a bicriteria model for locating a semi desirable facility in the plane we consider the problem of locating a facility in the plane customers want the facility to be close to obtain cheaply the service offered by it but customers also want the facility to be far away to avoid the pollution from it we model the situation using two criteria one is the well known minisum criterion in the other we want to minimize the weighted sum of euclidean distances raised to a negative power the second criterion is analyzed in some detail and we state some properties of this part of the model in the bicriteria model we minimize the weighted sum of the two criteria with weights adding to one we outline a method for determining the efficient frontier of facility locations and provide an illustrative numerical example

improvement and comparison of heuristics for solving the uncapacitated multisource weber problem the multisource weber problem is to locate simultaneouslym facilities in the euclidean plane to minimize the total transportation cost for satisfying the demand ofn fixed users each supplied from its closest facility many heuristics have been proposed for this problem as well as a few exact algorithms heuristics are needed to solve quickly large problems and to provide good initial solutions for exact algorithms we compare various heuristics i e alternative location allocation cooper 1964 projection bongartz et al 1994 tabu search brimberg and mladenovic 1996a p median plus weber hansen et al 1996 genetic search and several versions of variable neighbourhood search based on empirical tests that are reported it is found that most traditional and some recent heuristics give poor results when the number of facilities to locate is large and that variable neighbourhood search gives consistently best results on average in moderate computing time

a linear programming approach for the weighted graph matching problem a linear programming lp approach is proposed for the weighted graph matching problem a linear program is obtained by formulating the graph matching problem in l sub 1 norm and then transforming the resulting quadratic optimization problem to a linear one the linear program is solved using a simplex based algorithm then approximate 0 1 integer solutions are obtained by applying the hungarian method on the real solutions of the linear program the complexity of the proposed algorithm is polynomial time and it is o n sup 6 l for matching graphs of size n the developed algorithm is compared to two other algorithms one is based on an eigendecomposition approach and the other on a symmetric polynomial transform experimental results showed that the lp approach is superior in matching graphs than both other methods

symmetry aware graph matching visual symmetry encodes middle to high level geometric information and plays an important role in many computer vision applications not much effort however has been devoted to utilize symmetry information for graph matching in this paper we propose a new framework for symmetry aware graph matching in the context of image matching in the framework we first define symmetry matrices to characterize the geometric symmetry relation among image features and then develop two methods to discover such symmetry after that we design general strategies to boost graph matching algorithms with symmetry constraints and apply these strategies to several state of the art algorithms for evaluation the proposed symmetry aware graph matching algorithms are first applied to two datasets involving clear symmetry patterns a recently proposed architecture image set and a dental panoramic radiograph collection the results clearly demonstrate the benefits of using symmetry information an experiment is also conducted on a dataset where symmetry is less obvious the results show that our strategies still achieve better of similar performance compared with state of the arts highlightsit is the first time symmetry constraints that are introduced into graph matching the symmetry aware graph matching improves the matching performance a new dataset with annotation for evaluating graph matching is constructed

point correspondence by a new third order graph matching algorithm the correspondence between point sets is a fundamental problem in pattern recognition which is often formulated and solved by graph matching in this paper we propose to solve the correspondence problem by a new third order graph matching algorithm compared with some previous hyper graph matching algorithms the proposed one achieves considerable memory reduction and is applicable to both undirected and directed graphs specifically the correspondence is formulated by the matching between adjacency tensors encoding the third order structural information of each graph which is then transformed to be a tractable matrix form two types of gradient based optimization methods the graduated nonconvexity and concavity procedure gnccp and graduated assignment ga algorithm are generalized to solve the problem comparative experiments with state of the art algorithms on both synthetic and real data witness the effectiveness of the proposed method highlightsan adjacency tensor based third order graph matching algorithm is proposed it enjoys a much lower storage complexity than affinity tensor based high order algorithms instead of spectral decomposition based optimization it adopts gradient based optimization experiments on synthetic and real world data witness its state of the art performance

efficient high order matching we present a computational approach to high order matching of data sets in rd those are matchings based on data affinity measures that score the matching of more than two pairs of points at a time high order affinities are represented by tensors and the matching is then given by a rank one approximation of the affinity tensor and a corresponding discretization our approach is rigorously justified by extending zass and shashua s hypergraph matching to high order spectral matching this paves the way for a computationally efficient dual marginalization spectral matching scheme we also show that based on the spectral properties of random matrices affinity tensors can be randomly sparsified while retaining the matching accuracy our contributions are experimentally validated by applying them to synthetic as well as real data sets

control of stochastic discrete event systems modeled by probabilistic languages in garg et al 1999 and garg 1992 the formalism of probabilistic languages for modeling the stochastic qualitative behavior of discrete event systems dess was introduced in this paper we study their supervisory control where the control is exercised by dynamically disabling certain controllable events thereby nulling the occurrence probabilities of disabled events and increasing the occurrence probabilities of enabled events proportionately this is a special case of probabilistic supervision introduced in lawford and wonham 1993 the control objective is to design a supervisor such that the controlled system never executes any illegal traces their occurrence probability is zero and legal traces occur with minimum prespecified occurrence probabilities in other words the probabilistic language of the controlled system lies within a prespecified range where the upper bound is a nonprobabilistic language representing a legality constraint we provide a condition for the existence of a supervisor we also present an algorithm to test this existence condition when the probabilistic languages are regular so that they admit probabilistic automata representation with finitely many states next we give a technique to compute a maximally permissive supervisor online

