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

adaptive finite element methods for parabolic problems vi analytic semigroups we continue our work on adaptive finite element methods with a study of time discretization of analytic semigroups we prove optimal a priori and a posteriori error estimates for the discontinuous galerkin method showing in particular that analytic semigroups allow long time integration without error accumulation

set partition by globally optimized cluster seed points abstract a new method is proposed for solving set partition clustering problems the suggested approach is based on the application of global optimization methodology for selecting best cluster seed points the applicability of the method is illustrated by numerical examples

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

autocorrelation based fuzzy clustering of time series the traditional approaches to clustering a set of time series are generally applicable if there is a fixed underlying structure to the time series so that each will belong to one cluster or the other however time series often display dynamic behaviour in their evolution over time this dynamic behaviour should be taken into account when attempting to cluster time series for instance during a certain period a time series might belong to a certain cluster afterwards its dynamics might be closer to that of another cluster in this case the traditional clustering approaches are unlikely to find and represent the underlying structure in the given time series this switch from one time state to another which is typically vague can be naturally treated following a fuzzy approach this paper proposes a fuzzy clustering approach based on the autocorrelation functions of time series in which each time series is not assigned exclusively to only one cluster but it is allowed to belong to different clusters with various membership degrees

cluster differences scaling with a within clusters loss component and a fuzzy successive approximation strategy to avoid local minima cluster differences scaling is a method for partitioning a set of objects into classes and simultaneously finding a low dimensional spatial representation ofk cluster points to model a given square table of dissimilarities amongn stimuli or objects the least squares loss function of cluster differences scaling originally defined only on the residuals of pairs of objects that are allocated to different clusters is extended with a loss component for pairs that are allocated to the same cluster it is shown that this extension makes the method equivalent to multidimensional scaling with cluster constraints on the coordinates a decomposition of the sum of squared dissimilarities into contributions from several sources of variation is described including the appropriate degrees of freedom for each source after developing a convergent algorithm for fitting the cluster differences model it is argued that the individual objects and the cluster locations can be jointly displayed in a configuration obtained as a by product of the optimization finally the paper introduces a fuzzy version of the loss function which can be used in a successive approximation strategy for avoiding local minima a simulation study demonstrates that this strategy significantly outperforms two other well known initialization strategies and that it has a success rate of 92 out of 100 in attaining the global minimum

fuzzy clustering for data time arrays with inlier and outlier time trajectories in many knowledge discovery and data mining tasks fuzzy clustering is one of the most common tools for data partitioning in this paper dynamic fuzzy clustering models for classifying a set of multivariate time trajectories time series sequences are developed in particular by adopting an exploratory approach based on a geometric algebraic formulation of the data time array different kinds of dynamic fuzzy clustering models based on cross sectional and longitudinal aspects are suggested furthermore a modified version of the previous clustering models that can be seen as a generalization of these models is proposed by utilizing these models we can obtain beneficial effects in the clustering process when anomalous trajectories trajectories with anomalous positions and slopes are present in the dataset in fact the models are suitable for detecting structures of time trajectories with anomalous patterns that are not uniformly distributed over the structure s domains and are characterized by strange slopes in these models the disruptive effect of the anomalous trajectories is neutralized and smoothed and the information on the influence of individual time trajectories on the detected groups is given furthermore some remarks on dynamic three way extensions of a few robust fuzzy clustering models for two way data are suggested demonstrative examples are shown and a comparison assessment based on artificial multivariate time varying data is carried out

multipath clustering and cluster tracking for geometry based stochastic channel modeling this paper presents a clustering and tracking method that exploits the geometry of the scattering points sps obtained from the measurement based ray tracer the multipath components mpcs were categorized into clusters by applying the kpowermeans kpm framework to those sps the clusters were tracked by comparing the cluster centroid sps of the adjacent snapshots the clusters were estimated based on the indoor environment geometry at 11 ghz and their physical mechanisms were interpreted the complexity and performance of this method was assessed and compared with that of conventional kpm by comparing the number of floating point operations flops and the channel eigenvalues obtained from the reconstructed channel matrices which were calculated by superposing the mpcs randomly generated from intracluster parameters the verification of this method showed that most clusters were estimated and tracked according to the physical location of the scatterers in the environment with acceptable error moreover the eigenvalues reconstructed from the proposed method were closer to the measured ones with less number of flops which indicates both accuracy and complexity improvement the results also imply that multiple input multiple output performance is highly dependent on the radio propagation channel therefore it is imperative that clusters in the channel be determined accurately

