fast and robust fuzzy c means clustering algorithms incorporating local information for image segmentation fuzzy c means fcm algorithms with spatial constraints fcm s have been proven effective for image segmentation however they still have the following disadvantages 1 although the introduction of local spatial information to the corresponding objective functions enhances their insensitiveness to noise to some extent they still lack enough robustness to noise and outliers especially in absence of prior knowledge of the noise 2 in their objective functions there exists a crucial parameter a used to balance between robustness to noise and effectiveness of preserving the details of the image it is selected generally through experience and 3 the time of segmenting an image is dependent on the image size and hence the larger the size of the image the more the segmentation time in this paper by incorporating local spatial and gray information together a novel fast and robust fcm framework for image segmentation i e fast generalized fuzzy c means fgfcm clustering algorithms is proposed fgfcm can mitigate the disadvantages of fcm s and at the same time enhances the clustering performance furthermore fgfcm not only includes many existing algorithms such as fast fcm and enhanced fcm as its special cases but also can derive other new algorithms such as fgfcm s1 and fgfcm s2 proposed in the rest of this paper the major characteristics of fgfcm are 1 to use a new factor s i j as a local both spatial and gray similarity measure aiming to guarantee both noise immunity and detail preserving for image and meanwhile remove the empirically adjusted parameter a 2 fast clustering or segmenting image the segmenting time is only dependent on the number of the gray levels q rather than the size n q of the image and consequently its computational complexity is reduced from o nci 1 to o qci 2 where c is the number of the clusters i 1 and i 2

alternative c means clustering algorithms abstract in this paper we propose a new metric to replace the euclidean norm in c means clustering procedures on the basis of the robust statistic and the influence function we claim that the proposed new metric is more robust than the euclidean norm we then create two new clustering methods called the alternative hard c means ahcm and alternative fuzzy c means afcm clustering algorithms these alternative types of c means clustering have more robustness than c means clustering numerical results show that ahcm has better performance than hcm and afcm is better than fcm we recommend afcm for use in cluster analysis recently this afcm algorithm has successfully been used in segmenting the magnetic resonance image of ophthalmology to differentiate the abnormal tissues from the normal tissues

a modified fuzzy c means algorithm for bias field estimation and segmentation of mri data we present a novel algorithm for fuzzy segmentation of magnetic resonance imaging mri data and estimation of intensity inhomogeneities using fuzzy logic mri intensity inhomogeneities can be attributed to imperfections in the radio frequency coils or to problems associated with the acquisition sequences the result is a slowly varying shading artifact over the image that can produce errors with conventional intensity based classification our algorithm is formulated by modifying the objective function of the standard fuzzy c means fcm algorithm to compensate for such inhomogeneities and to allow the labeling of a pixel voxel to be influenced by the labels in its immediate neighborhood the neighborhood effect acts as a regularizer and biases the solution toward piecewise homogeneous labelings such a regularization is useful in segmenting scans corrupted by salt and pepper noise experimental results on both synthetic images and mr data are given to demonstrate the effectiveness and efficiency of the proposed algorithm

a modified forward backward splitting method for maximal monotone mappings we consider the forward backward splitting method for finding a zero of the sum of two maximal monotone mappings this method is known to converge when the inverse of the forward mapping is strongly monotone we propose a modification to this method in the spirit of the extragradient method for monotone variational inequalities under which the method converges assuming only the forward mapping is lipschitz continuous on some closed convex subset of its domain the modification entails an additional forward step and a projection step at each iteration applications of the modified method to decomposition in convex programming and monotone variational inequalities are discussed

two parallel distribution algorithms for convex constrained minimization problems abstract a parallel gradient distribution pgd approach for minimizing a nonsmooth convex function on a block separable convex set x of rn and a parallel variable distribution pvd approach for minimizing a nonsmooth convex function on an inseparable closed convex set x of rn are presented which are constructed by using the moreau yosida regularization of the convex functions the convergence analysis for the two approaches is given as well

fuzzy c means clustering with local information and kernel metric for image segmentation in this paper we present an improved fuzzy c means fcm algorithm for image segmentation by introducing a tradeoff weighted fuzzy factor and a kernel metric the tradeoff weighted fuzzy factor depends on the space distance of all neighboring pixels and their gray level difference simultaneously by using this factor the new algorithm can accurately estimate the damping extent of neighboring pixels in order to further enhance its robustness to noise and outliers we introduce a kernel distance measure to its objective function the new algorithm adaptively determines the kernel parameter by using a fast bandwidth selection rule based on the distance variance of all data points in the collection furthermore the tradeoff weighted fuzzy factor and the kernel distance measure are both parameter free experimental results on synthetic and real images show that the new algorithm is effective and efficient and is relatively independent of this type of noise

a parallel projection method for solving generalized linear least squares problems a parallel projection algorithm is proposed to solve the generalized linear least squares problem find a vector to minimize the 2 norm distance from its image under an affine mapping to a closed convex cone in each iteration of the algorithm the problem is decomposed into several independent small problems of finding projections onto subspaces which are simple and can be tackled parallelly the algorithm can be viewed as a dual version of the algorithm proposed by han and lou 8 for the special problem under consideration stronger convergence results are established the algorithm is also related to the block iterative methods of elfving 6 dennis and steihaug 5 and the primal dual method of springarn 14