learning with jensen tsallis kernels jensen type jensen shannon js and jensen tsallis kernels were first proposed by martins et al 2009 these kernels are based on js divergences that originated in the information theory in this paper we extend the jensen type kernels on probability measures to define positive definite kernels on euclidean space we show that the special cases of these kernels include dot product kernels since jensen type divergences are multidistribution divergences we propose their multipoint variants and study spectral clustering and kernel methods based on these we also provide experimental studies on benchmark image database and gene expression database that show the benefits of the proposed kernels compared with the existing kernels the experiments on clustering also demonstrate the use of constructing multipoint similarities

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

bayesian graph edit distance this paper describes a novel framework for comparing and matching corrupted relational graphs the paper develops the idea of edit distance originally introduced for graph matching by sanfeliu and fu 1983 we show how the levenshtein distance 1966 can be used to model the probability distribution for structural errors in the graph matching problem this probability distribution is used to locate matches using map label updates we compare the resulting graph matching algorithm with that recently reported by wilson and hancock the use of edit distance offers an elegant alternative to the exhaustive compilation of label dictionaries moreover the method is polynomial rather than exponential in its worst case complexity we support our approach with an experimental study on synthetic data and illustrate its effectiveness on an uncalibrated stereo correspondence problem this demonstrates experimentally that the gain in efficiency is not at the expense of quality of match

multi graph matching via affinity optimization with graduated consistency regularization this paper addresses the problem of matching common node correspondences among multiple graphs referring to an identical or related structure this multi graph matching problem involves two correlated components i the local pairwise matching affinity across pairs of graphs ii the global matching consistency that measures the uniqueness of the pairwise matchings by different composition orders previous studies typically either enforce the matching consistency constraints in the beginning of an iterative optimization which may propagate matching error both over iterations and across graph pairs or separate affinity optimization and consistency enforcement into two steps this paper is motivated by the observation that matching consistency can serve as a regularizer in the affinity objective function especially when the function is biased due to noises or inappropriate modeling we propose composition based multi graph matching methods to incorporate the two aspects by optimizing the affinity score meanwhile gradually infusing the consistency we also propose two mechanisms to elicit the common inliers against outliers compelling results on synthetic and real images show the competency of our algorithms

risk sensitive control of finite state machines on an infinite horizon i in this paper we consider robust and risk sensitive control of discrete time finite state systems on an infinite horizon the solution of the state feedback robust control problem is characterized in terms of the value of an average cost dynamic game the risk sensitive stochastic optimal control problem is solved using the policy iteration algorithm and the optimal rate is expressed in terms of the value of a stochastic dynamic game with average cost per unit time criterion by taking a small noise limit a deterministic dynamic game which is closely related to the robust control problem is obtained

a generalization of the rectangular bounding method for continuous location models abstract we develop a generalized bounding method for the weiszfeld iterative procedure used to solve the hyperbolically approximated l p norm single and multifacility minimum location problems we also show that at optimality the solution to the bound problem coincides with the solution to the original location problem we use this result to show that the rectangular bound value converges to the single facility location problem optimal objective function value

randomized algorithms for the low rank approximation of matrices we describe two recently proposed randomized algorithms for the construction of low rank approximations to matrices and demonstrate their application inter alia to the evaluation of the singular value decompositions of numerically low rank matrices being probabilistic the schemes described here have a finite probability of failure in most cases this probability is rather negligible 10 17 is a typical value in many situations the new procedures are considerably more efficient and reliable than the classical deterministic ones they also parallelize naturally we present several numerical examples to illustrate the performance of the schemes

l_p norm regularization algorithms for optimization over permutation matrices optimization problems over permutation matrices appear widely in facility layout chip design scheduling pattern recognition computer vision graph matching etc since this problem is np hard due to the combinatorial nature of permutation matrices we relax the variable to be the more tractable doubly stochastic matrices and add an l p norm 0 p 1 regularization term to the objective function the optimal solutions of the l p regularized problem are the same as the original problem if the regularization parameter is sufficiently large a lower bound estimation of the nonzero entries of the stationary points and some connections between the local minimizers and the permutation matrices are further established then we propose an l p regularization algorithm with local refinements the algorithm approximately solves a sequence of l p regularization subproblems by the projected gradient method using a nonmonotone line search with the barzilai borwein step sizes its performance can be fu

