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

blind deconvolution of multi input single output systems with binary sources the problem of blind source separation for multi input single output miso systems with binary inputs is treated in this paper our approach exploits the constellation properties of the successor values for each output sample in the absence of noise the successors of each output value form a characteristic finite set of clusters successor constellation the shape of this constellation is invariant of the predecessor value and it only depends on the last filter tap consequently the localization of the successors constellation can lead to the removal of the last filter tap thus reducing the length of the filter a process we call channel deflation based on the successor observation clustering soc we develop two algorithms for blind source separation soc 1 and soc 2 differing mainly on the required size of the data set furthermore the treatment of the system in the presence of noise is described using data clustering and data correction the problem of noise is attacked using a statistical mode based method moreover we correct the problem of misclassified observations using an iterative scheme based on the viterbi algorithm for the decoding of a hidden markov model hmm

application of renyi and tsallis entropies to topic modeling optimization abstract this study proposes to minimize renyi and tsallis entropies for finding the optimal number of topics t in topic modeling tm a promising tool to obtain knowledge about large text collections tm is a method whose properties are underresearched in particular parameter optimization in such models has been hindered by the use of monotonous quality functions with no clear thresholds in this research topic models obtained from large text collections are viewed as nonequilibrium complex systems where the number of topics is regarded as an equivalent of temperature this allows calculating free energy of such systems a value through which both renyi and tsallis entropies are easily expressed numerical experiments with four tm algorithms and two text collections show that both entropies as functions of the number of topics yield clear minima in the middle area of the range of t on the marked up dataset the minima of three algorithms correspond to the value of t detected by humans it is concluded that tsallis and especially renyi entropy can be used for t optimization instead of shannon entropy that decreases even when t becomes obviously excessive additionally some algorithms are found to be better suited for revealing local entropy minima finally we test whether the overall content of all topics taken together is resistant to the change of t and find out that this dependence has a quasi periodic structure which demands further research

generation of complex bipartite graphs by using a preferential rewiring process it is important in computer science sociology and so on to investigate complex bipartite graphs from a viewpoint of statistical physics we propose a model to generate complex bipartite graphs without growing the bipartite graphs are assumed to have two sets of the fixed numbers of nodes and a fixed number of edges between nodes belonging to different sets of nodes in this model essential ingredients are a preferential rewiring process and a fitness distribution function by using the preferential rewiring process we confirm that a bipartite graph reaches a stationary state after a sufficiently long time has passed we find that the obtained bipartite graph has a scale free like property when a suitable fitness distribution is used it turns out that a condensation of edges takes place in the cases of certain fitness distributions

models of social networks based on social distance attachment we propose a class of models of social network formation based on a mathematical abstraction of the concept of social distance social distance attachment is represented by the tendency of peers to establish acquaintances via a decreasing function of the relative distance in a representative social space we derive analytical results corroborated by extensive numerical simulations showing that the model reproduces the main statistical characteristics of real social networks large clustering coefficient positive degree correlations and the emergence of a hierarchy of communities the model is confronted with the social network formed by people that shares confidential information using the pretty good privacy pgp encryption algorithm the so called web of trust of pgp

dynamic clustering detection through multi valued descriptors of dermoscopic images this paper introduces a dynamic clustering methodology based on multi valued descriptors of dermoscopic images the main idea is to support medical diagnosis to decide if pigmented skin lesions belonging to an uncertain set are nearer to malignant melanoma or to benign nevi melanoma is the most deadly skin cancer and early diagnosis is a current challenge for clinicians most data analysis algorithms for skin lesions discrimination focus on segmentation and extraction of features of categorical or numerical type as an alternative approach this paper introduces two new concepts first it considers multi valued data that scalar variables not only describe but also intervals or histogram variables second it introduces a dynamic clustering method based on wasserstein distance to compare multi valued data the overall strategy of analysis can be summarized into the following steps first a segmentation of dermoscopic images allows to identify a set of multi valued descriptors second we performed a discriminant analysis on a set of images where there is an a priori classification so that it is possible to detect which features discriminate the benign and malignant lesions and third we performed the proposed dynamic clustering method on the uncertain cases which need to be associated to one of the two previously mentioned groups results based on clinical data show that the grading of specific descriptors associated to dermoscopic characteristics provides a novel way to characterize uncertain lesions that can help the dermatologist s diagnosis

a novel validity index with dynamic cut off for determining true clusters in a multi surveillance environment voluminous data is generated over a period of time data analysis for summarization and conclusion has paved a way for the need of an efficient clusterization clustering an unsupervised way of learning about data aims at defining clusters validation of clusters formed indicates the trueness of the clusters in this paper a novel validation technique with dynamic termination of clustering process has been proposed to obtain true clusters in the validation process the validity index is based on both global cluster proximity relationship and local proximity relationship the validity index is computed for validating the available clusters using within cluster sum of squares between cluster sum of squares total sum of squares intra cluster distances and inter cluster distances the ratio between two consecutive validity indices is the extent of variation which specifies the cut off point cut off terminates the clustering process dynamically indicating the number of clusters and validates the obtained clusters the proposed method is tested on several real and synthetic data sets comparisons with the existing methods demonstrate the efficiency of the proposed method in detecting true clusters a novel validation technique has been proposed to obtain true clusters the method dynamically terminates the clustering at true conception of clusters global and local proximity relationship of clusters are considered for validation

how many clusters are best an experiment this paper reports the results of a monte carlo study on the relative effectiveness of two internal indices in estimating the true number of clusters in multivariate data the two indices are the davies and bouldin 1 index and a new modification of the hubert statistic 2 data in d dimensions are clustered to create sequences of partitions estimates are based on plots of the indices as functions of the number of recovered clusters neither index uses a priori information the effects of sample size dimensionality cluster spread number of true clusters and sampling window are examined clustered data are generated to assure a given number of distinct clusters the degree of clustering in the data is verified by a separate monte carlo study based on the jaccard and corrected rand indices that exhibits the importance of correcting external indices for chance the modified hubert index proposed here for the first time is shown to perform better than the davies bouldin index under all experimental conditions recovery of the true number of clusters gets better as the number of true clusters decreases and as the number of dimensions increases no effect occurs due to sampling window the complete link clustering method and a square error clustering method recognize the true number of clusters consistently better than the single link method this study demonstrates the difficulty inherent in estimating the number of clusters