generalized fuzzy c means clustering strategies using l sub p norm distances fuzzy c means fcm is a useful clustering technique modifications of fcm using l sub 1 norm distances increase robustness to outliers object and relational data versions of fcm clustering are defined for the more general case where the l sub p norm p spl ges 1 or semi norm 0 0 in order to facilitate the empirical examination of the object data models both object and relational approaches are included in a numerical study

how to deal with the unbounded in optimization theory and algorithms the aim of this survey is to show how the unbounded arises in optimization problems and how it leads to fundamental notions which are not only useful for proving theoretical results such as convergence of algorithms and the existence of optimal solutions but also for constructing new methods

parallel ssle algorithm for large scale constrained optimization in this paper a parallel ssle algorithm is proposed for solving large scale constrained optimization with block separable structure at each iteration the pvd sub problems are solved inexactly by the ssle algorithm which successfully overcomes the constraint inconsistency exited in most sqp type algorithm and decreases the computation amount as well without assuming the convexity of the constraints the algorithm is proved to be globally convergent to a kkt point of the original problem

a successive projection method it is of both theoretical and practical interest to find the projection of a point to the intersection of a finite number of closed convex sets by a sequence of projections to the individual sets successively in this paper we study such a method and analyze its convergence properties a main feature of the method is its capability to decompose the projection problem into several small ones for some structured sparse problems these small subproblems can be solved independently and the presented method has a potential use in parallel computation

applications of splitting algorithm to decomposition in convex programming and variational inequalities recently han and lou proposed a highly parallelizable decomposition algorithm for minimizing a strongly convex cost over the intersection of closed convex sets it is shown that their algorithm is in fact a special case of a splitting algorithm analyzed by gabay for finding a zero of the sum of two maximal monotone operators gabay s convergence analysis for the splitting algorithm is sharpened and new applications of this algorithm to variational inequalities convex programming and the solution of linear complementarily problems are proposed for convex programs with a certain separable structure a multiplier method that is closely related to the alternating direction method of multipliers of gabay mercier and of glowinski marrocco but which uses both ordinary and augmented lagrangians is obtained

color image segmentation using histogram thresholding fuzzy c means hybrid approach this paper presents a novel histogram thresholding fuzzy c means hybrid htfcm approach that could find different application in pattern recognition as well as in computer vision particularly in color image segmentation the proposed approach applies the histogram thresholding technique to obtain all possible uniform regions in the color image then the fuzzy c means fcm algorithm is utilized to improve the compactness of the clusters forming these uniform regions experimental results have demonstrated that the low complexity of the proposed htfcm approach could obtain better cluster quality and segmentation results than other segmentation approaches that employing ant colony algorithm

on the convergence of asynchronous parallel algorithm for large scale linearly constrained minimization problem as a synchronization parallel framework the parallel variable transformation pvt algorithm is effective to solve unconstrained optimization problems in this paper based on the idea that a constrained optimization problem is equivalent to a differentiable unconstrained optimization problem by introducing the fischer function we propose an asynchronous pvt algorithm for solving large scale linearly constrained convex minimization problems this new algorithm can terminate when some processor satisfies terminal condition without waiting for other processors meanwhile it can enhances practical efficiency for large scale optimization problem global convergence of the new algorithm is established under suitable assumptions and in particular the linear rate of convergence does not depend on the number of processors

further applications of a splitting algorithm to decomposition in variational inequalities and convex programming a classical method for solving the variational inequality problem is the projection algorithm we show that existing convergence results for this algorithm follow from one given by gabay for a splitting algorithm for finding a zero of the sum of two maximal monotone operators moreover we extend the projection algorithm to solveany monotone affine variational inequality problem when applied to linear complementarity problems we obtain a matrix splitting algorithm that is simple and for linear quadratic programs massively parallelizable unlike existing matrix splitting algorithms this algorithm converges under no additional assumption on the problem when applied to generalized linear quadratic programs we obtain a decomposition method that unlike existing decomposition methods can simultaneously dualize the linear constraints and diagonalize the cost function this method gives rise to highly parallelizable algorithms for solving a problem of deterministic control in discrete time and for computing the orthogonal projection onto the intersection of convex sets

an information criterion for parameters under a simple order restriction suppose we have independent random samples from each of k populations specified by scalar valued unknown parameters 1 k satisfying the simple order restriction 1 k our concern is to seek distinct parameters among 1 k based on the data to find a configuration of distinct parameters among the 0 s one may consider employing akaike s information criterion akaike 1973 however the criterion is not appropriate for the order restricted maximum likelihood estimator of 1 k since the normality or the asymptotic normality of the estimator is not valid in this paper an information criterion is proposed for detecting the configuration of the true parameters with the simple order restriction this method may also be applied for detecting a changepoint in a sequence of parameters with a monotone trend a monte carlo study indicates that our new criterion is effective compared to akaike s information criterion for detecting the configuration of normal means satisfying the simple order restriction