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

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

open questions concerning weiszfeld s algorithm for the fermat weber location problem the fermat weber location problem is to find a point in n that minimizes the sum of the weighted euclidean distances fromm given points in n a popular iterative solution method for this problem was first introduced by weiszfeld in 1937 in 1973 kuhn claimed that if them given points are not collinear then for all but a denumerable number of starting points the sequence of iterates generated by weiszfeld s scheme converges to the unique optimal solution we demonstrate that kuhn s convergence theorem is not always correct we then conjecture that if this algorithm is initiated at the affine subspace spanned by them given points the convergence is ensured for all but a denumerable number of starting points

directional bias of the lp norm this paper concerns the use of the lp norm for estimating travel distances in a transportation network in previous empirical studies values of the parameter p 2 have been employed to characterize road networks after a detailed study of the directional bias of the lp norm it is shown here that such values need never be considered since the same degree of accuracy is obtained with a value of p in the interval 1 2 after rotating the axes 45

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

structural matching by discrete relaxation this paper describes a bayesian framework for performing relational graph matching by discrete relaxation our basic aim is to draw on this framework to provide a comparative evaluation of a number of contrasting approaches to relational matching broadly speaking there are two main aspects to this study firstly we focus on the issue of how relational inexactness may be quantified we illustrate that several popular relational distance measures can be recovered as specific limiting cases of the bayesian consistency measure the second aspect of our comparison concerns the way in which structural inexactness is controlled we investigate three different realizations of the matching process which draw on contrasting control models the main conclusion of our study is that the active process of graph editing outperforms the alternatives in terms of its ability to effectively control a large population of contaminating clutter

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

bounds on the extreme eigenvalues of positive definite toeplitz matrices easily computable bounds on the extreme eigenvalues of positive semidefinite psd toeplitz matrices are presented the bounds are especially suitable for matrices of relatively small dimension the bounds are derived for the wider class of psd hermitian matrices and interpreted via the levinson durbin algorithm for toeplitz matrices as a by product of this derivation an order recursive algorithm for the eigenvector eigenvalue decomposition is obtained and certain properties of the eigenvalues distribution are revealed

an optimal algorithm for approximate nearest neighbor searching fixed dimensions consider a set of s of n data points in real d dimensional space r d where distances are measured using any minkowski metric in nearest neighbor searching we preprocess s into a data structure so that given any query point q r d is the closest point of s to q can be reported quickly given any positive real e data point p is a 1 e approximate nearest neighbor of q if its distance from q is within a factor of 1 e of the distance to the true nearest neighbor we show that it is possible to preprocess a set of n points in r d in o dn log n time and o dn space so that given a query point q r d and e 0 a 1 e approximate nearest neighbor of q can be computed in o c d e log n time where c d e d 1 6d e d is a factor depending only on dimension and e in general we show that given an integer k 1 1 e approximations to the k nearest neighbors of q can be computed in additional o kd log n time

fast computation of low rank matrix approximations given a matrix a it is often desirable to find a good approximation to a that has low rank we introduce a simple technique for accelerating the computation of such approximations when a has strong spectral features that is when the singular values of interest are significantly greater than those of a random matrix with size and entries similar to a our technique amounts to independently sampling and or quantizing the entries of a thus speeding up computation by reducing the number of nonzero entries and or the length of their representation our analysis is based on observing that the acts of sampling and quantization can be viewed as adding a random matrix n to a whose entries are independent random variables with zero mean and bounded variance since with high probability n has very weak spectral features we can prove that the effect of sampling and quantization nearly vanishes when a low rank approximation to a p n is computed we give high probability bounds on the quality of our approximation both in the frobenius and the 2 norm

probabilistic supervisory control of probabilistic discrete event systems this paper considers supervisory control of probabilistic discrete event systems pdess pdess are modeled as generators of probabilistic languages the supervisory control problem considered is to find if possible a supervisor under whose control the behavior of a plant is identical to a given probabilistic specification the probabilistic supervisors we employ are a generalization of the deterministic ones previously employed in the literature at any state the supervisor enables disables events with certain probabilities necessary and sufficient conditions for the existence of such a supervisor and an algorithm for its computation are presented

global optimization procedures for the capacitated euclidean and lp distance multifacility location allocation problems in this paper we study the capacitated euclidean andlpdistance location allocation problems there exists no global optimization algorithm that has been developed and tested for this class of problems aside from a total enumeration approach beginning with the euclidean distance problem we design a branch and bound algorithm based on a partitioning of the allocation space that finitely converges to a global optimum for this nonconvex problem for deriving lower bounds at node subproblems in this partial enumeration scheme we employ two types of procedures the first approach computes a lower bound via a projected location space subproblem the second approach derives a significantly enhanced lower bound by using a reformulation linearization technique rlt to transform an equivalent representation of the original nonconvex problem into a higher dimensional linear programming relaxation in addition certain cut set inequalities are generated in the allocation space and objective function based cuts are derived in the location space to further tighten the lower bounding relaxation the rlt procedure is then extended to the generallpdistance problem forp 1 computational experience is provided on a set of test problems to investigate both the projected location space and the rlt lower bounding schemes the results indicate that the proposed global optimization approach using the rlt based scheme offers a promising viable solution procedure in fact among the problems solved for the only two test instances available in the literature for the euclidean distance case we report significantly improved solutions

