robust stability of uncertain linear systems with saturating actuators we consider the robust stability of uncertain linear systems with saturating actuators and present two sufficient conditions to guarantee the stability of the closed loop system we assume that the bound of the initial state is known and that the uncertainty is unstructured the obtained results meet our intuition that the lower bound of initial state and the higher bound of saturation level make it easy to design a controller finally we show the usefulness by an example

some koszul rings from geometry abstract we give examples of koszul rings that arise naturally in algebraic geometry in the first part we prove a general result on koszul property associated to an ample line bundle on a projective variety specifically we show how koszul property of multiples of a base point free ample line bundle depends on its castelnuovo mumford regularity in the second part we give examples of koszul rings that come from adjoint line bundles on minimal irregular surfaces of general type

linear free resolutions and minimal multiplicity let s k x x be a polynomial ring over a field and let a4 a m be a finitely generated graded module in the most interesting case a4 is an ideal of s for a given natural number p there is a great interest in the question can m be generated by homogeneous elements of degree p no simple answer say in terms of the local cohomology of m is known but somewhat surprisingly the stronger question can the jth syzygy of m be generated by elements of degree qp j for all j 0 l n does admit a simple response the following is neither new nor difficult to prove though it seems not well known

optimality tests for the fuzzy c means algorithm abstract because of lack of convexity of the fuzzy c means fcm objective functionals the fcm algorithm may converge to a local minimizer or a saddle point in this paper we present a new scheme for testing the optimality of the fixed points of the fcm algorithm one which needs much less computation than kim et al s scheme pattern recognition 21 651 663 1988 we also point out that kim et al s scheme is partly incorrect and propose a repair of it numerical experiments are presented for several sets of data they compare kim et al s scheme the repaired scheme and our scheme

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 fuzzy algorithm for color quantization of images in this paper we review a number of techniques for fuzzy color quantization we show that the fuzzy membership paradigm is particularly suited to color quantization where color cluster boundaries are not well defined we propose a new fuzzy color quantization technique which incorporates a term for partition index this algorithm produces better results than fuzzy c means at a reduced computational cost we test the results of the fuzzy algorithms using quality metrics which model the perception of the human visual system and illustrate that substantial quality improvements are achieved

estimation of parameters in latent class models using fuzzy clustering algorithms abstract a mixture approach to clustering is an important technique in cluster analysis a mixture of multivariate multinomial distributions is usually used to analyze categorical data with latent class model the parameter estimation is an important step for a mixture distribution described here are four approaches to estimating the parameters of a mixture of multivariate multinomial distributions the first approach is an extended maximum likelihood ml method the second approach is based on the well known expectation maximization em algorithm the third approach is the classification maximum likelihood cml algorithm in this paper we propose a new approach using the so called fuzzy class model and then create the fuzzy classification maximum likelihood fcml approach for categorical data the accuracy robustness and effectiveness of these four types of algorithms for estimating the parameters of multivariate binomial mixtures are compared using real empirical data and samples drawn from the multivariate binomial mixtures of two classes the results show that the proposed fcml algorithm presents better accuracy robustness and effectiveness overall the fcml algorithm has the superiority over the ml em and cml algorithms thus we recommend fcml as another good tool for estimating the parameters of mixture multivariate multinomial models

bias correction fuzzy clustering algorithms fuzzy clustering is generally an extension of hard clustering and it is based on fuzzy membership partitions in fuzzy clustering the fuzzy c means fcm algorithm is the most commonly used clustering method numerous studies have presented various generalizations of the fcm algorithm however the fcm algorithm and its generalizations are usually affected by initializations in this paper we propose a bias correction term with an updating equation to adjust the effects of initializations on fuzzy clustering algorithms we first propose the so called bias correction fuzzy clustering of the generalized fcm algorithm we then construct the bias correction fcm bias correction gustafson and kessel clustering and bias correction inter cluster separation algorithms we compared the proposed bias correction fuzzy clustering algorithms with other fuzzy clustering algorithms by using numerical examples we also applied the bias correction fuzzy clustering algorithms to real data sets the results indicated the superiority and effectiveness of the proposed bias correction fuzzy clustering methods

