational approach to higher order spectral graph matching exploiting the redundancy in a tensor representing the affinity between feature points we approximate the affinity tensor with the linear combination of kronecker products between bases and index tensors the bases and index tensors are highly compressed representations of the approximated affinity tensor requiring much smaller memory than in previous methods which store the full affinity tensor we compute the principal eigenvector of the approximated affinity tensor using the small bases and index tensors without explicitly storing the approximated tensor to compensate for the loss of matching accuracy by the approximation we also adopt and incorporate a marginalization scheme that maps a higher order tensor to matrix as well as a one to one mapping constraint into the eigenvector computation process the experimental results show that the proposed method is faster and requires smaller memory than the existing methods with little or no loss of accuracy

on maxima of periodograms of stationary processes we consider the limit distribution of maxima of periodograms for stationary processes our method is based on m dependent approximation for stationary processes and a moderate deviation result

asymptotic analysis of the flow deviation method for the maximum concurrent flow problem we analyze the asymptotic behavior of the flow deviation method first presented in 1971 by fratta gerla and kleinrock and show that when applied to packing linear programs such as the maximum concurrent flow problem it yields a fully polynomial time approximation scheme

segmentation of multiple salient closed contours from real images using a saliency measure based on the global property of contour closure we have developed a segmentation method which identifies smooth closed contours bounding objects of unknown shape in real images the saliency measure incorporates the gestalt principles of proximity and good continuity that previous methods have also exploited unlike previous methods we incorporate contour closure by finding the eigenvector with the largest positive real eigenvalue of a transition matrix for a markov process where edges from the image serve as states element i j of the transition matrix is the conditional probability that a contour which contains edge j will also contain edge i we show how the saliency measure defined for individual edges can be used to derive a saliency relation defined for pairs of edges and further show that strongly connected components of the graph representing the saliency relation correspond to smooth closed contours in the image finally we report for the first time results on large real images for which segmentation takes an average of about 10 seconds per object on a general purpose workstation

discrete particle swarm optimization for high order graph matching high order graph matching aims at establishing correspondences between two sets of feature points using high order constraints it is usually formulated as an np hard problem of maximizing an objective function this paper introduces a discrete particle swarm optimization algorithm for resolving high order graph matching problems which incorporates several re defined operations a problem specific initialization method based on heuristic information and a problem specific local search procedure the proposed algorithm is evaluated on both synthetic and real world datasets its outstanding performance is validated in comparison with three state of the art approaches