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

global convergence of a generalized iterative procedure for the minisum location problem with lp distances this paper considers a general form of the single facility minisum location problem also referred to as the fermat weber problem where distances are measured by an lp norm an iterative solution algorithm is given which generalizes the well known weiszfeld procedure for euclidean distances global convergence of the algorithm is proven for any value of the parameter p in the closed interval 1 2 provided an iterate does not coincide with a singular point of the iteration functions however for p 2 the descent property of the algorithm and as a result global convergence are no longer guaranteed these results generalize the work of kuhn for euclidean p 2 distances

on the global convergence of a generalized iterative procedure for the minisum location problem with l p distances for p 2 this paper presents a procedure to solve the classical location median problem where the distances are measured with lp norms with p 2 in order to do that we consider an approximated problem the global convergence of the sequence generated by this iterative scheme is proved therefore this paper closes the still open question of giving a modification of the weiszfeld algorithm that converges to an optimal solution of the median problem with lp norms and p in 2 infty the paper ends with a computational analysis of the different provided iterative schemes

minimizing nonsubmodular functions with graph cuts a review optimization techniques based on graph cuts have become a standard tool for many vision applications these techniques allow to minimize efficiently certain energy functions corresponding to pairwise markov random fields mrfs currently there is an accepted view within the computer vision community that graph cuts can only be used for optimizing a limited class of mrf energies e g submodular functions in this survey we review some results that show that graph cuts can be applied to a much larger class of energy functions in particular nonsubmodular functions while these results are well known in the optimization community to our knowledge they were not used in the context of computer vision and mrf optimization we demonstrate the relevance of these results to vision on the problem of binary texture restoration

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

l_q lq closest point to affine subspaces using the generalized weiszfeld algorithm this paper presents a method for finding an l q lq closest point to a set of affine subspaces that is a point for which the sum of the q th power of orthogonal distances to all the subspaces is minimized where 1 le q 2 1 q 2 we give a theoretical proof for the convergence of the proposed algorithm to a unique l q lq minimum the proposed method is motivated by the l q lq weiszfeld algorithm an extremely simple and rapid averaging algorithm that finds the l q lq mean of a set of given points in a euclidean space the proposed algorithm is applied to the triangulation problem in computer vision by finding the l q lq closest point to a set of lines in 3d our experimental results for the triangulation problem confirm that the l q lq closest point method for 1 le q 2 1 q 2 is more robust to outliers than the l 2 l2 closest point method

an eigendecomposition approach to weighted graph matching problems an approximate solution to the weighted graph matching problem is discussed for both undirected and directed graphs the weighted graph matching problem is that of finding the optimum matching between two weighted graphs which are graphs with weights at each arc the proposed method uses an analytic instead of a combinatorial or iterative approach to the optimum matching problem using the eigendecompositions of the adjacency matrices in the case of the undirected graph matching problem or hermitian matrices derived from the adjacency matrices in the case of the directed graph matching problem a matching close to the optimum can be found efficiently when the graphs are sufficiently close to each other simulation results are given to evaluate the performance of the proposed method

a comparison of affine region detectors the paper gives a snapshot of the state of the art in affine covariant region detectors and compares their performance on a set of test images under varying imaging conditions six types of detectors are included detectors based on affine normalization around harris mikolajczyk and schmid 2002 schaffalitzky and zisserman 2002 and hessian points mikolajczyk and schmid 2002 a detector of maximally stable extremal regions proposed by matas et al 2002 an edge based region detector tuytelaars and van gool 1999 and a detector based on intensity extrema tuytelaars and van gool 2000 and a detector of salient regions proposed by kadir zisserman and brady 2004 the performance is measured against changes in viewpoint scale illumination defocus and image compression the objective of this paper is also to establish a reference test set of images and performance software so that future detectors can be evaluated in the same framework

an image understanding system using attributed symbolic representation and inexact graph matching this paper presents a powerful image understanding system that utilizes a semantic syntactic or attributed synibolic representation scheme in the form of attributed relational graphs arg s for comprehending the global information contents of images nodes in the arg represent the global image features while the relations between those features are represented by attributed branches between their corresponding nodes the extraction of arg representation from images is achieved by a multilayer graph transducer scheme this scheme is basically a rule based system that uses a combination of model driven and data driven concepts in performing a hierarchical symbolic mapping of the image information content from the spatial domain representation into a global representation further analysis and inter pretation of the imagery data is performed on the extracted arg representation a distance measure between images is defined in terms of the distance between their respective arg representations the distance between two arg s and the inexact matching of their respective components are calculated by an efficient dynamic programming technique the system handles noise distortion and ambiguity in real world images by two means namely through modeling and embedding them into the transducer s mapping rules as well as through the appropriate cost of error transformation for the inexact matching of the arg image representation two illustrative experiments are presented to demonstrate some capabilities of the proposed system experiment i deals with locating objects in multiobject scenes while experiment ii is concerned with target detection in sar images

a quadratically convergent method for minimizing a sum of euclidean norms we consider the problem of minimizing a sum of euclidean norms f x sum nolimits i 1 m r i x here the residuals r i x are affine functions fromr n tor 1 n 1 2 m 2 this arises in a number of applications including single and multi facility location problems the functionf is in general not differentiable atx if at least oner i x is zero