optimality test for generalized fcm and its application to parameter selection in cluster analysis the fuzzy c means fcm clustering algorithm is the best known and most widely used method it was proven to converge to either a local minimum or saddle points by bezdek et al wei and mendel produced efficient optimality tests for fcm fixed points recently a weighting exponent selection for fcm was proposed by yu et al inspired by these results we unify several alternative fcm algorithms into one model called the generalized fuzzy c means gfcm this gfcm model presents a wide variation of fcm algorithms and can easily lead to new and interesting clustering algorithms moreover we construct a general optimality test for gfcm fixed points this is applied to theoretically choose the parameters in the gfcm model the experimental results demonstrate the precision of the theoretical analysis

gaussian clustering method based on maximum fuzzy entropy interpretation abstract a new method of fuzzy clustering is proposed this is a complete gaussian membership function derived by means of the maximum entropy interpretation compared to the traditional fuzzy c means fcm method our approach exhibits the following two advantages 1 having clearer physical meaning and well defined mathematical features 2 having an optimal choice for feature parameter in theory moreover we also review some existing measures of uncertainty of fuzzy sets and redefine fuzzy entropy as analogous to probabilistic entropy

analysis of parameter selections for fuzzy c means the weighting exponent m is called the fuzzifier that can influence the performance of fuzzy c means fcm it is generally suggested that email protected 1 5 2 5 on the basis of a robust analysis of fcm a new guideline for selecting the parameter m is proposed we will show that a large m value will make fcm more robust to noise and outliers however considerably large m values that are greater than the theoretical upper bound will make the sample mean a unique optimizer a simple and efficient method to avoid this unexpected case in fuzzy clustering is to assign a cluster core to each cluster we will also discuss some clustering algorithms that extend fcm to contain the cluster cores in fuzzy clusters for a large theoretical upper bound case we suggest the implementation of the fcm with a suitable large m value otherwise we suggest implementing the clustering methods with cluster cores when the data set contains noise and outliers the fuzzifier m 4 is recommended for both fcm and cluster core based methods in a large theoretical upper bound case

interval valued fuzzy relation based clustering with its application to performance evaluation a similarity relation with its partition tree has been applied in the performance evaluation area for obtaining an agglomerative hierarchical clustering these fuzzy relation based methods require a decision maker to perform pair wise comparisons for the similarity among criteria as forming a fuzzy relation matrix the approach is developed based on real membership values of fuzzy relations however interval valued memberships may be better than real membership values to represent higher order imprecision and vagueness for human perception thus in this paper we would like to extend fuzzy relations to interval valued fuzzy relations and then construct interval valued similarity relations for performance evaluation we first give some definitions for these interval valued types of fuzzy relation similarity relation and resolution form we then construct an interval valued fuzzy similarity relation into a hierarchical structure schema it is shown that both of procedures and results for the partition tree derived from interval valued and crisp valued similarity relation matrices have some corresponding relationships and different merits to demonstrate the usefulness of the proposed approach performance evaluations for academic departments of higher education are considered by using actual engineering school data in taiwan

a generalization of distance functions for fuzzy c means clustering with centroids of arithmetic means fuzzy c means fcm is a widely used fuzzy clustering method which allows an object to belong to two or more clusters with a membership grade between zero and one despite the considerable efforts made by the clustering community the common characteristics of distance functions suitable for fcm remain unclear to fill this crucial void in this paper we first provide a generalized definition of distance functions that fit fcm directly the goal is to provide more flexibility to fcm in the choice of distance functions while preserving the simplicity of fcm by using the centroids of arithmetic means indeed we show that any distance function that fits fcm directly can be derived by a continuously differentiable convex function and thus is an instance of the generalized point to centroid distance p2c d by definition in addition we prove that if the membership grade matrix is nondegenerate any instance of the p2c d fits fcm directly finally extensive experiments have been conducted to demonstrate that the p2c d leads to the global convergence of fcm and that the clustering performances are significantly affected by the choices of distance functions