density based geodesic distance for identifying the noisy and nonlinear clusters we propose a density based geodesic distance that resists noise for clustering the proposed distance is calculated based on the neighborhood graph for nonlinearity simulation and real case data demonstrate the accuracy of the proposed distance clustering analysis can facilitate the extraction of implicit patterns in a dataset and elicit its natural groupings without requiring prior classification information for superior clustering analysis results a number of distance measures have been proposed recently geodesic distance has been widely applied to clustering algorithms for nonlinear groupings however geodesic distance is sensitive to noise and hence geodesic distance based clustering may fail to discover nonlinear clusters in the region of the noise in this study we propose a density based geodesic distance that can identify clusters in nonlinear and noisy situations experiments on various simulation and benchmark datasets are conducted to examine the properties of the proposed geodesic distance and to compare its performance with that of existing distance measures the experimental results confirm that a clustering algorithm with the proposed distance measure demonstrated superior performance compared to the competitors this was especially true when the cluster structures in the data were inherently noisy and nonlinearly patterned

quantile autocovariances a powerful tool for hard and soft partitional clustering of time series abstract a key issue in cluster analysis is determining a proper dissimilarity measure between two data objects and many pairwise dissimilarities have been proposed to deal with time series assuming that the clustering purpose is to group series according to the underlying dependence structures a detailed study of the behavior in clustering of a dissimilarity based on comparing estimated quantile autocovariance functions qaf is carried out quantile autocovariances provide information about the serial dependence structure that other conventional features are not able to capture which suggests great potential to perform clustering of series the asymptotic behavior of the sample quantile autocovariances is studied and an algorithm to determine optimal combinations of lags and pairs of quantile levels to perform clustering is introduced the proposed metric is used to perform hard and soft partitioning based clustering first a broad simulation study examines the behavior of the proposed metric in crisp clustering with the pam procedure a novel fuzzy c medoids algorithm based on the qaf dissimilarity is then proposed and compared with other fuzzy procedures in a new simulation study conducted to cluster fuzzy scenarios involving ar and garch models in all cases the qaf based procedures outperform or are highly competitive with a range of dissimilarities reported in the literature particularly exhibiting high capability to cluster conditionally heteroskedastic time series and robustness to the distributional form of the errors two specific applications involving air quality data and financial time series illustrate the usefulness of the proposed procedures

simultaneous clustering and model selection algorithm theory and applications while clustering has been well studied in the past decade model selection has drawn much less attention due to the difficulty of the problem in this paper we address both problems in a joint manner by recovering an ideal affinity tensor from an imperfect input by taking into account the relationship of the affinities induced by the cluster structures we are able to significantly improve the affinity input such as repairing those entries corrupted by gross outliers more importantly the recovered ideal affinity tensor also directly indicates the number of clusters and their membership thus solving the model selection and clustering jointly to enforce the requisite global consistency in the affinities demanded by the cluster structure we impose a number of constraints specifically among others the tensor should be low rank and sparse and it should obey what we call the rank 1 sum constraint to solve this highly non smooth and non convex problem we exploit the mathematical structures and express the original problem in an equivalent form amenable for numerical optimization and convergence analysis to scale to large problem sizes we also propose an alternative formulation so that those problems can be efficiently solved via stochastic optimization in an online fashion we evaluate our algorithm with different applications to demonstrate its superiority and show it can adapt to a large variety of settings

fuzzy clustering of time series using extremes abstract in this study we explore the grouping together of time series with similar seasonal patterns using extreme value analysis with fuzzy clustering input features into the fuzzy clustering methods are parameter estimates of time varying location scale and shape obtained from fitting the generalised extreme value gev distribution to annual maxima or the r largest order statistics per year of the time series an innovative contribution of the study is the development of new generalised fuzzy clustering procedures taking into account weights and the derivation of iterative solutions based on the gev parameter estimators simulation studies conducted to evaluate the methods reveal good performance an application is made to a set of daily sea level time series from around the coast of australia where the identified clusters are well validated and they can be meaningfully interpreted