the convergence of the weiszfeld algorithm abstract we investigate the convergence properties of the weiszfeld procedure when it is applied to the approximated l p norm single facility location problem where p 2 we show that convergence for p 2 can be obtained by introducing a step size factor to the iterative procedure some numerical test results are also given

consistency driven alternating optimization for multigraph matching a unified approach the problem of graph matching gm in general is nondeterministic polynomial complete and many approximate pairwise matching techniques have been proposed for a general setting in real applications it typically requires to find the consistent matching across a batch of graphs sequentially performing pairwise matching is prone to error propagation along the pairwise matching sequence and the sequences generated in different pairwise matching orders can lead to contradictory solutions motivated by devising a robust and consistent multiple gm model we propose a unified alternating optimization framework for multi gm in addition we define and use two metrics related to graphwise and pairwise consistencies the former is used to find an appropriate reference graph which induces a set of basis variables and launches the iteration procedure the latter defines the order in which the considered graphs in the iterations are manipulated we show two embodiments under the proposed framework that can cope with the nonfactorized and factorized affinity matrix respectively our multi gm model has two major characters 1 the affinity information across multiple graphs are explored in each iteration by fixing part of the matching variables via a consistency driven mechanism and 2 the framework is flexible to incorporate various existing pairwise gm solvers in an out of box fashion and also can proceed with the output of other multi gm methods the experimental results on both synthetic data and real images empirically show that the proposed framework performs competitively with the state of the art

a heuristic algorithm for constrained multi source weber problem the variational inequality approach abstract for solving the well known multi source weber problem mwp each iteration of the heuristic alternate location allocation algorithm consists of a location phase and an allocation phase the task of the location phase is to solve finitely many single source weber problems swp which are reduced by the heuristic of nearest center reclassification for the customers in the previous allocation phase this paper considers the more general and practical case the mwp with constraints cmwp in particular a variational inequality approach is contributed to solving the involved constrained swp cswp and thus a new heuristic algorithm for cmwp is presented the involved cswp in the location phases are reformulated into some linear variational inequalities whose special structures lead to a new projection contraction pc method global convergence of the pc method is proved under mild assumptions the new heuristic algorithm using the pc method in the location phases approaches to the heuristic solution of cmwp efficiently which is verified by the preliminary numerical results reported in this paper

local convexity results in a generalized fermat weber problem abstract a generalized form of the fermat weber problem requires finding a point in r n to minimize a sum of nondecreasing functions of distances to m given points in this paper local convexity properties are investigated for the generalized problem sufficient conditions are derived which guarantee that the hessian matrix of the objective function will be positive definite the analysis also reveals that weiszfeld type iterative algorithms may have sublinear convergence rates since the hessian may only be positive semidefinite at a local minimum

image completion by diffusion maps and spectral relaxation we present a framework for image inpainting that utilizes the diffusion framework approach to spectral dimensionality reduction we show that on formulating the inpainting problem in the embedding domain the domain to be inpainted is smoother in general particularly for the textured images thus the textured images can be inpainted through simple exemplar based and variational methods we discuss the properties of the induced smoothness and relate it to the underlying assumptions used in contemporary inpainting schemes as the diffusion embedding is nonlinear and noninvertible we propose a novel computational approach to approximate the inverse mapping from the inpainted embedding space to the image domain we formulate the mapping as a discrete optimization problem solved through spectral relaxation the effectiveness of the presented method is exemplified by inpainting real images where it is shown to compare favorably with contemporary state of the art schemes

an extended path following algorithm for graph matching problem the path following algorithm was proposed recently to approximately solve the matching problems on undirected graph models and exhibited a state of the art performance on matching accuracy in this paper we extend the path following algorithm to the matching problems on directed graph models by proposing a concave relaxation for the problem based on the concave and convex relaxations a series of objective functions are constructed and the frank wolfe algorithm is then utilized to minimize them several experiments on synthetic and real data witness the validity of the extended path following algorithm

convergence of the weiszfeld algorithm for weber problems using a generalized distance function this paper considers a generalization of the single and multisource weber problem for the case when the distance function is some power k of the usual ip distance properties of the generalized problem are established and an appropriate generalization of the weiszfeld iterative approach is given a convergence proof is supplied for an approximation to the original problem under certain restrictions on p and k

an algorithm for finding the most similar given sized subgraphs in two weighted graphs we propose a weighted common subgraph wcs matching algorithm to find the most similar subgraphs in two labeled weighted graphs wcs matching as a natural generalization of equal sized graph matching and subgraph matching has found wide applications in many computer vision and machine learning tasks in this brief wcs matching is first formulated as a combinatorial optimization problem over the set of partial permutation matrices then it is approximately solved by a recently proposed combinatorial optimization framework graduated nonconvexity and concavity procedure experimental comparisons on both synthetic graphs and real world images validate its robustness against noise level problem size outlier number and edge density