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

possibilistic and probabilistic fuzzy clustering unification within the framework of the non extensive thermostatistics fuzzy clustering algorithms are becoming the major technique in cluster analysis in this paper we consider the fuzzy clustering based on objective functions they can be divided into two categories possibilistic and probabilistic approaches leading to two different function families depending on the conditions required to state that fuzzy clusters are a fuzzy c partition of the input data recently we have presented in menard and eboueya fuzzy sets and systems 27 to be published an axiomatic derivation of the possibilistic and maximum entropy inference mei clustering approaches based upon an unifying principle of physics that of extreme physical information epi defined by frieden physics from fisher information a unification cambridge university press cambridge 1999 here using the same formalism we explicitly give a new criterion in order to provide a theoretical justification of the objective functions constraint terms membership functions and weighting exponent m used in the probabilistic and possibilistic fuzzy clustering moreover we propose an unified framework including the two procedures this approach is inspired by the work of frieden and plastino and plastino and miller physics a 235 577 extending the principle of extremal information in the framework of the non extensive thermostatistics then we show how with the help of epi one can propose extensions of the fcm and possibilistic algorithms

some wonderful rings in algebraic geometry abstract let a k a1 be a graded ring over a field k the ring is wonderful if torai k k has pure degree i for all i where k a a 1 in a previous paper 4 it was discovered that the ring of regular functions on many cones over abelian varieties is wonderful similarly in 1 backelin has shown that embeddings by high enough trists on ample sheaf on projective schemes give wonderful rings we will estimate high enough and we will note that the coordinate ring of grassmannians in plucker coordinates gives wonderful rings more exactly

clustering construction on a multimodal probability model in 2009 yu et al proposed a multimodal probability model mpm for clustering this paper makes advanced clustering constructions on the mpm we first reconstruct most existing clustering algorithms such as the k means fuzzy c means possibilistic c means mean shift classification maximum likelihood and latent class methods by establishing the relationships between these clustering algorithms and the mpm under our clustering construction we find that the mpm can be seen as a basic probability model for most existing clustering algorithms we then construct new clustering frameworks based on the mpm one of the frameworks develops new penalized type clustering algorithms another one induces entropy type clustering algorithms especially with sample weighted clustering several numerical and real data sets are made for comparisons these experimental results show that our clustering constructions based on the mpm can produce useful and effective clustering algorithms

koszul homology and syzygies of veronese subalgebras a graded k algebra r has property np if it is generated in degree 1 has relations in degree 2 and the syzygies of order p on the relations are linear the green lazarsfeld index of r is the largest p such that it satisfies the property np our main results assert that under a mild assumption on the base field the cth veronese subring of a polynomial ring has green lazarsfeld index c 1 the same conclusion also holds for an arbitrary standard graded algebra provided c gg 0

establishing performance evaluation structures by fuzzy relation based cluster analysis the purpose of this study is to establish hierarchical structures for the performance evaluation of vague humanistic complicated systems to overcome the difficulties due to partial information and the vagueness of human knowledge and recognition a fuzzy relation based clustering method is proposed to model this evaluation first the effects of different max t i compositions on the formation of clusters are discussed then an improved clustering algorithm is developed to produce several partition trees with different levels and clusters according to different t i norm compositions to demonstrate the usefulness of the proposed algorithm the academic departments of higher education were considered using actual engineering school data in taiwan three performance evaluation structures are established by using max t 1 max t 2 and max t 3 compositions the results show that the proposed fuzzy hierarchical approach is useful and practical for performance evaluations of complicated humanistic systems

finite regularity and koszul algebras we determine the positively graded commutative algebras over which the residue field modulo the homogeneous maximal ideal has finite castelnuovo mumford regularity they are the polynomial rings in finitely many indeterminates over koszul algebras this proves a conjecture of avramov and eisenbud we also show that if the residue field of a finitely generated graded algebras has finite regularity then so do all finitely generated graded modules

multiple kernel fuzzy clustering while fuzzy c means is a popular soft clustering method its effectiveness is largely limited to spherical clusters by applying kernel tricks the kernel fuzzy c means algorithm attempts to address this problem by mapping data with nonlinear relationships to appropriate feature spaces kernel combination or selection is crucial for effective kernel clustering unfortunately for most applications it is uneasy to find the right combination we propose a multiple kernel fuzzy c means mkfc algorithm that extends the fuzzy c means algorithm with a multiple kernel learning setting by incorporating multiple kernels and automatically adjusting the kernel weights mkfc is more immune to ineffective kernels and irrelevant features this makes the choice of kernels less crucial in addition we show multiple kernel k means to be a special case of mkfc experiments on both synthetic and real world data demonstrate the effectiveness of the proposed mkfc algorithm