a new sequential classifier using information criterion window abstract we propose a model based parametric unsupervised sequential classifier with an information criterion window icw based on the assumption that the number of clusters changes smoothly from a stage to the following stage to determine the number of clusters at each stage and to perform classification on the observed mixture data the proposed approach provides possible solutions for two problems of pattern recognition adaptive classification and sequential clustering validation simulation results demonstrate that the proposed algorithm provides good results for pure mixed data and successfully performs clustering for the mixed gaussian data in the large sample limit

finding community structure in networks using the eigenvectors of matrices we consider the problem of detecting communities or modules in networks groups of vertices with a higher than average density of edges connecting them previous work indicates that a robust approach to this problem is the maximization of the benefit function known as modularity over possible divisions of a network here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix which plays a role in community detection similar to that played by the graph laplacian in graph partitioning calculations this result leads us to a number of possible algorithms for detecting community structure as well as several other results including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong the algorithms and measures proposed are illustrated with applications to a variety of real world complex networks

finding the number of clusters in a dataset one of the most difficult problems in cluster analysis is identifying the number of groups in a dataset most previously suggested approaches to this problem are either somewhat ad hoc or require parametric assumptions and complicated calculations in this article we develop a simple yet powerful nonparametric method for choosing the number of clusters based on distortion a quantity that measures the average distance per dimension between each observation and its closest cluster center our technique is computationally efficient and straightforward to implement we demonstrate empirically its effectiveness not only for choosing the number of clusters but also for identifying underlying structure on a wide range of simulated and real world datasets in addition we give a rigorous theoretical justification for the method based on information theoretic ideas specifically results from the subfield of electrical engineering known as rate distortion theory allow us to describe the behavior of the dist

blind separation of parametric nonlinear mixtures of possibly autocorrelated and non stationary sources in this paper we present a new method formulated in a maximum likelihood framework for blindly separating nonlinear mixtures of statistically independent signals our method exploits on the one hand the knowledge of the parametric model of the mixing transformation with unknown parameter values and on the other hand the possible structure of source signals i e their autocorrelation and or nonstationarity one of the main advantages of the proposed method is that it can be implemented even if the analytical expression of the inverse model is unknown the method is first addressed in a general configuration then detailed for two special cases i e a simple bijective toy model and a linear quadratic model the study of the toy model is interesting because of its simplicity and its global bijectivity which allows us to focus our efforts on parameter estimation the linear quadratic model is chosen due to its capacity to describe real world mixing phenomena simulation results using the toy model and using a subclass of the linear quadratic model i e the bilinear model show that taking into account the nonlinearity of the mixing transformations and the structure of signals considerably improves separation performance

a modified k means algorithm for circular invariant clustering several important pattern recognition applications are based on feature vector extraction and vector clustering directional patterns are commonly represented by rotation variant vectors f sub d formed from features uniformly extracted in m directions it is often desirable that pattern recognition algorithms are invariant under pattern rotation this paper introduces a distance measure and a k means based algorithm namely circular k means ck means to cluster vectors containing directional information such as f sub d in a circular shift invariant manner a circular shift of f sub d corresponds to pattern rotation thus the algorithm is rotation invariant an efficient fourier domain representation of the proposed measure is presented to reduce computational complexity a split and merge approach smck means suited to the proposed ck means technique is proposed to reduce the possibility of converging at local minima and to estimate the correct number of clusters experiments performed for textural images illustrate the superior performance of the proposed algorithm for clustering directional vectors f sub d compared to the alternative approach that uses the original k means and rotation invariant feature vectors transformed from f sub d

a bayesian bootstrap for censored data a bayesian bootstrap for a censored data model is introduced its small sample distributional properties are discussed and found to be similar to efron s bootstrap for censored data in the absence of censoring the bayesian bootstrap for censored data reduces to rubin s bayesian bootstrap for complete data a first order large sample theory is developed this theory shows that both censored data bootstraps are consistent bootstraps for approximating the sampling distribution of the kaplan meier estimator it also shows that both bootstraps are consistent bootstraps for approximating a posterior distribution of the survival function with respect to each member of the class of conjugate beta neutral process priors

variance based cluster selection criteria in a k means framework for one mode dissimilarity data one of the main problems in cluster analysis is that of determining the number of groups in the data in general the approach taken depends on the cluster method used for k means some of the most widely employed criteria are formulated in terms of the decomposition of the total point scatter regarding a two mode data set of n points in p dimensions which are optimally arranged into k classes this paper addresses the formulation of criteria to determine the number of clusters in the general situation in which the available information for clustering is a one mode n times n dissimilarity matrix describing the objects in this framework p and the coordinates of points are usually unknown and the application of criteria originally formulated for two mode data sets is dependent on their possible reformulation in the one mode situation the decomposition of the variability of the clustered objects is proposed in terms of the corresponding block shaped partition of the dissimilarity matrix within block and between block dispersion values for the partitioned dissimilarity matrix are derived and variance based criteria are subsequently formulated in order to determine the number of groups in the data a monte carlo experiment was carried out to study the performance of the proposed criteria for simulated clustered points in p dimensions greater efficiency in recovering the number of clusters is obtained when the criteria are calculated from the related euclidean distances instead of the known two mode data set in general for unequal sized clusters and for low dimensionality situations for simulated dissimilarity data sets the proposed criteria always outperform the results obtained when these criteria are calculated from their original formulation using dissimilarities instead of distances

company size distribution for developing countries abstract we analyze company size distribution for developing countries using the framework proposed by ramsden and kiss haypal physica a 277 2000 220 although this distribution does not fit developing countries data as good as it does to developed ones the parameters of the distribution and for developing countries are remarkably different to those for developed countries this result supports the hypothesis that parameter plays a role analogous to the temperature of the economy which could be related to the level of economic development as reported previously by saslow am j phys 67 1999 1239 also this supports the hypothesis that is related to the competitive exclusion in economics as tending to zero implies the competition free limit case where company size distribution is predicted to be a power law as reported by takayasu and okuyama fractals 6 1998 67 finally we report the goodness of fit for two functions a finite size scaling and a log normal we found that these functions fit the data better in some cases however this is not in itself sufficient evidence that those functions are an appropriate representation of the phenomenon