a location allocation heuristic for the capacitated multi facility weber problem with probabilistic customer locations abstract the capacitated multi facility weber problem is concerned with locating m facilities in the euclidean plane and allocating their capacities to n customers at minimum total cost the deterministic version of the problem which assumes that customer locations and demands are known with certainty is a non convex optimization problem and difficult to solve in this work we focus on a probabilistic extension and consider the situation where the customer locations are randomly distributed according to a bivariate distribution we first present a mathematical programming formulation which is even more difficult than its deterministic version we then propose an alternate location allocation local search heuristic generalizing the ideas used originally for the deterministic problem in its original form the applicability of the heuristic depends on the calculation of the expected distances between the facilities and customers which can be done for only very few distance and probability density function combinations we therefore propose approximation methods which make the method applicable for any distance function and bivariate location distribution

the fermat weber location problem revisited the fermat weber location problem requires finding a point in n that minimizes the sum of weighted euclidean distances tom given points a one point iterative method was first introduced by weiszfeld in 1937 to solve this problem since then several research articles have been published on the method and generalizations thereof global convergence of weiszfeld s algorithm was proven in a seminal paper by kuhn in 1973 however since them given points are singular points of the iteration functions convergence is conditional on none of the iterates coinciding with one of the given points in addressing this problem kuhn concluded that whenever them given points are not collinear weiszfeld s algorithm will converge to the unique optimal solution except for a denumerable set of starting points as late as 1989 chandrasekaran and tamir demonstrated with counter examples that convergence may not occur for continuous sets of starting points when the given points are contained in an affine subspace of n we resolve this open question by proving that weiszfeld s algorithm converges to the unique optimal solution for all but a denumerable set of starting points if and only if the convex hull of the given points is of dimensionn

factorized graph matching graph matching gm is a fundamental problem in computer science and it plays a central role to solve correspondence problems in computer vision gm problems that incorporate pairwise constraints can be formulated as a quadratic assignment problem qap although widely used solving the correspondence problem through gm has two main limitations 1 the qap is np hard and difficult to approximate 2 gm algorithms do not incorporate geometric constraints between nodes that are natural in computer vision problems to address aforementioned problems this paper proposes factorized graph matching fgm fgm factorizes the large pairwise affinity matrix into smaller matrices that encode the local structure of each graph and the pairwise affinity between edges four are the benefits that follow from this factorization 1 there is no need to compute the costly in space and time pairwise affinity matrix 2 the factorization allows the use of a path following optimization algorithm that leads to improved optimization strategies and matching performance 3 given the factorization it becomes straight forward to incorporate geometric transformations rigid and non rigid to the gm problem 4 using a matrix formulation for the gm problem and the factorization it is easy to reveal commonalities and differences between different gm methods the factorization also provides a clean connection with other matching algorithms such as iterative closest point experimental results on synthetic and real databases illustrate how fgm outperforms state of the art algorithms for gm the code is available at http humansensing cs cmu edu fgm

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

correspondence matching using kernel principal components analysis and label consistency constraints this paper investigates spectral approaches to the problem of point pattern matching we make two contributions first we consider rigid point set alignment here we show how kernel principal components analysis kernel pca can be effectively used for solving the rigid point correspondence matching problem when the point sets are subject to outliers and random position jitter specifically we show how the point proximity matrix can be kernelised and spectral correspondence matching transformed into one of kernel pca second we turn our attention to the matching of articulated point sets here we show label consistency constraints can be incorporated into definition of the point proximity matrix the new methods are compared to those of shapiro and brady and scott and longuet higgins together with multidimensional scaling we provide experiments on both synthetic data and real world data

a note on convergence in the single facility minisum location problem abstract the single facility minisum location problem requires finding a point in rn that minimizes a sum of weighted distances to m given points the distance measure is typically assumed in the literature to be either euclidean or rectangular or the more general lp norm global convergence of a well known iterative solution method named the weiszfeld procedure has been proven under the proviso that none of the iterates coincide with a singular point of the iteration functions the purpose of this paper is to examine the corresponding set of bad starting points which result in failure of the algorithm for a general lp norm an important outcome of this analysis is that the set of bad starting points will always have a measure zero in the solution space rn thereby validating the global convergence properties of the weiszfeld procedure for any lp norm p 1 2

a probabilistic language formalism for stochastic discrete event systems the formalism of probabilistic languages has been introduced for modeling the qualitative behavior of stochastic discrete event systems a probabilistic language is a unit interval valued map over the set of traces of the system satisfying certain consistency constraints regular language operators such as choice concatenation and kleene closure have been defined in the setting of probabilistic languages to allow modeling of complex systems in terms of simpler ones the set of probabilistic languages is closed under such operators thus forming an algebra it also is a complete partial order under a natural ordering in which the operators are continuous hence recursive equations can be solved in this algebra this is alternatively derived by using the contraction mapping theorem on the set of probabilistic languages which is shown to be a complete metric space the notion of regularity i e finiteness of automata representation of probabilistic languages has been defined and it is shown that regularity is preserved under choice concatenation and kleene closure we show that this formalism is also useful in describing system performance measures such as completion time reliability etc and present properties to aide their computation

