segmentation and classification of range images the recognition of objects in three dimensional space is a desirable capability of a computer vision system range images which directly measure 3 d surface coordinates of a scene are well suited for this task in this paper we report a procedure to detect connected planar convex and concave surfaces of 3 d objects this is accomplished in three stages the first stage segments the range image into surface patches by a square error criterion clustering algorithm using surface points and associated surface normals the second stage classifies these patches as planar convex or concave based on a non parametric statistical test for trend curvature values and eigenvalue analysis in the final stage boundaries between adjacent surface patches are classified as crease or noncrease edges and this information is used to merge compatible patches to produce reasonable faces of the object s this procedure has been successfully applied to a large number of real and synthetic images four of which we present in this paper

a fuzzy extension of the silhouette width criterion for cluster analysis the present paper proposes a new cluster validity measure as an additional criterion to help the decision making process in fuzzy cluster analysis this measure named fuzzy silhouette is a generalization to the fuzzy case of the average silhouette width criterion originally conceived to assess crisp non fuzzy data partitions the fuzzy silhouette is more appealing than its crisp counterpart in the context of fuzzy cluster analysis since it makes explicit use of the fuzzy partition matrix provided by the clustering algorithm in addition it has been designed to improve performance of the original silhouette criterion in detecting regions with higher data density when the data set involves overlapping clusters the performance of the fuzzy silhouette is evaluated and compared to that of five well known cluster validity measures six data sets are used to illustrate different scenarios in which the proposed fuzzy silhouette performs similar to or better than these other criteria thus becoming eligible to join a pool of measures to be used all together in fuzzy cluster analysis

image filtering edge detection and edge tracing using fuzzy reasoning we characterize the problem of detecting edges in images as a fuzzy reasoning problem the edge detection problem is divided into three stages filtering detection and tracing images are filtered by applying fuzzy reasoning based on local pixel characteristics to control the degree of gaussian smoothing filtered images are then subjected to a simple edge detection algorithm which evaluates the edge fuzzy membership value for each pixel based on local image characteristics finally pixels having high edge membership are traced and assembled into structures again using fuzzy reasoning to guide the tracing process the filtering detection and tracing algorithms are tested on several test images comparison is made with a standard edge detection technique

on the monotonicity of hierarchical sum product fuzzy systems abstract motivated by the authors previous work on the control of queueing systems the assessment of sustainable development and the measurement of material recyclability this paper provides sufficient conditions on the parameters of hierarchical fuzzy systems under which the output of the system is monotonic with respect to its inputs this property could be useful in designing multistage fuzzy inference systems and fuzzy controllers

general c means clustering model partitional clustering is an important part of cluster analysis based on various theories numerous clustering algorithms have been developed and new clustering algorithms continue to appear in the literature it is known that occam s razor plays a pivotal role in data based models and partitional clustering is categorized as a data based model however no relation had previously been discovered between occam s razor and partitional clustering as we discuss in this paper the three main contributions of this paper can be summarized as follows 1 according to a novel definition of the mean a unifying generative framework for partitional clustering algorithms called a general c means clustering model gcm is presented and studied and 2 based on the local optimality test of the gcm the connection between occam s razor and partitional clustering is established for the first time as its application a comprehensive review of the existing objective function based clustering algorithms is presented based on gcm 3 under a common assumption about partitional clustering a theoretical guide for devising and implementing clustering algorithm is discovered these conclusions are verified by numerical experimental results

a robust em clustering algorithm for gaussian mixture models clustering is a useful tool for finding structure in a data set the mixture likelihood approach to clustering is a popular clustering method in which the em algorithm is the most used method however the em algorithm for gaussian mixture models is quite sensitive to initial values and the number of its components needs to be given a priori to resolve these drawbacks of the em we develop a robust em clustering algorithm for gaussian mixture models first creating a new way to solve these initialization problems we then construct a schema to automatically obtain an optimal number of clusters therefore the proposed robust em algorithm is robust to initialization and also different cluster volumes with automatically obtaining an optimal number of clusters some experimental examples are used to compare our robust em algorithm with existing clustering methods the results demonstrate the superiority and usefulness of our proposed method