validity guided re clustering with applications to image segmentation when clustering algorithms are applied to image segmentation the goal is to solve a classification problem however these algorithms do not directly optimize classification duality as a result they are susceptible to two problems 1 the criterion they optimize may not be a good estimator of true classification quality and 2 they often admit many suboptimal solutions this paper introduces an algorithm that uses cluster validity to mitigate problems 1 and 2 the validity guided re clustering vgc algorithm uses cluster validity information to guide a fuzzy re clustering process toward better solutions it starts with a partition generated by a soft or fuzzy clustering algorithm then it iteratively alters the partition by applying novel split and merge operations to the clusters partition modifications that result in improved partition validity are retained vgc is tested on both synthetic and real world data for magnetic resonance image mri segmentation evaluations by radiologists show that vgc outperforms the unsupervised fuzzy c means algorithm and vgc s performance approaches that of the supervised k nearest neighbors algorithm

a note on the ics algorithm with corrections and theoretical analysis ozdemir and akarun 2001 proposed an intercluster separation ics fuzzy clustering algorithm the ics algorithm is useful in combined quantization and dithering however there are two errors in the update equations for the ics algorithm this correspondence first points out these errors and gives their corrections since the parameters m c and are important factors in the performance of ics we also conduct a theoretical analysis of these ics parameters in order to analyze the parameters in ics we devise a theorem for the calculation of the hessian matrix from the ics objective function we establish the fixed point property of ics based on the decomposition of the hessian matrix and then analyze the effect of the parameters finally we propose a numerical approach in choosing the appropriate parameters m and for ics these experimental results give a better numerical perspective on the effect of parameters in ics and have conclusions consistent with our theoretical analysis

vector quantization in dct domain using fuzzy possibilistic c means based on penalized and compensated constraints in this paper fuzzy possibilistic c means fpcm approach based on penalized and compensated constraints are proposed to vector quantization vq in discrete cosine transform dct for image compression these approaches are named penalized fuzzy possibilistic c means pfpcm and compensated fuzzy possibilistic c means cfpcm the main purpose is to modify the fpcm strategy with penalized or compensated constraints so that the cluster centroids can be updated with penalized or compensated terms iteratively in order to 4nd near global solution in optimal problem the information transformed by dct was separated into dc and ac coe5cients then the ac coe5cients are trained by using the proposed methods to generate better codebook based on vq the compression performances using the proposed approaches are compared with fpcm and conventional vq method from the experimental results the promising performances can be obtained using the proposed approaches 2002 pattern recognition society published by elsevier science ltd all rights reserved

a method of identifying influential data in fuzzy clustering in multivariate statistical methods it is important to identify influential observations for a reasonable interpretation of the data structure in this paper we propose a method for identifying influential data in the fuzzy c means fcm algorithm to investigate such data we consider a perturbation of the data points and evaluate the effect of a perturbation as a perturbation we consider two cases one is the case in which the direction of a perturbation is specified and the other is the case in which the direction of a perturbation is not specified by computing the change in the clustering result of fcm when given data points are slightly perturbed we can look for data points that greatly affect the result also we confirm an efficacy of the proposed method by numerical examples

on a class of fuzzy classification maximum likelihood procedures classification maximum likelihood cml procedure is a remarkable mixture of maximum likelihood approach to clustering this has been well documented in the book of mclachlan and basford in this paper we make the fuzzy extension of the cml procedure based on this class of fuzzy cml procedures we extend the fuzzy clustering algorithms of trauwaert kaufman and rousseeuw by adding a penalty term especially we derive a generalized type of fuzzy c means fcm clustering algorithms called the penalized fcm clustering algorithms then we create some asymptotic behaviors of these penalized fcm procedures by doing some numerical examples we find that the penalized fcm is more meaningful and effective than fcm

regularity of modules over a koszul algebra abstract we prove that every module over a commutative homogeneous koszul algebra has regularity bounded by its regularity over a polynomial ring of which the koszul algebra is a homomorphic image from this we derive a result conjectured by george kempf to the effect that a sufficiently high truncation of any module over a homogeneous koszul algebra has a linear free resolution