a path following algorithm for the graph matching problem we propose a convex concave programming approach for the labeled weighted graph matching problem the convex concave programming formulation is obtained by rewriting the weighted graph matching problem as a least square problem on the set of permutation matrices and relaxing it to two different optimization problems a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices the concave relaxation has the same global minimum as the initial graph matching problem but the search for its global minimum is also a hard combinatorial problem we therefore construct an approximation of the concave problem solution by following a solution path of a convex concave problem obtained by linear interpolation of the convex and concave formulations starting from the convex relaxation this method allows to easily integrate the information on graph label similarities into the optimization problem and therefore perform labeled weighted graph matching the algorithm is compared with some of the best performing graph matching methods on four data sets simulated graphs qaplib retina vessel images and handwritten chinese characters in all cases the results are competitive with the state of the art

controlled markov chains with safety upper bound in this note we introduce and study the notion of safety control of stochastic discrete event systems dess modeled as controlled markov chains for nonstochastic dess modeled by state machines or automata safety is specified as a set of forbidden states or equivalently by a binary valued vector that imposes an upper bound on the set of states permitted to be visited we generalize this notion of safety to the setting of stochastic dess by specifying it as an unit interval valued vector that imposes an upper bound on the state probability distribution vector under the assumption of complete state observation we identify 1 the set of all state feedback controllers that satisfy the safety requirement for any given safe initial state probability distribution and 2 the set of all safe initial state probability distributions for a given state feedback controller

generalized weiszfeld algorithms for lq optimization in many computer vision applications a desired model of some type is computed by minimizing a cost function based on several measurements typically one may compute the model that minimizes the l 2 cost that is the sum of squares of measurement errors with respect to the model however the lq solution which minimizes the sum of the q th power of errors usually gives more robust results in the presence of outliers for some values of q for example q 1 the weiszfeld algorithm is a classic algorithm for finding the geometric l1 mean of a set of points in euclidean space it is provably optimal and requires neither differentiation nor line search the weiszfeld algorithm has also been generalized to find the l1 mean of a set of points on a riemannian manifold of non negative curvature this paper shows that the weiszfeld approach may be extended to a wide variety of problems to find an lq mean for 1 le q lt 2 while maintaining simplicity and provable convergence we apply this problem to both single rotation averaging under which the algorithm provably finds the global lq optimum and multiple rotation averaging for which no such proof exists experimental results of lq optimization for rotations show the improved reliability and robustness compared to l 2 optimization

technical communique maximizing the set of recurrent states of an mdp subject to convex constraints this paper focuses on the design of time homogeneous fully observed markov decision processes mdps with finite state and action spaces the main objective is to obtain policies that generate the maximal set of recurrent states subject to convex constraints on the set of invariant probability mass functions we propose a design method that relies on a finitely parametrized convex program inspired on principles of entropy maximization a numerical example is provided to illustrate these ideas

gnccp graduated nonconvexityand concavity procedure in this paper we propose the graduated nonconvexity and concavity procedure gnccp as a general optimization framework to approximately solve the combinatorial optimization problems defined on the set of partial permutation matrices gnccp comprises two sub procedures graduated nonconvexity which realizes a convex relaxation and graduated concavity which realizes a concave relaxation it is proved that gnccp realizes exactly a type of convex concave relaxation procedure ccrp but with a much simpler formulation without needing convex or concave relaxation in an explicit way actually gnccp involves only the gradient of the objective function and is therefore very easy to use in practical applications two typical related np hard problems partial graph matching and quadratic assignment problem qap are employed to demonstrate its simplicity and state of the art performance

on solving the planar k centrum problem with euclidean distances this paper presents a solution procedure based on a gradient descent method for the k centrum problem in the plane the particular framework of this problem for the euclidean norm leads to bisector lines whose analytical expressions are easy to handle this allows us to develop different solution procedures which are tested on different problems and compared with existing procedures in the literature of location analysis the computational analysis reports that our procedures provide better results than the existing ones for the k centrum problem

a unified continuous optimization framework for center based clustering methods center based partitioning clustering algorithms rely on minimizing an appropriately formulated objective function and different formulations suggest different possible algorithms in this paper we start with the standard nonconvex and nonsmooth formulation of the partitioning clustering problem we demonstrate that within this elementary formulation convex analysis tools and optimization theory provide a unifying language and framework to design analyze and extend hard and soft center based clustering algorithms through a generic algorithm which retains the computational simplicity of the popular k means scheme we show that several well known and more recent center based clustering algorithms which have been derived either heuristically or and have emerged from intuitive analogies in physics statistical techniques and information theoretic perspectives can be recovered as special cases of the proposed analysis and we streamline their relationships