feature selection using structural similarity a new method of feature selection is developed based on structural similarity the topological neighborhood information about pairs of objects or patterns to partition s is taken into consideration while computing a measure of structural similarity this is termed proximity and is defined in terms of membership values multi objective evolutionary optimization is employed to arrive at a consensus solution in terms of the contradictory criteria pair involving fuzzy proximity and feature set cardinality results for real and synthetic datasets of low medium and high dimensionality show that the method led to a correct selection of the reduced feature subset comparative study is also provided and quantified in terms of accuracy of classification and clustering validity indices

cluster based population initialization for differential evolution frameworks this article proposes a procedure to perform an intelligent initialization for population based algorithms the proposed pre processing procedure namely cluster based population initialization cbpi consists of three consecutive stages at the first stage the individuals belonging to a randomly sampled population undergo two subsequent local search algorithms i e a simple local search that performs moves along the axes and rosenbrock algorithm at the second stage the solutions processed by the two local searches undergo the k means clustering algorithm and are grouped into sets on the basis of their euclidean distance at the third stage the best individuals belonging to each cluster are saved into the initial population of a generic optimization algorithm if the population has not been yet filled the other individuals of the population are sampled within the clusters by using a fitness based probabilistic criterion this three stage procedure implicitly performs an initial screening of the problem features in order to roughly estimate the most interesting regions of the decision space the proposed cbpi has been tested on multiple classical and modern differential evolution variants on a wide array of test problems and dimensionality values as well as on a real world problem the proposed intelligent sampling appears to have a significant impact on the algorithmic functioning as it consistently enhances the performance of the algorithms with which it is integrated

shadowed c means integrating fuzzy and rough clustering a new method of partitive clustering is developed in the framework of shadowed sets the core and exclusion regions of the generated shadowed partitions result in a reduction in computations as compared to conventional fuzzy clustering unlike rough clustering here the choice of threshold parameter is fully automated the number of clusters is optimized in terms of various validity indices it is observed that shadowed clustering can efficiently handle overlapping among clusters as well as model uncertainty in class boundaries the algorithm is robust in the presence of outliers a comparative study is made with related partitive approaches experimental results on synthetic as well as real data sets demonstrate the superiority of the proposed approach

modeling simulating and parameter fitting of biochemical kinetic experiments in many chemical and biological applications systems of differential equations containing unknown parameters are used to explain empirical observations and experimental data the differential equations are typically nonlinear and difficult to analyze requiring numerical methods to approximate the solutions compounding this difficulty are the unknown parameters in the differential equation system which must be given specific numerical values in order for simulations to be run estrogen receptor protein dimerization is used as an example to demonstrate model construction reduction simulation and parameter estimation mathematical computational and statistical methods are applied to empirical data to deduce kinetic parameter estimates and guide decisions regarding future experiments and modeling the process demonstrated serves as a pedagogical example of quantitative methods being used to extract parameter values from biochemical data models

a novel clustering method based on hybrid k nearest neighbor graph abstract most of the existing clustering methods have difficulty in processing complex nonlinear data sets to remedy this deficiency in this paper a novel data model termed hybrid k nearest neighbor hknn graph which combines the advantages of mutual k nearest neighbor graph and k nearest neighbor graph is proposed to represent the nonlinear data sets moreover a clustering method based on the hknn graph chknn is proposed the chknn first generates several tight and small subclusters then merges these subclusters by exploiting the connectivity among them in order to select the optimal parameters for chknn we further propose an internal validity index termed k nearest neighbor index knni which can also be used to evaluate the validity of nonlinear clustering results by varying a control parameter experimental results on synthetic and real world data sets as well as that on the video clustering have demonstrated the significant improvement on performance over existing nonlinear clustering methods and internal validity indices