a rank statistics approach to the consistency of a general bootstrap a general notion of a bootstrapped mean constructed by exchangeably weighting sample points is introduced consistency of this generalized bootstrapped mean which includes proposals of efron and rubin among others is proved by classical linear rank statistics theory the consistency of generalized bootstrapped empirical and quantile processes is also established

preferential urn model and nongrowing complex networks a preferential urn model which is based on the concept the rich get richer is proposed from a relationship between a nongrowing model for complex networks and the preferential urn model in regard to degree distributions it is revealed that a fitness parameter in the nongrowing model is interpreted as an inverse local temperature in the preferential urn model furthermore it is clarified that the preferential urn model with randomness generates a fat tailed occupation distribution the concept of the local temperature enables us to understand the fat tailed occupation distribution intuitively since the preferential urn model is a simple stochastic model it can be applied to research on not only the nongrowing complex networks but also many other fields such as econophysics and social sciences

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

cluster based blind nonlinear channel estimation a cluster based maximum likelihood sequence estimator mlse for nonlinear channels was described which consists of a clustering network and an mlse implemented by the viterbi algorithm the cluster based mlse can be used for digital communication through nonlinear finite length channels because channel mapping estimation is used instead of channel estimation in the conventional mlse the clustering network of the cluster based mlse which estimates the channel mapping between the signal input vectors and the noiseless channel outputs is a supervised network and requires a training sequence we propose a blind channel mapping estimator to estimate the channel mapping without using the training sequence the blind channel mapping estimator has a clustering block and a mapping block the clustering block estimates the channel outputs which represent the channel mapping subject to an unknown permutation operation because no training sequence is utilized that permutation operation is resolved by the mapping block and therefore the channel mapping is obtained introducing the blind channel mapping estimator into the cluster based mlse a blind cluster based mlse for nonlinear channels can be done computer simulations of the blind channel mapping estimator and the blind mlse for nonlinear channels are presented

curvature based method for determining the number of clusters abstract determining the number of clusters is one of the research questions attracting considerable interests in recent years majority of the existing methods require parametric assumptions and substantiated computations in this paper we propose a simple yet powerful method for determining the number of clusters based on curvature our technique is computationally efficient and straightforward to implement we compare our method with 6 other approaches on a wide range of simulated and real world datasets theoretical motivation underlying the proposed method is also presented

bayesian bootstrap for proportional hazards models we propose two bayesian bootstrap extensions the binomial and poisson forms for proportional hazards models the binomial form bayesian bootstrap is the limit of the posterior distribution with a beta process prior as the amount of the prior information vanishes and thus can be considered as a default nonparametric bayesian analysis it is also the same as lo s bayesian bootstrap for censored data when covariates are absent the poisson form bayesian bootstrap is equivalent to the bayesian analysis with cox s profile likelihood when the baseline distribution is discrete thus when the data set has many ties simulation study suggests that the binomial form bayesian bootstrap performs better than standard frequentist procedures in the frequentist sense an advantage of the proposed bayesian bootstrap procedures over the standard bayesian analysis is conceptual and computational simplicity finally it is shown that both bayesian bootstrap posteriors are asymptotically equivalent to the sampling distribution of the maximum likelihood estimator

comparative evaluation of two superior stopping rules for hierarchical cluster analysis a split sample replication stopping rule for hierarchical cluster analysis is compared with the internal criterion previously found superior by milligan and cooper 1985 in their comparison of 30 different procedures the number and extent of overlap of the latent population distributions was systematically varied in the present evaluation of stopping rule validity equal and unequal population base rates were also considered both stopping rules correctly identified the actual number of populations when there was essentially no overlap and clusters occupied visually distinct regions of the measurement space the replication criterion which is evaluated by clustering of cluster means from preliminary analyses that are accomplished on random partitions of an original data set was superior as the degree of overlap in population distributions increased neither method performed adequately when overlap obliterated visually discernible density nodes

statistical significance of clustering for high dimension low sample size data clustering methods provide a powerful tool for the exploratory analysis of high dimension low sample size hdlss data sets such as gene expression microarray data a fundamental statistical issue in clustering is which clusters are really there as opposed to being artifacts of the natural sampling variation we propose sigclust as a simple and natural approach to this fundamental statistical problem in particular we define a cluster as data coming from a single gaussian distribution and formulate the problem of assessing statistical significance of clustering as a testing procedure this gaussian null assumption allows direct formulation of p values that effectively quantify the significance of a given clustering hdlss covariance estimation for sigclust is achieved by a combination of invariance principles together with a factor analysis model the properties of sigclust are studied simulated examples as well as an application to a real cancer microarray data set show that the proposed method

a hybrid clustering method for identifying high density clusters abstract a hybrid method for clustering multivariate observations is proposed which combines elements of the k means and the single linkage clustering techniques one purpose of the proposed method is to discover the high density clusters given a random sample of size n from some underlying population a high density cluster at level c in a population with density f is defined as a maximal connected set of points x with f x c this clustering procedure is practicable for very large numbers of observations and is shown to be consistent under certain regularity conditions in one dimension