bounded feedback stabilization and global separation principle of distributed parameter systems we show that the infinite dimensional system spl sigma x spl dot t ax t bu t x sub 0 spl epsiv h is globally strongly asymptotically stabilizable by an arbitrarily small smooth feedback here the operator a is the infinitesimal generator of a c sub 0 semigroup of contractions e sup ta on real hilbert space h and b is a bounded linear operator mapping a hilbert space of controls u into h an explicit smooth feedback control law is given further we identify the class of perturbations for which the system is still stabilizable by the same feedback law as for the nominal system based on these results and some differential lyapunov operator equations we then establish a global separation principle for the system spl sigma with a kalman like observer finally these results are illustrated via an example dealing with the wave equation

frbc a fuzzy rule based clustering algorithm fuzzy clustering is superior to crisp clustering when the boundaries among the clusters are vague and ambiguous however the main limitation of both fuzzy and crisp clustering algorithms is their sensitivity to the number of potential clusters and or their initial positions moreover the comprehensibility of obtained clusters is not expertized whereupon in data mining applications the discovered knowledge is not understandable for human users to overcome these restrictions a novel fuzzy rule based clustering algorithm frbc is proposed in this paper like fuzzy rule based classifiers the frbc employs a supervised classification approach to do the unsupervised cluster analysis it tries to automatically explore the potential clusters in the data patterns and identify them with some interpretable fuzzy rules simultaneous classification of data patterns with these fuzzy rules can reveal the actual boundaries of the clusters to illustrate the capability of frbc to explore the clusters in data the experimental results on some benchmark datasets are obtained and compared with other fuzzy clustering algorithms the clusters specified by fuzzy rules are human understandable with acceptable accuracy

subalgebras of bigraded koszul algebras abstract we show that diagonal subalgebras and generalized veronese subrings of a bigraded koszul algebra are koszul we give upper bounds for the regularity of side diagonal and relative veronese modules and apply the results to symmetric algebras and rees rings

fuzzy partition based soft subspace clustering and its applications in high dimensional data as one of the most popular clustering techniques for high dimensional data soft subspace clustering ssc algorithms have been receiving a great deal of attention in recent years unfortunately most existing works do not cluster high dimensional sparse data and noisy data in an effective manner in this study a novel soft subspace clustering algorithm called pi ssc is proposed by introducing a partition index pi into the objective function a novel soft subspace clustering algorithm that combines the concepts of hard and fuzzy clustering is proposed furthermore the robust property of pi ssc is analyzed from the viewpoint of e insensitive distance a convergence theorem for pi ssc is also established by applying zangwill s convergence theorem the results of the experiment demonstrate the effectiveness of the proposed algorithm in high dimensional sparse text data and noisy texture data

enhanced soft subspace clustering integrating within cluster and between cluster information while within cluster information is commonly utilized in most soft subspace clustering approaches in order to develop the algorithms other important information such as between cluster information is seldom considered for soft subspace clustering in this study a novel clustering technique called enhanced soft subspace clustering essc is proposed by employing both within cluster and between class information first a new optimization objective function is developed by integrating the within class compactness and the between cluster separation in the subspace based on this objective function the corresponding update rules for clustering are then derived followed by the development of the novel essc algorithm the properties of this algorithm are investigated and the performance is evaluated experimentally using real and synthetic datasets including synthetic high dimensional datasets uci benchmarking datasets high dimensional cancer gene expression datasets and texture image datasets the experimental studies demonstrate that the accuracy of the proposed essc algorithm outperforms most existing state of the art soft subspace clustering algorithms

fuzzy algorithms for combined quantization and dithering color quantization reduces the number of the colors in a color image while the subsequent dithering operation attempts to create the illusion of more colors with this reduced palette in quantization the palette is designed to minimize the mean squared error mse however the dithering that follows enhances the color appearance at the expense of increasing the mse we introduce three joint quantization and dithering algorithms to overcome this contradiction the basic idea is the same in two of the approaches introducing the dithering error to the quantizer in the training phase the fuzzy c means fcm and the fuzzy learning vector quantization flvq algorithms are used to develop two combined mechanisms in the third algorithm we minimize an objective function including an inter cluster separation ics term to obtain a color palette which is more suitable for dithering the goal is to enlarge the convex hull of the quantization colors to obtain the illusion of more colors after error diffusion the color contrasts of images are also enhanced with the proposed algorithm we test the results of these three new algorithms using quality metrics which model the perception of the human visual system and illustrate that substantial improvements are achieved after dithering