a novel approach to fuzzy clustering based on a dissimilarity relation extracted from data using a ts system clustering refers to the process of unsupervised partitioning of a data set based on a dissimilarity measure which determines the cluster shape considering that cluster shapes may change from one cluster to another it would be of the utmost importance to extract the dissimilarity measure directly from the data by means of a data model on the other hand a model construction requires some kind of supervision of the data structure which is exactly what we look for during clustering so the lower the supervision degree used to build the data model the more it makes sense to resort to a data model for clustering purposes conscious of this we propose to exploit very few pairs of patterns with known dissimilarity to build a ts system which models the dissimilarity relation among other things the rules of the ts system provide an intuitive description of the dissimilarity relation itself then we use the ts system to build a dissimilarity matrix which is fed as input to an unsupervised fuzzy relational clustering algorithm denoted any relation clustering algorithm arca which partitions the data set based on the proximity of the vectors containing the dissimilarity values between each pattern and all the other patterns in the data set we show that combining the ts system and the arca algorithm allows us to achieve high classification performance on a synthetic data set and on two real data sets further we discuss how the rules of the ts system represent a sort of linguistic description of the dissimilarity relation

left ventricle automated detection method in gated isotopic ventriculography using fuzzy clustering a method that uses the fuzzy isodata clustering algorithm and fourier analysis is proposed for automated detection of heart left ventricle contours this operation is used for quantitative analysis of cardiac function the computation begins by finding the phase image the fuzzy isodata algorithm is first applied to this image to generate a number of clusters that correspond to the organ substructures ventricles atria second the ventricles cluster is isolated and the intensities of its points are replaced by the corresponding ones from the original end diastolic frame finally a reduced image representing the ventricular region is obtained and an additional clustering is performed to find the left ventricular boundary automatically this algorithm is tested by application of 105 sets of 16 images each these results are compared with the measurements obtained with two semi automatic methods used respectively on the philips and the sopha medical gamma cameras

a validity measure for fuzzy clustering the authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c partitions without assumptions as to the number of substructures inherent in the data this function depends on the data set geometric distance measure distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used the function is mathematically justified via its relationship to a well defined hard clustering validity function the separation index for which the condition of uniqueness has already been established the performance of this validity function compares favorably to that of several others the application of this validity function to color image segmentation in a computer color vision system for recognition of ic wafer defects which are otherwise impossible to detect using gray scale image processing is discussed

unsupervised optimal fuzzy clustering this study reports on a method for carrying out fuzzy classification without a priori assumptions on the number of clusters in the data set assessment of cluster validity is based on performance measures using hypervolume and density criteria an algorithm is derived from a combination of the fuzzy k means algorithm and fuzzy maximum likelihood estimation the unsupervised fuzzy partition optimal number of classes algorithm performs well in situations of large variability of cluster shapes densities and number of data points in each cluster the algorithm was tested on different classes of simulated data and on a real data set derived from sleep eeg signal

monotonicity and uniqueness results in identifying an unknown coefficient in a nonlinear diffusion equation we consider the problem of identifying an unknown diffusion coefficient in a nonlinear diffusion equation from overspecified data measured on the boundary conditions ensuring compatibility of the data are derived and it is shown that the mapping which carries the diffusion coefficient into the data is isotonic this result is then used to derive a uniqueness result for the inverse problem and for an associated identification problem some results of numerical experiments are presented to illustrate the various results

kernel induced fuzzy clustering of image pixels with an improved differential evolution algorithm a modified differential evolution de algorithm is presented for clustering the pixels of an image in the gray scale intensity space the algorithm requires no prior information about the number of naturally occurring clusters in the image it uses a kernel induced similarity measure instead of the conventional sum of squares distance use of the kernel function makes it possible to partition data that is linearly non separable and non hyper spherical in the original input space into homogeneous groups in a transformed high dimensional feature space a novel search variable representation scheme is adopted for selecting the optimal number of clusters from several possible choices extensive performance comparison over a test suite of 10 gray scale images and objective comparison with manually segmented ground truth indicates that the proposed algorithm has an edge over a few state of the art algorithms for automatic multi class image segmentation

bootstrap technique in cluster analysis abstract we define a method to estimate the number of clusters in a data set e using the bootstrap technique this approach involves the generation of several fake data sets by sampling patterns with replacement in e bootstrapping for each number k of clusters a measure of stability of the k cluster partitions over the bootstrap samples is used to characterize the significance of the k cluster partition for the original data set the value of k which provides the most stable partitions is the estimate of the number of clusters in e the performance of this new technique is demonstrated on both synthetic and real data and is applied to the segmentation of range images