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

material identification of real impact sounds effects of size variation in steel glass wood and plexiglass plates identification of the material of struck objects of variable size was investigated previous studies on this issue assumed recognition to be based on acoustical measures of damping this assumption was tested comparing the power of a damping measure in explaining identification data with that of several other acoustical descriptors listeners performance was perfect with respect to gross material categories steel glass and wood plexiglass comprising materials of vastly different mechanical properties impaired performance was observed for materials within the same gross category identification being based on the size of the objects alone the damping descriptor accounted for the identification of the gross categories however other descriptors such as signal duration explained the results equally well materials within the same gross category were identified mainly on the basis of signal frequency overall poor support for the relevance of damping to material perception was found an analysis of the acoustical support for perfect material identification was carried out sufficient acoustical information for perfect performance was found thus procedural biases for the origin of the effects of size could be discarded pointing toward their cognitive rather than methodological nature identification performance was explained in terms of the regularities of the everyday acoustical environment

on comparing two sequences of numbers and its applications to clustering analysis a conceptual problem that appears in different contexts of clustering analysis is that of measuring the degree of compatibility between two sequences of numbers this problem is usually addressed by means of numerical indexes referred to as sequence correlation indexes this paper elaborates on why some specific sequence correlation indexes may not be good choices depending on the application scenario in hand a variant of the product moment correlation coefficient and a weighted formulation for the goodman kruskal and kendall s indexes are derived that may be more appropriate for some particular application scenarios the proposed and existing indexes are analyzed from different perspectives such as their sensitivity to the ranks and magnitudes of the sequences under evaluation among other relevant aspects of the problem the results help suggesting scenarios within the context of clustering analysis that are possibly more appropriate for the application of each index

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

probabilistic data association for systems with multiple simultaneous measurements we consider the problem of estimating the state of a discrete time linear stochastic system whose observation process consists of a finite set of known linear measurement models the correspondence of the measurements with the models is unknown assuming all the measurements relate to the state we derive a recursive algorithm the multiple simultaneous measurement filter msmf which provides a fixed complexity sub optimal solution to this problem the msmf is a generalization of the discrete time kalman filter and reduces to the latter when a single measurement model applies simulations are provided that demonstrate the superior performance of the msmf over the probabilistic data association filter for tracking a single target in an environment where up to three measurements of the state are received simultaneously

bootstrapping for significance of compact clusters in multidimensional datasets this article proposes a bootstrap approach for assessing significance in the clustering of multidimensional datasets the procedure compares two models and declares the more complicated model a better candidate if there is significant evidence in its favor the performance of the procedure is illustrated on two well known classification datasets and comprehensively evaluated in terms of its ability to estimate the number of components via extensive simulation studies with excellent results the methodology is also applied to the problem of k means color quantization of several standard images in the literature and is demonstrated to be a viable approach for determining the minimal and optimal numbers of colors needed to display an image without significant loss in resolution additional illustrations and performance evaluations are provided in the online supplementary material

cluster analysis and mathematical programming given a set of entities cluster analysis aims at finding subsets called clusters which are homogeneous and or well separated as many types of clustering and criteria for homogeneity or separation are of interest this is a vast field a survey is given from a mathematical programming viewpoint steps of a clustering study types of clustering and criteria are discussed then algorithms for hierarchical partitioning sequential and additive clustering are studied emphasis is on solution methods i e dynamic programming graph theoretical algorithms branch and bound cutting planes column generation and heuristics

three mode component analysis with crisp or fuzzy partition of units a new methodology is proposed for the simultaneous reduction of units variables and occasions of a three mode data set units are partitioned into a reduced number of classes while simultaneously components for variables and occasions accounting for the largest common information for the classification are identified the model is a constrained three mode factor analysis and it can be seen as a generalization of the redkm model proposed by de soete and carroll for two mode data the least squares fitting problem is mathematically formalized as a constrained problem in continuous and discrete variables an iterative alternating least squares algorithm is proposed to give an efficient solution to this minimization problem in the crisp and fuzzy classification context the performances of the proposed methodology are investigated by a simulation study comparing our model with other competing methodologies different procedures for starting the proposed algorithm have also been tested a discussion of some interesting differences in the results follows finally an application to real data illustrates the ability of the proposed model to provide substantive insights into the data complexities

self organized scale free networks growth and preferential attachments have been coined as the two fundamental mechanisms responsible for the scale free feature in complex networks as characterized by an algebraic degree distribution there are situations particularly in biological networks where growth is absent or not important yet some of these networks still exhibit the scale free feature with a small degree exponent here we propose two classes of models to account for this phenomenon we show analytically and numerically that in the first model a spectrum of algebraic degree distributions with a small exponent can be generated the second model incorporates weights for nodes and it is able to generate robust scale free degree distribution with larger algebraic exponents our results imply that it is natural for a complex network to self organize itself into a scale free

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

segmentation of textured images based on fractals and image filtering this paper describes a new approach to the segmentation of textured gray scale images based on image pre ltering and fractal features traditionally lter bank decomposition methods consider the energy in each band as the textural feature a parameter that is highly dependent on image intensity in this paper we use fractal based features which depend more on textural characteristics and not intensity information to reduce the total number of features used in the segmentation the signi cance of each feature is examined using a test similar to the f test and less signi cant features are not used in the clustering process the commonly used k means algorithm is extended to an iterative k means by using a variable window size that preserves boundary details the number of clusters is estimated using an improved hierarchical approach that ignores information extracted around region boundaries 2001 pattern recognition society published by elsevier science ltd all rights reserved

automatic aspect discrimination in data clustering the attributes describing a data set may often be arranged in meaningful subsets each of which corresponds to a different aspect of the data an unsupervised algorithm scad that simultaneously performs fuzzy clustering and aspects weighting was proposed in the literature however scad may fail and halt given certain conditions to fix this problem its steps are modified and then reordered to reduce the number of parameters required to be set by the user in this paper we prove that each step of the resulting algorithm named ascad globally minimizes its cost function with respect to the argument being optimized the asymptotic analysis of ascad leads to a time complexity which is the same as that of fuzzy c means a hard version of the algorithm and a novel validity criterion that considers aspect weights in order to estimate the number of clusters are also described the proposed method is assessed over several artificial and real data sets

the bayesian bootstrap the bayesian bootstrap is the bayesian analogue of the bootstrap instead of simulating the sampling distribution of a statistic estimating a parameter the bayesian bootstrap simulates the posterior distribution of the parameter operationally and inferentially the methods are quite similar because both methods of drawing inferences are based on somewhat peculiar model assumptions and the resulting inferences are generally sensitive to these assumptions neither method should be applied without some consideration of the reasonableness of these model assumptions in this sense neither method is a true bootstrap procedure yielding inferences unaided by external assumptions