regularity over homomorphisms and a frobenius characterization of koszul algebras abstract let r be a standard graded algebra over an f finite field of characteristic p 0 let r r be the frobenius endomorphism for each finitely generated graded r module m let m be the abelian group m with the r module structure induced by the frobenius endomorphism the r module m has a natural grading given by deg x j if x m j p i for some 0 i p 1 in this paper we prove that r is koszul if and only if there exists a non zero finitely generated graded r module m such that reg r m this result supplies another instance for the ability of the frobenius in detecting homological properties as exemplified by kunz s famous regularity criterion the main technical tool is the notion of castelnuovo mumford regularity over certain homomorphisms between n graded algebras the latter notion is a common generalization of the relative and absolute castelnuovo mumford regularity of modules

sample weighted clustering methods although there have been many researches on cluster analysis considering feature or variable weights little effort has been made regarding sample weights in clustering in practice not every sample in a data set has the same importance in cluster analysis therefore it is interesting to obtain the proper sample weights for clustering a data set in this paper we consider a probability distribution over a data set to represent its sample weights we then apply the maximum entropy principle to automatically compute these sample weights for clustering such method can generate the sample weighted versions of most clustering algorithms such as k means fuzzy c means fcm and expectation maximization em etc the proposed sample weighted clustering algorithms will be robust for data sets with noise and outliers furthermore we also analyze the convergence properties of the proposed algorithms this study also uses some numerical data and real data sets for demonstration and comparison experimental results and comparisons actually demonstrate that the proposed sample weighted clustering algorithms are effective and robust clustering methods

a simple statistics based nearest neighbor cluster detection algorithm we propose a new method for autonomously finding clusters in spatial data the proposed method belongs to the so called nearest neighbor approaches for finding clusters it is a repetitive technique which produces changing averages and deviations of nearest neighbor distance parameters and results in a final set of clusters the proposed technique is capable of eliminating background noise outliers and detection of clusters with different densities in a given data set using a wide variety of data sets we demonstrate that the proposed cluster seeking algorithm performs at least as well as various other currently popular algorithms and in several cases surpasses them in performance highlightsa new clustering algorithm based on simple statistics and lattice metrics is given mathematical rationale is explained in detail and theorem proofs are provided performance classification of the ssnn algorithm is illustrated with 2d datasets jain s benchmark dataset is used to show the ssnn cluster finding capability high dimensional image patterns are included as additional clustering examples

fuzzy c means optimality of solutions and effective termination of the algorithm abstract in this paper the solutions produced by the fuzzy c means algorithm for a general class of problems are examined and a method to test for the local optimality of such solutions is established an equivalent mathematical program is defined for the c means problem utilizing a generalized norm then the properties of the resulting optimization problem are investigated it is shown that the gradient of the resulting objective function at the solution produced by the c means algorithm in this case takes a special structure which can be used in terminating the algorithm moreover the local optimality of the solution obtained is checked utilizing the hessian of the criterion function the solution is a local minimum point if the hessian matrix at this point is positive semidefinite simple rules are proposed to help in checking the definiteness of the matrix

non commutative castelnuovo mumford regularity and as regular algebras abstract let a be a connected graded k algebra with a balanced dualizing complex we prove that a is a koszul as regular algebra if and only if that the castelnuovo mumford regularity and the ext regularity coincide for all finitely generated a modules this can be viewed as a non commutative version of t romer on the regularity over positively graded algebras j algebra 319 2008 1 15 theorem 1 3 by using castelnuovo mumford regularity we prove that any koszul standard as gorenstein algebra is as regular as a preparation to prove the main result we also prove that the following statements are equivalent 1 a is as gorenstein 2 a has finite left injective dimension 3 the dualizing complex has finite left projective dimension this generalizes i mori homological properties of balanced cohen macaulay algebras trans amer math soc 355 2002 1025 1042 corollary 5 9