designing fuzzy inference systems from data an interpretability oriented review fuzzy inference systems fis are widely used for process simulation or control they can be designed either from expert knowledge or from data for complex systems fis based on expert knowledge only may suffer from a loss of accuracy this is the main incentive for using fuzzy rules inferred from data designing a fis from data can be decomposed into two main phases automatic rule generation and system optimization rule generation leads to a basic system with a given space partitioning and the corresponding set of rules system optimization can be done at various levels variable selection can be an overall selection or it can be managed rule by rule rule base optimization aims to select the most useful rules and to optimize rule conclusions space partitioning can be improved by adding or removing fuzzy sets and by tuning membership function parameters structure optimization is of a major importance selecting variables reducing the rule base and optimizing the number of fuzzy sets over the years many methods have become available for designing fis from data their efficiency is usually characterized by a numerical performance index however for human computer cooperation another criterion is needed the rule interpretability an implicit assumption states that fuzzy rules are by nature easy to be interpreted this could be wrong when dealing with complex multivariable systems or when the generated partitioning is meaningless for experts the paper analyzes the main methods for automatic rule generation and structure optimization they are grouped into several families and compared according to the rule interpretability criterion for this purpose three conditions for a set of rules to be interpretable are defined

enhancement of the classification and reconstruction performance of fuzzy c means with refinements of prototypes abstract owning to their abilities to reveal structural relationships in data fuzzy clustering plays a pivotal role in fuzzy modeling pattern recognition and data analysis as supporting an unsupervised mode of learning fuzzy clustering brings about unique opportunities to build a structural backbone of numerous constructs in the areas identified above a follow up phase is required when the structural findings developed in the form of fuzzy clusters need some refinements usually when the clustering results are used afterwards in the model being developed in a supervised mode following this general line of thought in this study we propose a novel approach to optimize the clustering and classification performance of the fuzzy c means fcm algorithm proceeding with a collection of clusters information granules produced by the fcm we carry out the refinements of the results in order to improve the representation or classification capabilities of fuzzy clusters by adjusting a location of the prototypes so that a certain performance index becomes optimized at this phase the optimization is carried out in a supervised mode with the aid of differential evolution de we propose five different strategies to adjust a location of the prototypes experimental studies completed on synthetic data and publicly available real world data quantify the improvement of the representation and classification abilities of the clustering method

a novel cluster validity index for fuzzy clustering based on bipartite modularity a novel cluster validity index whose implementation is based on the membership degrees and improved bipartite modularity of bipartite network is proposed for the validation of partitions produced by the fuzzy c means fcm algorithm fcm algorithm is employed to group the dataset in order to obtain the membership degree of samples then a weighted bipartite network is constructed by samples and centroids of each cluster this allows the introduction of a new measurement for optimizing the numbers of clusters for fuzzy partitions the proposed index utilizes the optimum membership as its global property and the modularity of bipartite network as its local independent property the proposed index is compared with a number of popular validation indices on fifteen datasets the experimental results show that the effectiveness and reliability of the proposal is superior to other indices

a clustering performance measure based on fuzzy set decomposition clustering is primarily used to uncover the true underlying structure of a given data set and for this purpose it is desirable to subject the same data to several different clustering algorithms this paper attempts to put an order on the various partitions of a data set obtained from different clustering algorithms the goodness of each partition is expressed by means of a performance measure based on a fuzzy set decomposition of the data set under consideration several experiments reported in here show that the proposed performance measure puts an order on different partitions of the same data which is consistent with the error rate of a classifier designed on the basis of the obtained cluster labelings

performance evaluation of some clustering algorithms and validity indices in this article we evaluate the performance of three clustering algorithms hard k means single linkage and a simulated annealing sa based technique in conjunction with four cluster validity indices namely davies bouldin index dunn s index calinski harabasz index and a recently developed index i based on a relation between the index i and the dunn s index a lower bound of the value of the former is theoretically estimated in order to get unique hard k partition when the data set has distinct substructures the effectiveness of the different validity indices and clustering methods in automatically evolving the appropriate number of clusters is demonstrated experimentally for both artificial and real life data sets with the number of clusters varying from two to ten once the appropriate number of clusters is determined the sa based clustering technique is used for proper partitioning of the data into the said number of clusters

fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation ii shell clustering algorithms are ideally suited for computer vision tasks such as boundary detection and surface approximation particularly when the boundaries have jagged or scattered edges and when the range data is sparse this is because shell clustering is insensitive to local aberrations it can be performed directly in image space and unlike traditional approaches it does assume dense data and does not use additional features such as curvatures and surface normals the shell clustering algorithms introduced in part i of this paper assume that the number of clusters is known however which is not the case in many boundary detection and surface approximation applications this problem can be overcome by considering cluster validity we introduce a validity measure called surface density which is explicitly meant for the type of applications considered in this paper we show through theoretical derivations that surface density is relatively invariant to size and partiality incompleteness of the clusters we describe unsupervised clustering algorithms that use the surface density measure and other measures to determine the optimum number of shell clusters automatically and illustrate the application of the proposed algorithms to boundary detection in the case of intensity images and to surface approximation in the case of range images