approximate bayesian inference with the weighted likelihood bootstrap we introduce the weighted likelihood bootstrap wlb as a way to simulate approximately from a posterior distribution this method is often easy to implement requiring only an algorithm for calculating the maximum likelihood estimator such as iteratively reweighted least squares in the generic weighting scheme the wlb is first order correct under quite general conditions inaccuracies can be removed by using the wlb as a source of samples in the sampling importance resampling sir algorithm which also allows incorporation of particular prior information the sir adjusted wlb can be a competitive alternative to other integration methods in certain models asymptotic expansions elucidate the second order properties of the wlb which is a generalization of rubin s bayesian bootstrap the calculation of approximate bayes factors for model comparison is also considered we note that given a sample simulated from the posterior distribution the required marginal likelihood may be simulation consistently estimated by the harmonic mean of the associated likelihood values a modification of this estimator that avoids instability is also noted these methods provide simple ways of calculating approximate bayes factors and posterior model probabilities for a very wide class of models

simultaneous classification and multidimensional scaling with external information for the exploratory analysis of a matrix of proximities or dis similarities between objects one often uses cluster analysis ca or multidimensional scaling mds solutions resulting from such analyses are sometimes interpreted using external information on the objects usually the procedures of ca mds and using external information are carried out independently and sequentially although combinations of two of the three procedures ca and mds or multidimensional scaling and using external information have been proposed in the literature the present paper offers a procedure that combines all three procedures in one analysis using a model that describes a partition of objects with cluster centroids represented in a low dimensional space which in turn is related to the information in the external variables a simulation study is carried out to demonstrate that the method works satisfactorily for data with a known underlying structure also to illustrate the method it is applied to two empirical data sets

a large sample study of the bayesian bootstrap on donne une justification asymptotique du bootstrap bayesien on obtient des resultats lies a l article de rubin 1981 dans le meme sens que bickel et freedman 1981 et singh 1981 se rapportant a l article d efron 1979

exact solution for the time evolution of network rewiring models we consider the rewiring of a bipartite graph using a mixture of random and preferential attachment the full mean field equations for the degree distribution and its generating function are given the exact solution of these equations for all finite parameter values at any time is found in terms of standard functions it is demonstrated that these solutions are an excellent fit to numerical simulations of the model we discuss the relationship between our model and several others in the literature including examples of urn backgammon and balls in boxes models the watts and strogatz rewiring problem and some models of zero range processes our model is also equivalent to those used in various applications including cultural transmission family name and gene frequencies glasses and wealth distributions finally some voter models and an example of a minority game also show features described by our model

finding community structure in very large networks the discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community but most methods proposed so far are unsuitable for very large networks because of their computational cost here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms its running time on a network with n vertices and m edges is o md phantom rule 0 2em 0ex mathrm log phantom rule 0 2em 0ex n where d is the depth of the dendrogram describing the community structure many real world networks are sparse and hierarchical with m ensuremath sim n and d ensuremath sim mathrm log phantom rule 0 2em 0ex n in which case our algorithm runs in essentially linear time o n phantom rule 0 2em 0ex mathrm log 2 phantom rule 0 2em 0ex n as an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on line retailer items in the network being linked if they are frequently purchased by the same buyer the network has more than 400 000 vertices and 2 ifmmode times else texttimes fi 10 6 edges we show that our algorithm can extract meaningful communities from this network revealing large scale patterns present in the purchasing habits of customers

an examination of indexes for determining the number of clusters in binary data sets the problem of choosing the correct number of clusters is as old as cluster analysis itself a number of authors have suggested various indexes to facilitate this crucial decision one of the most extensive comparative studies of indexes was conducted by milligan and cooper 1985 the present piece of work pursues the same goal under different conditions in contrast to milligan and cooper s work the emphasis here is on high dimensional empirical binary data binary artificial data sets are constructed to reflect features typically encountered in real world data situations in the field of marketing research the simulation includes 162 binary data sets that are clustered by two different algorithms and lead to recommendations on the number of clusters for each index under consideration index results are evaluated and their performance is compared and analyzed

selected tree classifier combination based on both accuracy and error diversity this paper proposes a method for combining multiple tree classifiers based on both classifier ensemble bagging and dynamic classifier selection schemes dcs the proposed method is composed of the following procedures 1 building individual tree classifiers based on bootstrap samples 2 calculating the distance between all possible two trees 3 clustering the trees based on single linkage clustering 4 selecting two clusters by local region in terms of accuracy and error diversity and 5 voting the results of tree classifiers selected in the two clusters empirical evaluation using publicly available data sets confirms the superiority of our proposed approach over other classifier combining methods

evolutionary fuzzy clustering of relational data this paper is concerned with the computational efficiency of fuzzy clustering algorithms when the data set to be clustered is described by a proximity matrix only relational data and the number of clusters must be automatically estimated from such data a fuzzy variant of an evolutionary algorithm for relational clustering is derived and compared against two systematic pseudo exhaustive approaches that can also be used to automatically estimate the number of fuzzy clusters in relational data an extensive collection of experiments involving 18 artificial and two real data sets is reported and analyzed

an extensive comparative study of cluster validity indices the validation of the results obtained by clustering algorithms is a fundamental part of the clustering process the most used approaches for cluster validation are based on internal cluster validity indices although many indices have been proposed there is no recent extensive comparative study of their performance in this paper we show the results of an experimental work that compares 30 cluster validity indices in many different environments with different characteristics these results can serve as a guideline for selecting the most suitable index for each possible application and provide a deep insight into the performance differences between the currently available indices

channel dependent constrained combinatorial clustering constrained combinatorial clustering ccc is a new approach for grouping multiple features where the clustering metric depends on an unknown communication channel assignment features assigned to the same channel cannot be from the same source and conversely channels assigned to the same source must be distinct while the number of sources and their states are unknown the channels are assumed to be known except for additive noise potential clustering assignments are checked for compatibility with the constraints in a structured way that results in significant computational savings with respect to exhaustive enumeration especially when combined with a k best channel assignment algorithm that has polynomial complexity by combining two channel assignment methods exhaustive and k best with two clustering techniques ccc and greedy four new algorithms are presented to solve this novel problem along with detailed computational complexity analyses the main algorithm ccc is a top down clustering strategy based on assignment aggregation in a channel constrained environment the approaches are compared on a one dimensional simulation significant performance differences in source estimation accuracy and estimated number of sources are observed at low signal to noise ratios snrs and for low values of k some novel permutation symmetry properties arising from the study which lead to a new type of self affine set or discrete fractal are also presented