a generalized fuzzy clustering regularization model with optimality tests and model complexity analysis in this paper we propose a generalized fuzzy clustering regularization gfcr model and then study its theoretical properties gfcr unifies several fuzzy clustering algorithms such as fuzzy c means fcm maximum entropy clustering mec fuzzy clustering based on fermi dirac entropy and fuzzy bidirectional associative clustering network etc the proposed gfcr becomes an alternative model of the generalized fcm gfcm that was recently proposed by yu and yang to advance theoretical study we have the following three considerations 1 we give an optimality test to monitor if gfcr converges to a local minimum 2 we relate the gfcr optimality tests to occam s razor principle and then analyze the model complexity for fuzzy clustering algorithms 3 we offer a general theoretical method to evaluate the performance of fuzzy clustering algorithms finally some numerical experiments are used to demonstrate the validity of our theoretical results and complexity analysis

stabilization of some distributed parameter systems the question of stabilization of perturbed or uncertain infinite dimensional systems is considered one class of perturbations for which the system remains stabilizable by the same feedback law as for the nominal system is identified sufficient conditions are presented that generate strong stabilizability of the perturbed system given that the unperturbed system has similar properties it is also shown that for deterministic as well as stochastic systems exponential stability can be achieved by choice of a suitable feedback controller the theoretical results are illustrated by some numerical examples

fuzzy linear discriminant analysis guided maximum entropy fuzzy clustering algorithm linear discriminant analysis lda is a classical statistical approach for supervised feature extraction and dimensionality reduction hard c means hcm is a classical unsupervised learning algorithm for clustering based on the analysis of the relationship between lda and hcm linear discriminant analysis guided adaptive subspace hard c means clustering algorithm lda hcm had been proposed lda hcm combines lda and hcm into a coherent framework and can adaptively reduce the dimension of data while performing data clustering simultaneously seeing that lda hcm is still a hard clustering algorithm we consider the fuzzy extension version of lda hcm in this paper to this end firstly we propose a new optimization criterion of fuzzy linear discriminant analysis flda by extending the value of membership function in classical lda from binary 0 or 1 into closed interval 0 1 in the meantime we present an efficient algorithm for the proposed flda secondly we show the close relationship between flda and maximum entropy fuzzy clustering algorithm mefca they both are maximizing fuzzy between class scatter and minimizing within class scatter simultaneously finally based on the above analysis combining flda and mefca into a joint framework we propose fuzzy linear discriminant analysis guided maximum entropy fuzzy clustering algorithm flda mefca lda mefca is a natural and effective fuzzy extension of lda hcm due to the introduction of soft decision strategy flda mefca can yield fuzzy partition of data set and is more flexible than lda hcm we also give the convergence proof of flda mefca extensive experiments on a collection of benchmark data sets are presented to show the effectiveness of the proposed algorithm

a novel fuzzy clustering algorithm with between cluster information for categorical data in this paper we present a new fuzzy clustering algorithm for categorical data in the algorithm the objective function of the fuzzy k modes algorithm is modified by adding the between cluster information so that we can simultaneously minimize the within cluster dispersion and enhance the between cluster separation for obtaining the local optimal solutions of the modified objective function the corresponding update formulas of the membership matrix and the cluster prototypes are strictly derived the convergence of the proposed algorithm under the optimization framework is proved on several real data sets from uci the performance of the proposed algorithm is studied the experimental results illustrate that the algorithm is effective and suitable for categorical data sets

minimal free resolution of a finitely generated module over a regular local ring abstract numerical invariants of a minimal free resolution of a module m over a regular local ring r n can be studied by taking advantage of the rich literature on the graded case the key is to fix suitable n stable filtrations m of m and to compare the betti numbers of m with those of the associated graded module gr m m this approach has the advantage that the same module m can be detected by using different filtrations on it it provides interesting upper bounds for the betti numbers and we study the modules for which the extremal values are attained among others the koszul modules have this behavior as a consequence of the main result we extend some results by aramova conca herzog and hibi on the rigidity of the resolution of standard graded algebras to the local setting