a symmetry based multiobjective clustering technique for automatic evolution of clusters in this paper the problem of automatic clustering a data set is posed as solving a multiobjective optimization moo problem optimizing a set of cluster validity indices simultaneously the proposed multiobjective clustering technique utilizes a recently developed simulated annealing based multiobjective optimization method as the underlying optimization strategy here variable number of cluster centers is encoded in the string the number of clusters present in different strings varies over a range the points are assigned to different clusters based on the newly developed point symmetry based distance rather than the existing euclidean distance two cluster validity indices one based on the euclidean distance xb index and another recently developed point symmetry distance based cluster validity index sym index are optimized simultaneously in order to determine the appropriate number of clusters present in a data set thus the proposed clustering technique is able to detect both the proper number of clusters and the appropriate partitioning from data sets either having hyperspherical clusters or having point symmetric clusters a new semi supervised method is also proposed in the present paper to select a single solution from the final pareto optimal front of the proposed multiobjective clustering technique the efficacy of the proposed algorithm is shown for seven artificial data sets and six real life data sets of varying complexities results are also compared with those obtained by another multiobjective clustering technique mock two single objective genetic algorithm based automatic clustering techniques vgaps clustering and gcuk clustering

observer biased fuzzy clustering as generated by clustering algorithms clusterings or partitions are hypotheses on data explanation which are better evaluated by experts from the application domain in general clustering algorithms allow a limited usage of domain knowledge about the cluster formation process in this study we propose both a design technique and a new partitioning based clustering algorithm which can be used to assist the data analyst while looking for a set of meaningful clusters i e clusters that actually correspond to the underlying data structure following an observer metaphor according to which the perception of a group of objects depends on the observer position the closer an observer is from an image more details s he perceives we resort to shrinkage to incorporate a regularization term accounting for the observation point within the objective function of an otherwise unbiased clustering algorithm this technique allows our resulting biased algorithm to generate a set of reasonable partitions i e partitions validated by a given cluster validity index corresponding to views of data with different levels of granularity levels of detail in different regions of the data space for the illustration of the design technique we adopted the fuzzy c means fcm algorithm as the unbiased clustering algorithm and include a convergence theorem assuring that changing the point of observation in the corresponding biased algorithm fcm with focal point fcmfp does not jeopardize its convergence experimental studies on both synthetic and real data are included to illustrate the usefulness of the approach in addition and as a convenient side effect of using shrinkage the experimental results suggest that our biased algorithm fcmfp not only seems to scale better than the successive runs of the unbiased one fcm but on the average seems to produce clusters exhibiting higher validity index values as well in addition less sensitivity to initialization was observed for the biased algorithm when compared with the unbiased one

an efficient approach for unsupervised fuzzy clustering based on grouping evolution strategies fuzzy data clustering plays an important role in practical use and has become a prerequisite step for decision making in fuzzy environment in this paper we propose a new algorithm called fuzzyges for unsupervised fuzzy clustering based on adaptation of the recently proposed grouping evolution strategy ges to adapt ges for fuzzy clustering we devise a fuzzy counterpart of the grouping mutation operator typically used in ges and employ it in a two phase procedure to generate a new clustering solution unlike conventional clustering algorithms which should get the number of clusters as an input fuzzyges tries to determine the true number of clusters as well as providing the optimal cluster centroids after several iterations the proposed approach is validated through using several data sets and results are compared with those of fuzzy c means algorithm particle swarm optimization algorithm pso differential evolution de and league championship algorithm lca we also investigate the performance of fuzzyges through using different cluster validity indices our results indicate that fuzzyges is fast and provides acceptable results in terms of both determining the correct number of clusters and the accurate cluster centroids

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

quantum probabilities as dempster shafer probabilities in the lattice of subspaces the orthocomplemented modular lattice of subspaces l h d of a quantum system with d dimensional hilbert space h d is considered a generalized additivity relation which holds for kolmogorov probabilities is violated by quantum probabilities in the full lattice l h d it is only valid within the boolean subalgebras of l h d this suggests the use of more general than kolmogorov probability theories and here the dempster shafer probability theory is adopted an operator d h1 h2 which quantifies deviations from kolmogorov probability theory is introduced and it is shown to be intimately related to the commutator of the projectors p h1 p h2 to the subspaces h1 h2 as an application it is shown that the proof of the inequalities of clauser horne shimony and holt for a system of two spin 1 2 particles is valid for kolmogorov probabilities but it is not valid for dempster shafer probabilities the violation of these inequalities in experiments supports the interpretation of quantum proba