measure projection analysis a probabilistic approach to eeg source comparison and multi subject inference a crucial question for the analysis of multi subject and or multi session electroencephalographic eeg data is how to combine information across multiple recordings from different subjects and or sessions each associated with its own set of source processes and scalp projections here we introduce a novel statistical method for characterizing the spatial consistency of eeg dynamics across a set of data records measure projection analysis mpa first finds voxels in a common template brain space at which a given dynamic measure is consistent across nearby source locations then computes local mean eeg measure values for this voxel subspace using a statistical model of source localization error and between subject anatomical variation finally clustering the mean measure voxel values in this locally consistent brain subspace finds brain spatial domains exhibiting distinguishable measure features and provides 3 d maps plus statistical significance estimates for each eeg measure of interest applied to sufficient high quality data the scalp projections of many maximally independent component ic processes contributing to recorded high density eeg data closely match the projection of a single equivalent dipole located in or near brain cortex we demonstrate the application of mpa to a multi subject eeg study decomposed using independent component analysis ica compare the results to k means ic clustering in eeglab sccn ucsd edu eeglab and use surrogate data to test mpa robustness a measure projection toolbox mpt plug in for eeglab is available for download sccn ucsd edu wiki mpt together mpa and ica allow use of eeg as a 3 d cortical imaging modality with near cm scale spatial resolution

an examination of procedures for determining the number of clusters in a data set a monte carlo evaluation of 30 procedures for determining the number of clusters was conducted on artificial data sets which contained either 2 3 4 or 5 distinct nonoverlapping clusters to provide a variety of clustering solutions the data sets were analyzed by four hierarchical clustering methods external criterion measures indicated excellent recovery of the true cluster structure by the methods at the correct hierarchy level thus the clustering present in the data was quite strong the simulation results for the stopping rules revealed a wide range in their ability to determine the correct number of clusters in the data several procedures worked fairly well whereas others performed rather poorly thus the latter group of rules would appear to have little validity particularly for data sets containing distinct clusters applied researchers are urged to select one or more of the better criteria however users are cautioned that the performance of some of the criteria may be data dependent

a byy scale incremental em algorithm for gaussian mixture learning abstract gaussian mixture model has been used extensively in the fields of information processing and data analysis however its model selection i e the selection of number of components or gaussians in the mixture is still a difficult problem fortunately the new established bayesian ying yang byy harmony function provides an efficient criterion for the model selection of gaussian mixture with a set of sample data in this paper we propose a byy scale incremental em algorithm for gaussian mixture learning via a component split rule to increase the byy harmony function incrementally particularly starting from two components and adding one component sequentially via the split rule after each em procedure until a maximum number of components the algorithm increases the scale of the mixture incrementally and leads to the maximization of the byy harmony function together with the correct model selection and a good parameter estimation of the gaussian mixture it is demonstrated well by the simulation experiments that this byy scale incremental em algorithm can make both model selection and parameter estimation efficiently for gaussian mixture modeling moreover the byy scale incremental em algorithm is successfully applied to two real life data sets including iris data classification and unsupervised color image segmentation

the problem of regions in the problem of regions we wish to know which one of a discrete set of possibilities applies to a continuous parameter vector this problem arises in the following way we compute a descriptive statistic from a set of data notice an interesting feature and wish to assign a confidence level to that feature for example we compute a density estimate and notice that the estimate is bimodal what confidence can we assign to bimodality a natural way to measure confidence is via the bootstrap we compute our descriptive statistic on a large number of bootstrap data sets and record the proportion of times that the feature appears this seems like a plausible measure of confidence for the feature the paper studies the construction of such confidence values and examines to what extent they approximate frequentist p values and bayesian a posteriori probabilities we derive more accurate confidence levels using both frequentist and objective bayesian approaches the methods are illustrated with a number of examples including polynomial model selection and estimating the number of modes of a density

a monte carlo study of thirty internal criterion measures for cluster analysis a monte carlo evaluation of thirty internal criterion measures for cluster analysis was conducted artificial data sets were constructed with clusters which exhibited the properties of internal cohesion and external isolation the data sets were analyzed by four hierarchical clustering methods the resulting values of the internal criteria were compared with two external criterion indices which determined the degree of recovery of correct cluster structure by the algorithms the results indicated that a subset of internal criterion measures could be identified which appear to be valid indices of correct cluster recovery indices from this subset could form the basis of a permutation test for the existence of cluster structure or a clustering algorithm

the effect of cluster size dimensionality and the number of clusters on recovery of true cluster structure an evaluation of four clustering methods and four external criterion measures was conducted with respect to the effect of the number of clusters dimensionality and relative cluster sizes on the recovery of true cluster structure the four methods were the single link complete link group average upgma and ward s minimum variance algorithms the results indicated that the four criterion measures were generally consistent with each other of which two highly similar pairs were identified the tirst pair consisted of the rand and corrected rand statistics and the second pair was the jaccard and the fowlkes and mallows indexes with respect to the methods recovery was found to improve as the number of clusters increased and as the number of dimensions increased the relative cluster size factor produced differential performance effects with ward s procedure providing the best recovery when the clusters were of equal size the group average method gave equivalent or better recovery when the clusters were of unequal size

self organization of collaboration networks we study collaboration networks in terms of evolving self organizing bipartite graph models we propose a model of a growing network which combines preferential edge attachment with the bipartite structure generic for collaboration networks the model depends exclusively on basic properties of the network such as the total number of collaborators and acts of collaboration the mean size of collaborations etc the simplest model defined within this framework already allows us to describe many of the main topological characteristics degree distribution clustering coefficient etc of one mode projections of several real collaboration networks without parameter fitting we explain the observed dependence of the local clustering on degree and the degree degree correlations in terms of the aging of collaborators and their physical impossibility to participate in an unlimited number of collaborations