homological properties of powers of the maximal ideal of a local ring abstract it is known that the powers m n of the maximal ideal of a local noetherian ring share certain homological properties for all sufficiently large integers n for example the natural homomorphisms r r m n are golod respectively small for all large n we give effective bounds on the smallest integers n for which such properties begin to hold

optimality tests for fixed points of the fuzzy c means algorithm abstract the fuzzy c means fcm clustering algorithms are known to converge to either local minima or saddle points of the objective function which defines the fcm method the object of this paper is to derive efficient numerical tests for local extrema of the fcm functional that enable one to identify each candidate as a local minimum or saddle point numerical examples of the theory derived illustrate that the tests proposed cover all possible cases

on the local optimality of the fuzzy isodata clustering algorithm the convergence of the fuzzy isodata clustering algorithm was proved by bezdek 3 two sets of conditions were derived and it was conjectured that they are necessary and sufficient for a local minimum point in this paper we address this conjecture and explore the properties of the underlying optimization problem the notions of reduced objective function and improving and feasible directions are used to examine this conjecture finally based on the derived properties of the problem a new stopping criterion for the fuzzy isodata algorithm is proposed

the k means type algorithms versus imbalanced data distributions k means is a partitional clustering technique that is well known and widely used for its low computational cost the representative algorithms include the hard k means and the fuzzy k means however the performance of these algorithms tends to be affected by skewed data distributions i e imbalanced data they often produce clusters of relatively uniform sizes even if input data have varied cluster sizes which is called the uniform effect in this paper we analyze the causes of this effect and illustrate that it probably occurs more in the fuzzy k means clustering process than the hard k means clustering process as the fuzzy index m increases the uniform effect becomes evident to prevent the effect of the uniform effect we propose a multicenter clustering algorithm in which multicenters are used to represent each cluster instead of one single center the proposed algorithm consists of the three subalgorithms the fast global fuzzy k means best m plot and grouping multicenter algorithms they will be respectively used to address the three important problems 1 how are the reliable cluster centers from a dataset obtained 2 how are the number of clusters which these obtained cluster centers represent determined 3 how is it judged as to which cluster centers represent the same clusters the experimental studies on both synthetic and real datasets illustrate the effectiveness of the proposed clustering algorithm in clustering balanced and imbalanced data

structural stabilization of uncertain systems necessity of the matching condition this paper investigates one aspect of the problem of stabilizing an uncertain linear system that is the systems under consideration contain uncertain parameters which are unknown but bounded the question arises as to whether such a system can be stabilized via feedback control in some of the previous papers in this area the system is assumed to satisfy a so called matching condition this type of assumption is used to assure that the uncertain system can be stabilized it is known however that the matching condition is not a necessary condition for stabilizability this paper introduces a strengthened notion of stabilizability referred to as structural stabilizability via a nominally determined quadratic lyapunov function it is then shown that if a system is to have this stronger property the matching condition must necessarily be satisfied

koszul blowup algebras associated to three dimensional ferrers diagrams abstract we investigate the rees algebra and the toric ring of the squarefree monomial ideal associated to the three dimensional ferrers diagram under the projection property condition we describe explicitly the presentation ideals of the rees algebra and the toric ring we show that the toric ring is a koszul cohen macaulay normal domain while the rees algebra is koszul and the defining ideal is of fiber type

koszul property of projections of the veronese cubic surface abstract let v p 9 be the veronese cubic surface we classify the projections of v to p 8 whose coordinate rings are koszul in particular we obtain a purely theoretical proof of the koszulness of the pinched veronese a result obtained originally by caviglia using filtrations deformations and computer assisted computations to this purpose we extend to certain complete intersections results of conca herzog trung and valla concerning homological properties of diagonal algebras

rationality of the poincare series for koszul algebras abstract in this paper we study the rationality of the poincare series of a finitely generated graded left module over a koszul connected algebra in particular we show the following result let a be a koszul connected algebra and a be its koszul dual suppose that a is noetherian and having a balanced dualizing complex if a is either 1 an artinian algebra 2 a graded quotient algebra of a noetherian as regular algebra or 3 an fbn algebra e g a noetherian pi algebra then the poincare series of every finitely generated graded left a module is a rational function over the complex numbers