relational generalizations of cluster validity indices numerous computational schemes have arisen over the years that attempt to learn information about objects based upon the similarity or dissimilarity of one object to another one such scheme clustering looks for self similar groups of objects to use clustering algorithms an investigator must often have a priori knowledge of the number of clusters i e c to search for in the data moreover it is often convenient to have ways to rank the returned results either for a single value of c a range of c s different clustering methods or any combination thereof however the task of assessing the quality of the results so that c may be determined objectively is currently ill defined for object object relationships to bridge this gap we generalize three well known validity indices the modified hubert s gamma xie beni and the generalized dunn s indices to relational data in doing so we develop a framework to convert many other validity indices to a relational form numerical examples on 12 datasets samples from four normal mixtures four real world object datasets and four real world pure relational datasets using the relational duals of the hard fuzzy and possibilistic c means cluster algorithms are offered to illustrate and evaluate the new indices

application of finite difference method to analysis an ill posed problem abstract in this paper a numerical solution of an inverse non dimensional heat conduction problem will be considered by using a sensor located at a point inside the body and measuring the temperature at a point x x 1 0 x 1

some new qualitative insights into quality of fuzzy rule based models rules in fuzzy rule based models convey essential knowledge about the system under discussion as such they capture the essence of relationships occurring among input and output variables while the quality of such fuzzy models is predominantly related with the accuracy and eventual interpretability of rules although to a limited extent the quality of rules being regarded as generic pieces of knowledge has not been studied so far in this study we formulate and investigate this problem by looking at the quality of rules including aspects of a stability b generalizability and c conflict we identify a concept of rule multiplicity conflict and study an emergence of rule generalization a number of pertinent performance indices are developed and their usage is presented through a series of experimental studies

a numerical method for solving of a nonlinear inverse diffusion problem in this paper we will first study the existence and uniqueness of the solution for a one dimensional nonlinear inverse diffusion problem via an auxiliary problem and the schauder fixed point theorem furthermore a numerical algorithm based on the finite difference method and the least squares scheme for solving a nonlinear inverse problem is proposed at the beginning of the numerical algorithm taylor s series expansion is employed to linearize nonlinear terms and then the finite difference method is used to discretize the problem domain the present approach is to rearrange the matrix forms of the differential governing equations and estimate the unknown diffusion coefficient the least squares method is adopted to find the solution it is assumed that no prior information is available on the functional form of the unknown diffusion coefficient in the present study and thus it is classified as the function estimation in inverse calculation results show that an excellent estimation on the diffusion coefficient can be obtained within a couple of minutes of cpu time on a pentium iv 2 4ghz pc

iterative fuzzy clustering algorithm with supervision to construct probabilistic fuzzy rule base from numerical data to deal with data patterns with linguistic ambiguity and with probabilistic uncertainty in a single framework we construct an interpretable probabilistic fuzzy rule based system that requires less human intervention and less prior knowledge than other state of the art methods specifically we present a new iterative fuzzy clustering algorithm that incorporates a supervisory scheme into an unsupervised fuzzy clustering process the learning process starts in a fully unsupervised manner using fuzzy c means fcm clustering algorithm and a cluster validity criterion and then gradually constructs meaningful fuzzy partitions over the input space the corresponding fuzzy rules with probabilities are obtained through an iterative learning process of selecting clusters with supervisory guidance based on the notions of cluster pureness and class separability the proposed algorithm is tested first with synthetic data sets and benchmark data sets from the uci repository of machine learning database and then with real facial expression data and tv viewing data

fuzzy clustering with supervision this study is concerned with clustering carried out in presence of labeled patterns an objective of this optimization is to reconcile between the structure residing in data and being primarily discovered by the underlying clustering mechanism and the labels of the patterns forming such structure in this sense one can consider the supervised fuzzy clustering to be a framework of preliminary data analysis providing with a thorough insight into the structure of the data and supporting the ensuing design of detailed classifiers the proposed method augments the standard fuzzy c means algorithm by extending the original objective function by the supervision component labeled patterns experimental results illustrate the approach and discuss the use of this type of clustering in vector quantization