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

an efficient multilinear optimization framework for hypergraph matching hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows the use of higher order geometric information hypergraph matching can be formulated as a third order optimization problem subject to assignment constraints which turns out to be np hard in recent work we have proposed an algorithm for hypergraph matching which first lifts the third order problem to a fourth order problem and then solves the fourth order problem via optimization of the corresponding multilinear form this leads to a tensor block coordinate ascent scheme which has the guarantee of providing monotonic ascent in the original matching score function and leads to state of the art performance both in terms of achieved matching score and accuracy in this paper we show that the lifting step to a fourth order problem can be avoided yielding a third order scheme with the same guarantees and performance but being two times faster moreover we introduce a homotopy type method which further improves the performance

convex necessary and sufficient conditions for density safety constraints in markov chain synthesis this paper introduces a new approach for the synthesis of markov chains with density safety constraints specific safety constraints considered are i density upper bound constraints ii bound on the rate of change of density the proposed approach is based on a new mathematical result that formulates these constraints as linear and hence convex inequality constraints the main contribution of the paper is that the new convex constraints are proved to be equivalent necessary and sufficient to the original constraints this result enables the formulation of the markov chain synthesis problem as a linear matrix inequality lmi optimization problem with additional constraints on the steady state probability distribution ergodicity and feasible state transitions the lmi formulation presents a necessary and sufficient design condition for reversible markov chains that is it is not conservative when the reversibility is not required the lmi condition is only sufficient due to the ergodicity constraint since lmi problems can be solved to global optimality in polynomial time by using interior point method algorithms the proposed lmi based design approach is numerically tractable

a probabilistic approach to spectral graph matching spectral matching sm is a computationally efficient approach to approximate the solution of pairwise matching problems that are np hard in this paper we present a probabilistic interpretation of spectral matching schemes and derive a novel probabilistic matching pm scheme that is shown to outperform previous approaches we show that spectral matching can be interpreted as a maximum likelihood ml estimate of the assignment probabilities and that the graduated assignment ga algorithm can be cast as a maximum a posteriori map estimator based on this analysis we derive a ranking scheme for spectral matchings based on their reliability and propose a novel iterative probabilistic matching algorithm that relaxes some of the implicit assumptions used in prior works we experimentally show our approaches to outperform previous schemes when applied to exhaustive synthetic tests as well as the analysis of real image sequences

continuous location under the effect of refraction in this paper we address the problem of locating a new facility on a d dimensional space when the distance measure ell p lp or polyhedral norms is different at each one of the sides of a given hyperplane mathcal h h we relate this problem with the physical phenomenon of refraction and extend it to any finite dimensional space and different distances at each one of the sides of any hyperplane an application to this problem is the location of a facility within or outside an urban area where different distance measures must be used we provide a new second order cone programming formulation based on the ell p lp norm representation given in blanco et al comput optim appl 58 3 563 595 2014 that allows to solve the problem in any finite dimensional space with second order cone or semidefinite programming tools we also extend the problem to the case where the hyperplane is considered as a rapid transit media a different third norm is also considered over mathcal h h that allows the demand to travel whenever it is convenient through mathcal h h to reach the new facility extensive computational experiments run in gurobi are reported in order to show the effectiveness of the approach some extensions of these models are also presented

graph matching by simplified convex concave relaxation procedure the convex and concave relaxation procedure ccrp was recently proposed and exhibited state of the art performance on the graph matching problem however ccrp involves explicitly both convex and concave relaxations which typically are difficult to find and thus greatly limit its practical applications in this paper we propose a simplified ccrp scheme which can be proved to realize exactly ccrp but with a much simpler formulation without needing the concave relaxation in an explicit way thus significantly simplifying the process of developing ccrp algorithms the simplified ccrp can be generally applied to any optimizations over the partial permutation matrix as long as the convex relaxation can be found based on two convex relaxations we obtain two graph matching algorithms defined on adjacency matrix and affinity matrix respectively extensive experimental results witness the simplicity as well as state of the art performance of the two simplified ccrp graph matching algorithms

ridge network detection in crumpled paper via graph density maximization crumpled sheets of paper tend to exhibit a specific and complex structure which is described by physicists as ridge networks existing literature shows that the automation of ridge network detection in crumpled paper is very challenging because of its complex structure and measuring distortion in this paper we propose to model the ridge network as a weighted graph and formulate the ridge network detection as an optimization problem in terms of the graph density first we detect a set of graph nodes and then determine the edge weight between each pair of nodes to construct a complete graph next we define a graph density criterion and formulate the detection problem to determine a subgraph with maximal graph density further we also propose to refine the graph density by including a pairwise connectivity into the criterion to improve the connectivity of the detected ridge network our experimental results show that with the density criterion our proposed method effectively automates the ridge network detection

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

spectral correspondence for point pattern matching this paper investigates the correspondence matching of point sets using spectral graph analysis in particular we are interested in the problem of how the modal analysis of point sets can be rendered robust to contamination and drop out we make three contributions first we show how the modal structure of point sets can be embedded within the framework of the em algorithm second we present several methods for computing the probabilities of point correspondences from the modes of the point proximity matrix third we consider alternatives to the gaussian proximity matrix we evaluate the new method on both synthetic and real world data here we show that the method can be used to compute useful correspondences even when the level of point contamination is as large as 50 we also provide some examples on deformed point set tracking