interacting individuals leading to zipf s law institut de physique th eorique universit e de fribourg ch 1700 february 1 2008 we present a general approach to explain the zipf s law of city distribution if the simplestinteraction pairwise is assumed individuals tend to form cities in agreement with the well knownstatisticspacs numbers 89 50 r 05 20 y 05 40 j

clustered common factor exploration in factor analysis the factor analysis fa model does not permit unique estimation of the common and unique factor scores this weakness is notorious as the factor indeterminacy in fa luckily some part of the factor scores can be uniquely determined thus as a whole they can be viewed as a sum of determined and undetermined parts the paper proposes to select the undetermined part such that the resulting common factor scores have the following feature the rows i e individuals of the common factor score matrix are as well classified as possible into few clusters the clear benefit is that we can easily interpret the factor scores simply by focusing on the clusters the procedure is called clustered common factor exploration ccfe an alternating least squares algorithm is developed for ccfe it is illustrated with real data examples the proposed approach can be viewed as a parallel to the rotation techniques in fa they exploit another fa indeterminacy the rotation indeterminacy which is resolved by choosing the rotation that transforms the loading matrix into the most interpretable one according to a pre specified criterion in contrast to the rotational indeterminacy the factor indeterminacy is utilized to achieve well clustered factor scores by ccfe to the best of our knowledge such an approach to the fa interpretation has not been studied yet

a meta learning approach for determining the number of clusters with consideration of nearest neighbors an important and challenging problem in data clustering is the determination of the best number of clusters a variety of estimation methods has been proposed over the years to address this problem most of these methods depend on several nontrivial assumptions about the data structure and such methods may thus fail to discover the true clusters in a dataset that does not satisfy those assumptions we develop a new approach that takes as a starting point the simple and intuitive observation that close objects should fall within the same cluster whereas distant ones should not based on this simple notion we utilize a new measurement of good clustering called disconnectivity as well as existing goodness measurements and we embed these measures into a meta learning approach for estimating the number of clusters a simulation experiment based on 13 representative models and an application to real world datasets are conducted to show the effectiveness of the proposed method

on the use of fuzzy constraints in semisupervised clustering this paper introduces fuzzy hss a semisupervised hierarchical clustering approach that uses fuzzy instance level constraints these constraints are external information on the shape of fuzzy must link and fuzzy cannot link restrictions they allow uncertainty when indicating whether two instances of a dataset belong to the same group fuzzy must link constraints give a degree of belief of two instances belonging to the same group analogously fuzzy cannot link constraints indicate the degree of belief of two instances not belonging to the same group these constraints have been introduced in a hierarchical clustering process allowing us to obtain the optimal number of groups in a dendrogram when the number of clusters is not known the optimal amount of constraints needed in the process is determined by means of fuzzy entropy an extensive experimental study is provided by comparing this fuzzy semisupervised approach with classic unsupervised methods as well as a crisp semisupervised alternative

multicommunity weight driven bipartite network model community structure and rewiring phenomena exist in many complex networks particularly in bipartite networks we construct a model for the degree distribution of the rewiring problem in a multicommunity weight driven bipartite network mcwbn the network consists of many interconnected communities each of which holds a bipartite graph the bipartite graph consists of two sets of nodes we name each node in one set a producer and each node in the other set a consumer a weight value matrix defining the trade barrier between any two communities is used to characterize the structure of the communities which ensures the higher preferential attachment probability in intracommunity than in intercommunity the size of one producer is defined as the number of consumers connected to it we find that the nonlinear dynamics of the scale of production or the total size of all producers in each community is dependent only on the initial scale of production in each community and independent of the distribution of the producer size furthermore if the nonlinear system of the scale of production in each community is at an equilibrium state the distribution of the producer size in each community of the mcwbn model is equivalent to that in a one community model

a cautionary note on using internal cross validation to select the number of clusters a highly popular method for examining the stability of a data clustering is to split the data into two parts cluster the observations in part a assign the objects in part b to their nearest centroid in part a and then independently cluster the part b objects one then examines how close the two partitions are say by the rand measure another proposal is to split the data into k parts and see how their centroids cluster by means of synthetic data analyses we demonstrate that these approaches fail to identify the appropriate number of clusters particularly as sample size becomes large and the variables exhibit higher correlations

estimating the number of clusters in a numerical data set via quantization error modeling in this paper we consider the problem of unsupervised clustering vector quantization of multidimensional numerical data we propose a new method for determining an optimal number of clusters in the data set the method is based on parametric modeling of the quantization error the model parameter can be treated as the effective dimensionality of the data set the proposed method was tested with artificial and real numerical data sets and the results of the experiments demonstrate empirically not only the effectiveness of the method but its ability to cope with difficult cases where other known methods fail a parameterized model for the clustering error is introduced the model parameter is a measure of the data dimension and homogeneity a new cost criterion is derived from the properties of the model the method demonstrates good results for numerical data sets

order constrained solutions in k means clustering even better than being globally optimal this paper proposes an order constrained k means cluster analysis strategy and implements that strategy through an auxiliary quadratic assignment optimization heuristic that identifies an initial object order a subsequent dynamic programming recursion is applied to optimally subdivide the object set subject to the order constraint we show that although the usual k means sum of squared error criterion is not guaranteed to be minimal a true underlying cluster structure may be more accurately recovered also substantive interpretability seems generally improved when constrained solutions are considered we illustrate the procedure with several data sets from the literature

a stability based validity method for fuzzy clustering an important goal in cluster analysis is the internal validation of results using an objective criterion of particular relevance in this respect is the estimation of the optimum number of clusters capturing the intrinsic structure of your data this paper proposes a method to determine this optimum number based on the evaluation of fuzzy partition stability under bootstrap resampling the method is first characterized on synthetic data with respect to hyper parameters like the fuzzifier and spatial clustering parameters such as feature space dimensionality clusters degree of overlap and number of clusters the method is then validated on experimental datasets furthermore the performance of the proposed method is compared to that obtained using a number of traditional fuzzy validity rules based on the cluster compactness to separation criteria the proposed method provides accurate and reliable results and offers better generalization capabilities than the classical approaches

recovering the number of clusters in data sets with noise features using feature rescaling factors in this paper we introduce three methods for re scaling data sets aiming at improving the likelihood of clustering validity indexes to return the true number of spherical gaussian clusters with additional noise features our method obtains feature re scaling factors taking into account the structure of a given data set and the intuitive idea that different features may have different degrees of relevance at different clusters we experiment with the silhouette using squared euclidean manhattan and the pth power of the minkowski distance dunn s calinski harabasz and hartigan indexes on data sets with spherical gaussian clusters with and without noise features we conclude that our methods indeed increase the chances of estimating the true number of clusters in a data set