lda based clustering algorithm and its application to an unsupervised feature extraction research has shown fuzzy c means fcm clustering to be a powerful tool to partition samples into different categories however the objective function of fcm is based only on the sum of distances of samples to their cluster centers which is equal to the trace of the within cluster scatter matrix in this study we propose a clustering algorithm based on both within and between cluster scatter matrices extended from linear discriminant analysis lda and its application to an unsupervised feature extraction fe our proposed methods comprise between and within cluster scatter matrices modified from the between and within class scatter matrices of lda the scatter matrices of lda are special cases of our proposed unsupervised scatter matrices the results of experiments on both synthetic and real data show that the proposed clustering algorithm can generate similar or better clustering results than 11 popular clustering algorithms k means k medoid fcm the gustafson kessel gath geva possibilistic c means pcm fuzzy pcm possibilistic fcm fuzzy compactness and separation a fuzzy clustering algorithm based on a fuzzy treatment of finite mixtures of multivariate student s t distributions algorithms and a fuzzy mixture of the student s t factor analyzers model the results also show that the proposed fe outperforms principal component analysis and independent component analysis

a multiresolution image segmentation technique based on pyramidal segmentation and fuzzy clustering in this paper an unsupervised image segmentation technique is presented which combines pyramidal image segmentation with the fuzzy c means clustering algorithm each layer of the pyramid is split into a number of regions by a root labeling technique and then fuzzy c means is used to merge the regions of the layer with the highest image resolution a cluster validity functional is used to find the optimal number of objects automatically segmentation of a number of synthetic as well as clinical images is illustrated and two fully automatic segmentation approaches are evaluated which determine the left ventricular volume lv in 140 cardiovascular magnetic resonance mr images first fuzzy c means is applied without pyramids in the second approach the regions generated by pyramidal segmentation are merged by fuzzy c means the correlation coefficients of manually and automatically defined lv lumen of all 140 and 20 end diastolic images were equal to 0 86 and 0 79 respectively when images were segmented with fuzzy c means alone these coefficients increased to 0 90 and 0 93 when the pyramidal segmentation was combined with fuzzy c means this method can be applied to any dimensional representation and at any resolution level of an image series the evaluation study shows good performance in detecting lv lumen in mr images

comonotonicity and choquet integrals of hermitian operators and their applications in a quantum system with d dimensional hilbert space the q function of a hermitian positive semidefinite operator is defined in terms of the d 2 coherent states in this system the choquet integral of the q function of is introduced using a ranking of the values of the q function and mobius transforms which remove the overlaps between coherent states it is a figure of merit of the quantum properties of hermitian operators and it provides upper and lower bounds to various physical quantities in terms of the q function comonotonicity is an important concept in the formalism which is used to formalize the vague concept of physically similar operators comonotonic operators are shown to be bounded with respect to an order based on choquet integrals applications of the formalism to the study of the ground state of a physical system are discussed bounds for partition functions are also derived

detecting change points for shifts in mean and variance using fuzzy classification maximum likelihood change point algorithms knowing the time of changes called change point cp in a process is crucial for engineers to recognize the root cause fast and accurately since special causes may induce simultaneous changes in mean and variance detecting changes in both at once is required many methodologies in quality control were developed for detecting changes in either mean or variance only and process parameters were assumed known often however they are rarely known exactly and a small estimation error may lead to unfavorable cp estimates fuzzy partitioning is better suited to cases of vague boundaries between two segments which appear very often in reality a new mechanism called fuzzy classification maximum likelihood change point fcml cp algorithm is proposed to detect shifts in mean and variance simultaneously a cp framework is transferred into a mixture model and then a fcml cp algorithm is created through fuzzy classification maximum likelihood procedures the proposed fcml cp can be applied to phase i and ii processes without knowledge of in control process parameters it can estimate multiple cps of process mean or and variance simultaneously the effectiveness and superiority of fcml cp are shown by extensive experiments with numerical and real data sets specifically the proposed fcml cp is superior to the commonly used statistical mixture likelihood approach using expectation maximization em algorithm it is much more time saving especially the remarkable performance of fcml cp in detecting cps for small changes is particularly important and helpful for engineers to recognize the special cause fast and correctly since an out of control signal resulted from small changes is usually delayed long we propose a new algorithm fcml cp to detect change points in a statistical process the mixture likelihood embedded fuzzy c partition is utilized to estimate the change points the method outperforms statistical likelihood approaches various experiments show the effectiveness and practicability of the proposed method excellent performance in detecting small changes is helpful for root cause analyses

fuzzy system modeling in pharmacology an improved algorithm in this paper we propose an improved fuzzy system modeling algorithm to address some of the limitations of the existing approaches identified during our modeling with pharmacological data this algorithm differs from the existing ones in its approach to the cluster validity problem i e number of clusters the projection schema i e input membership assignment and rule determination and significant input determination the new algorithm is compared with the bazoon turksen model which is based on the well known sugeno yasukawa approach the comparison was made in terms of predictive performance using two different data sets the first comparison was with a two variable nonlinear function prediction problem and the second comparison was with a clinical pharmacokinetic modeling problem it is shown that the proposed algorithm provides more precise predictions determining the degree of significance for each input variable allows the user to distinguish their relative importance