computational acceleration of projection algorithms for the linear best approximation problem abstract this is an experimental computational account of projection algorithms for the linear best approximation problem we focus on the sequential and simultaneous versions of dykstra s algorithm and the halpern lions wittmann bauschke algorithm for the best approximation problem from a point to the intersection of closed convex sets in the euclidean space these algorithms employ different iterative approaches to reach the same goal but no mathematical connection has yet been found between their algorithmic schemes we compare these algorithms on linear best approximation test problems that we generate so that the solution will be known a priori and enable us to assess the relative computational merits of these algorithms for the simultaneous versions we present a new component averaging variant that substantially accelerates their initial behavior for sparse systems

fuzzy c means based clustering for linearly and nonlinearly separable data in this paper we present a new distance metric that incorporates the distance variation in a cluster to regularize the distance between a data point and the cluster centroid it is then applied to the conventional fuzzy c means fcm clustering in data space and the kernel fuzzy c means kfcm clustering in a high dimensional feature space experiments on two dimensional artificial data sets real data sets from public data libraries and color image segmentation have shown that the proposed fcm and kfcm with the new distance metric generally have better performance on non spherically distributed data with uneven density for linear and nonlinear separation

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

a row action method for convex programming we present a new method for minimizing a strictly convex function subject to general convex constraints constraints are used one at a time no changes are made in the constraint functions thus the row action nature of the algorithm and at each iteration a subproblem is solved consisting of minimization of the objective function subject to one or two linear equations convergence of the algorithm is established and the method is compared with other row action algorithms for several relevant particular cases

semi supervised clustering with metric learning an adaptive kernel method most existing representative works in semi supervised clustering do not sufficiently solve the violation problem of pairwise constraints on the other hand traditional kernel methods for semi supervised clustering not only face the problem of manually tuning the kernel parameters due to the fact that no sufficient supervision is provided but also lack a measure that achieves better effectiveness of clustering in this paper we propose an adaptive semi supervised clustering kernel method based on metric learning sckmm to mitigate the above problems specifically we first construct an objective function from pairwise constraints to automatically estimate the parameter of the gaussian kernel then we use pairwise constraint based k means approach to solve the violation issue of constraints and to cluster the data furthermore we introduce metric learning into nonlinear semi supervised clustering to improve separability of the data for clustering finally we perform clustering and metric learning simultaneously experimental results on a number of real world data sets validate the effectiveness of the proposed method

a proximal based decomposition method for convex minimization problems this paper presents a decomposition method for solving convex minimization problems at each iteration the algorithm computes two proximal steps in the dual variables and one proximal step in the primal variables we derive this algorithm from rockafellar s proximal method of multipliers which involves an augmented lagrangian with an additional quadratic proximal term the algorithm preserves the good features of the proximal method of multipliers with the additional advantage that it leads to a decoupling of the constraints and is thus suitable for parallel implementation we allow for computing approximately the proximal minimization steps and we prove that under mild assumptions on the problem s data the method is globally convergent and at a linear rate the method is compared with alternating direction type methods and applied to the particular case of minimizing a convex function over a finite intersection of closed convex sets

alternating projection proximal methods for convex programming and variational inequalities we consider a mixed problem composed in part of finding a zero of a maximal monotone operator and in part of solving a monotone variational inequality problem we propose a solution method for this problem that alternates between a proximal step for the maximal monotone operator part and a projection type step for the monotone variational inequality part and analyze its convergence and rate of convergence this method extends a decomposition method of chen and teboulle math programming 64 1994 pp 81 101 for convex programming and yields as a by product new decomposition methods

a parallel algorithm for a class of convex programs a parallel algorithm is proposed in this paper for solving the problem min q x x in c 1 cap cdots cap c m where q is an uniformly convex function and c i are closed convex sets in r n in each iteration of the method we solve in parallel m independent subproblems each minimizing a definite quadratic function over an individual set c i the method has attractive convergence properties and can be implemented as parallel algorithms for tackling definite quadratic programs linear programs systems of linear equations and systems of generalized nonlinear inequalities

a variable penalty alternating directions method for convex optimization we study a generalized version of the method of alternating directions as applied to the minimization of the sum of two convex functions subject to linear constraints the method consists of solving consecutively in each iteration two optimization problems which contain in the objective function both lagrangian and proximal terms the minimizers determine the new proximal terms and a simple update of the lagrangian terms follows we prove a convergence theorem which extends existing results by relaxing the assumption of uniqueness of minimizers another novelty is that we allow penalty matrices and these may vary per iteration this can be beneficial in applications since it allows additional tuning of the method to the problem and can lead to faster convergence relative to fixed penalties as an application we derive a decomposition scheme for block angular optimization and present computational results on a class of dual block angular problems

on the convergence of han s method for convex programming with quadratic objective we present an iterative method for minimizing strictly convex quadratic functions over the intersection of a finite number of convex sets the method consists in computing projections onto the individual sets simultaneously and the new iterate is a convex combination of those projections we give convergence proofs even for the inconsistent case i e when the intersection of the sets is empty