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

validating clusters with the lower bound for sum of squares error given that a minor condition holds e g the number of variables is greater than the number of clusters a nontrivial lower bound for the sum of squares error criterion in k means clustering is derived by calculating the lower bound for several different situations a method is developed to determine the adequacy of cluster solution based on the observed sum of squares error as compared to the minimum sum of squares error

a robust competitive clustering algorithm with applications in computer vision this paper addresses three major issues associated with conventional partitional clustering namely sensitivity to initialization difficulty in determining the number of clusters and sensitivity to noise and outliers the proposed robust competitive agglomeration rca algorithm starts with a large number of clusters to reduce the sensitivity to initialization and determines the actual number of clusters by a process of competitive agglomeration noise immunity is achieved by incorporating concepts from robust statistics into the algorithm rca assigns two different sets of weights for each data point the first set of constrained weights represents degrees of sharing and is used to create a competitive environment and to generate a fuzzy partition of the data set the second set corresponds to robust weights and is used to obtain robust estimates of the cluster prototypes by choosing an appropriate distance measure in the objective function rca can be used to find an unknown number of clusters of various shapes in noisy data sets as well as to fit an unknown number of parametric models simultaneously several examples such as clustering mixture decomposition line plane fitting segmentation of range images and estimation of motion parameters of multiple objects are shown

approximate spectral clustering with utilized similarity information using geodesic based hybrid distance measures spectral clustering has been popular thanks to its ability to extract clusters of varying characteristics without using a parametric model in expense of high computational cost required for eigendecomposition of pairwise similarities in order to utilize its advantages in large datasets where it is infeasible due to its computational burden approximate spectral clustering asc methods apply spectral clustering on a reduced set of points data representatives selected by sampling or quantization this two step approach i e finding the representatives and then clustering them brings new opportunities for precise similarity definition such as manifold based topological relations data distribution within the voronoi polyhedra of the representatives and their geodesic distance information which are often ignored in similarity definition for asc in this study we propose geodesic based hybrid similarity criteria which enable the use of different types of information for accurate similarity representation in asc despite the fact that geodesic concept has been widely used in clustering our contribution is the unique way of representing data topology to form geodesic relations and jointly harnessing various information types including topology distance and density the proposed criteria are tested using both sampling selective sampling and quantization neural gas and k means approaches experiments on artificial datasets well known small medium size real datasets and four large datasets four remote sensing images with different types of clusters show that the proposed geodesic based hybrid similarity criteria outperform traditional similarity criteria in terms of clustering accuracies and several cluster validity indices highlightsgeodesic based hybrid similarity measures are proposed for approximate spectral clustering neighborhood graph required for geodesic approach is effectively constructed by weighted delaunay triangulation conn the proposed geodesic based hybrid similarities outperform in terms of both accuracies and cluster validity indices the proposed geodesic based hybrid similarities can be powerful for clustering of large remote sensing images the proposed similarities are significant especially for quantization based approximate spectral clustering

why social networks are different from other types of networks we argue that social networks differ from most other types of networks including technological and biological networks in two important ways first they have nontrivial clustering or network transitivity and second they show positive correlations also called assortative mixing between the degrees of adjacent vertices social networks are often divided into groups or communities and it has recently been suggested that this division could account for the observed clustering we demonstrate that group structure in networks can also account for degree correlations we show using a simple model that we should expect assortative mixing in such networks whenever there is variation in the sizes of the groups and that the predicted level of assortative mixing compares well with that observed in real world networks

sep cop an efficient method to find the best partition in hierarchical clustering based on a new cluster validity index hierarchical clustering algorithms provide a set of nested partitions called a cluster hierarchy since the hierarchy is usually too complex it is reduced to a single partition by using cluster validity indices we show that the classical method is often not useful and we propose sep a new method that efficiently searches in an extended partition set furthermore we propose a new cluster validity index cop since many of the commonly used indices cannot be used with sep experiments performed with 80 synthetic and 7 real datasets confirm that sep cop is superior to the method currently used and furthermore it is less sensitive to noise

estimating the number of clusters in a data set via the gap statistic we propose a method the gap statistic for estimating the number of clusters groups in a set of data the technique uses the output of any clustering algorithm e g k means or hierarchical comparing the change in within cluster dispersion with that expected under an appropriate reference null distribution some theory is developed for the proposal and a simulation study shows that the gap statistic usually outperforms other methods that have been proposed in the literature

a partitional clustering algorithm validated by a clustering tendency index based on graph theory applying graph theory to clustering we propose a partitional clustering method and a clustering tendency index no initial assumptions about the data set are requested by the method the number of clusters and the partition that best fits the data set are selected according to the optimal clustering tendency index value

the clustering of regression models method with applications in gene expression data summary identification of differentially expressed genes and clustering of genes are two important and complementary objectives addressed with gene expression data for the differential expression question many per gene analytic methods have been proposed these methods can generally be characterized as using a regression function to independently model the observations for each gene various adjustments for multiplicity are then used to interpret the statistical significance of these per gene regression models over the collection of genes analyzed motivated by this common structure of per gene models we proposed a new model based clustering method the clustering of regression models method which groups genes that share a similar relationship to the covariate s this method provides a unified approach for a family of clustering procedures and can be applied for data collected with various experimental designs in addition when combined with per gene methods for assessing differential expression that employ the same regression modeling structure an integrated framework for the analysis of microarray data is obtained the proposed methodology was applied to two microarray data sets one from a breast cancer study and the other from a yeast cell cycle study