a novel binary artificial bee colony algorithm based on genetic operators this study proposes a novel binary version of the artificial bee colony algorithm based on genetic operators gb abc such as crossover and swap to solve binary optimization problems integrated to the neighbourhood searching mechanism of the basic abc algorithm the modification comprises four stages 1 in neighbourhood of a current food source randomly select two food sources from population and generate a solution including zeros zero outside the population 2 apply two point crossover operator between the current two neighbourhood global best and zero food sources to create children food sources 3 apply swap operator to the children food sources to generate grandchildren food sources and 4 select the best food source as a neighbourhood food source of the current solution among the children and grandchildren food sources in this way the global local search ability of the basic abc algorithm is improved in binary domain the effectiveness of the proposed algorithm gb abc is tested on two well known binary optimization problems dynamic image clustering and 0 1 knapsack problems the obtained results clearly indicate that gb abc is the most suitable algorithm in binary optimization when compared with the other well known existing binary optimization algorithms in addition the achievement of the proposed algorithm is supported by applying it to the cec2005 benchmark numerical problems

cluster validity for fuzzy clustering algorithms abstract the proportion exponent is introduced as a measure of the validity of the clustering obtained for a data set using a fuzzy clustering algorithm it is assumed that the output of an algorithm includes a fuzzy nembership function for each data point we show how to compute the proportion of possible memberships whose maximum entry exceeds the maximum entry of a given membership function and use these proportions to define the proportion exponent its use as a validity functional is illustrated with four numerical examples and its effectiveness compared to other validity functionals namely classification entropy and partition coefficient

clustering of the self organizing map using a clustering validity index based on inter cluster and intra cluster density the self organizing map som has been widely used in many industrial applications classical clustering methods based on the som often fail to deliver satisfactory results specially when clusters have arbitrary shapes in this paper through some preprocessing techniques for filtering out noises and outliers we propose a new two level som based clustering algorithm using a clustering validity index based on inter cluster and intra cluster density experimental results on synthetic and real data sets demonstrate that the proposed clustering algorithm is able to cluster data better than the classical clustering algorithms based on the som and find an optimal number of clusters

use of a fuzzy granulation degranulation criterion for assessing cluster validity the identification of a suitable clustering algorithm to partition data and assessment of the validity of the resultant partitioning are ongoing quests in unsupervised learning in this study a fuzzy granulation degranulation criterion is proposed to evaluate the goodness of a fuzzy partitioning of the data this in turn is used to determine the appropriate clustering algorithm suitable for a particular data set in general the quality of a partitioning is measured by computing the variance within it which is a measure of compactness of the obtained partitioning here a new error function which reflects how well the computed cluster centers represent the whole data set is used as the goodness measure of the obtained partitioning thus a clustering algorithm providing a good set of cluster centers which approximate well the whole data set is considered to be the most suited thereafter this new fuzzy granulation degranulation criterion is used to develop six new cluster validity indices these indices mimic the definitions of the existing and well known cluster validity indices such as pbm index xb index ps index fs index k index and sv index but use the new fuzzy granulation degranulation based error function instead of cluster compactness in order to evaluate the effectiveness of the proposed error function in correctly identifying the appropriate clustering algorithm for a particular data set eight well known clustering algorithms k means fuzzy c means gak means genetic algorithm based k means algorithm a newly developed genetic point symmetry based clustering technique gaps clustering average linkage clustering algorithm expectation maximization em clustering algorithm self organizing map som and spectral clustering technique are evaluated on a set of six artificially generated and six real life data sets results show that gak means is the most appropriate for most of the data sets used for the experiments thereafter the effectiveness of the proposed cluster validity indices in identifying the appropriate number of clusters automatically from different data sets are shown for above mentioned 12 data sets for the purpose of comparison results obtained with the original versions of the proposed cluster validity indices and results obtained by a density based clustering technique are also presented

quasi solution approach for a two dimensional nonlinear inverse diffusion problem this paper is related to a class of inverse problems for identification of the coefficient in a square porous medium the unknown coefficient depends on the solution and belongs the class of admissible coefficients using continuous dependence of solutions on the coefficient convergence in the corresponding direct problems the existence of the quasi solution of the inverse problem is obtained in the appropriate class of admissible coefficients

cluster validity for the fuzzy c means clustering algorithrm the uniform data function is a function which assigns to the output of the fuzzy c means fc m or fuzzy isodata algorithm a number which measures the quality or validity of the clustering produced by the algorithm for the preselected number of cluster c the fc m algorithm produces c vectors in the space in which the data lie called cluster centers which represent points about which the data are concentrated it also produces for each data point c membership values numbers between zero and one which measure the similarity of the data points to each of the cluster centers it is these membership values which indicate how the point is classified they also indicate how well the point has been classified in that values close to one indicate that the point is close to a particular center but uniformly low memberships indicate that the point has not been classified clearly the uniform data functional udf combines the memberships in such a way as to indicate how well the data have been classified and is computed as follows for each data point compute the ratio of its smallest membership to its largest and then compute the probability that one could obtain a smaller ratio indicating better classification from a clustering of a standard data set in which there is no cluster structure these probabilities are then averaged over the data set to obtain the values of the udf

a new fuzzy clustering validity index with a median factor for centroid based clustering determining the number of clusters which is usually approved by domain experts or evaluated by clustering validity indexes is an important issue in clustering analysis this study discusses the effectiveness of clustering validity indexes for centroid based partitional clustering algorithms most general purpose clustering validity indexes take the minimum maximum distance between a pair of data objects a pair of cluster centroids or an object and a centroid as an important evaluation factor however they may present unstable results especially when two centroids are allocated closely to alleviate this problem a new clustering validity index which is termed the wu and li index wli is proposed in this paper our proposed wli partially allows to some extent the existence of closely allocated centroids in the clustering results by considering not only the minimum but the median distances between a pair of centroids as well therefore possessing better stability the performances of wli and some existing clustering validity indexes are evaluated and compared by running the fuzzy c means algorithm for clustering various types of datasets including artificial datasets uci datasets and images experimental results have shown that wli has the more accurate and satisfactory performance than other indexes

hierarchical unsupervised fuzzy clustering a recursive algorithm for hierarchical fuzzy partitioning is presented the algorithm has the advantages of hierarchical clustering while maintaining fuzzy clustering rules each pattern can have a nonzero membership in more than one subset of the data in the hierarchy optimal feature extraction and reduction is optionally reapplied for each subset combining hierarchical and fuzzy concepts is suggested as a natural feasible solution to the cluster validity problem of real data the convergence and membership conservation of the algorithm are proven the algorithm is shown to be effective for a variety of data sets with a wide dynamic range of both covariance matrices and number of members in each class

a clustering procedure for exploratory mining of vector time series a two step procedure is developed for the exploratory mining of real valued vector multivariate time series using partition based clustering methods the proposed procedure was tested with model generated data multiple sensor based process data as well as simulation data the test results indicate that the proposed procedure is quite effective in producing better clustering results than a hidden markov model hmm based clustering method if there is a priori knowledge about the number of clusters in the data two existing validity indices were tested and found ineffective in determining the actual number of clusters determining the appropriate number of clusters in the case that there is no a priori knowledge is a known unresolved research issue not only for our proposed procedure but also for the hmm based clustering method and further development is necessary

single point iterative weighted fuzzy c means clustering algorithm for remote sensing image segmentation in this paper a remote sensing image segmentation procedure that utilizes a single point iterative weighted fuzzy c means clustering algorithm is proposed based upon the prior information this method can solve the fuzzy c means algorithm s problem that the clustering quality is greatly affected by the data distributing and the stochastic initializing the centrals of clustering after the probability statistics of original data the weights of data attribute are designed to adjust original samples to the uniform distribution and added in the process of cyclic iteration which could be suitable for the character of fuzzy c means algorithm so as to improve the precision furthermore appropriate initial clustering centers adjacent to the actual final clustering centers can be found by the proposed single point adjustment method which could promote the convergence speed of the overall iterative process and drastically reduce the calculation time otherwise the modified algorithm is updated from multidimensional data analysis to color images clustering moreover with the comparison experiments of the uci data sets public berkeley segmentation dataset and the actual remote sensing data the real validity of proposed algorithm is proved

a theory of fuzzy measures representations the choquet integral and null sets abstract some theorems of t murofushi and m sugeno fuzzy sets and systems 29 1989 201 227 concerning representation of fuzzy measures and the choquet integral are generalized it is shown that if there is a certain relation between two measurable functions then the choquet integral is additive for these two functions in addition this article discusses null sets with respect to fuzzy measures and also fuzzy measures defined on a class which is not a algebra

existence and uniqueness of a solution for a two dimensional nonlinear inverse diffusion problem abstract the problem of identifying the coefficient in a square porous medium is considered it is shown that under certain conditions of data f g and for a properly specified class a of admissible coefficients there exists at least one a a such that a u is a solution of the corresponding inverse problem