cpcq contrast pattern based clustering quality index for categorical data clustering validation is concerned with assessing the quality of clustering solutions since clustering is unsupervised and highly explorative clustering validation has been an important and long standing research problem existing validity measures including entropy based and distance based indices have significant shortcomings indeed for many datasets from the uci repository they fail to recognize that the expert determined classes are the best clusters and they frequently give preference to clusterings with larger number of clusters their weakness reflects their inability to accurately capture intra cluster coherence and inter cluster separation this paper proposes a novel contrast pattern based clustering quality index cpcq for categorical data by utilizing the quality and diversity of the contrast patterns which contrast the clusters in given clusterings high quality contrast patterns can serve to characterize the clusters and discriminate one cluster against the others the cpcq index is based on the rationale that a high quality clustering should have many diversified high quality contrast patterns among its clusters the quality of individual contrast patterns is defined in terms of their length support and the length of their corresponding closed pattern the quality measure concerning many diversified contrast patterns is defined in terms of the quality and diversity of some selected groups of contrast patterns with minimal overlap among contrast patterns and groups in terms of items and matching transactions experiments show that the cpcq index 1 does not require a user to provide a distance function 2 does not give inappropriate preference to larger number of clusters 3 can recognize that expert determined classes are the best clusters for many datasets from the uci repository

the heterogeneous p median problem for categorization based clustering the p median offers an alternative to centroid based clustering algorithms for identifying unobserved categories however existing p median formulations typically require data aggregation into a single proximity matrix resulting in masked respondent heterogeneity a proposed three way formulation of the p median problem explicitly considers heterogeneity by identifying groups of individual respondents that perceive similar category structures three proposed heuristics for the heterogeneous p median hpm are developed and then illustrated in a consumer psychology context using a sample of undergraduate students who performed a sorting task of major u s retailers as well as a through monte carlo analysis

silhouettes a graphical aid to the interpretation and validation of cluster analysis a new graphical display is proposed for partitioning techniques each cluster is represented by a so called silhouette which is based on the comparison of its tightness and separation this silhouette shows which objects lie well within their cluster and which ones are merely somewhere in between clusters the entire clustering is displayed by combining the silhouettes into a single plot allowing an appreciation of the relative quality of the clusters and an overview of the data configuration the average silhouette width provides an evaluation of clustering validity and might be used to select an appropriate number of clusters

an a posteriori error estimate and adaptive timestep control for a backward euler discretization of a parabolic problem a simple algorithm for adaptive timestep control is presented for a backward euler discretization of a linear parabolic problem the algorithm is based on an a posteriori error estimate involving the computed approximate solution it is proved that with only very rough a priori information on the exact solution the algorithm will choose a sequence of timesteps for which the error will be controlled up to a constant uniformly in time on a given tolerance level

least squares galerkin methods for parabolic problems ii the fully discrete case and adaptive algorithms in this second part of our series on least squares galerkin methods for parabolic initial boundary value problems we study the full discretization in time and space these methods are based on the minimization of a least squares functional for an equivalent first order system over space and time with respect to suitable discrete spaces based on the analysis of the semi discretization in time carried out in the first part we construct a posteriori error estimators for the approximation error components associated with time and space for the space discretization error we use a hierarchical basis estimator with respect to the functional minimization problem we prove a strengthened cauchy schwarz inequality between coarse and hierarchical surplus space and a bound on the condition number of the auxiliary problem both uniform in the mesh size h and the time step tau implying efficiency and reliability of the error estimator this allows for an adaptive strategy for both the time step size and the spatial triangulation keeping a proper balance between these two components numerical experiments illustrate the performance of the resulting adaptive schemes in time and space

multiway spectral clustering with out of sample extensions through weighted kernel pca a new formulation for multiway spectral clustering is proposed this method corresponds to a weighted kernel principal component analysis pca approach based on primal dual least squares support vector machine ls svm formulations the formulation allows the extension to out of sample points in this way the proposed clustering model can be trained validated and tested the clustering information is contained on the eigendecomposition of a modified similarity matrix derived from the data this eigenvalue problem corresponds to the dual solution of a primal optimization problem formulated in a high dimensional feature space a model selection criterion called the balanced line fit blf is also proposed this criterion is based on the out of sample extension and exploits the structure of the eigenvectors and the corresponding projections when the clusters are well formed the blf criterion can be used to obtain clustering parameters in a learning framework experimental results with difficult toy problems and image segmentation show improved performance in terms of generalization to new samples and computation times

adaptive finite element methods for parabolic problems i a linear model problem this paper is the first part in a series of papers on adaptive finite element methods for parabolic problems in this paper an adaptive algorithm is presented and analyzed for choosing the space a

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

multi manifold matrix decomposition for data co clustering we propose a novel multi manifold matrix decomposition for co clustering m3dc algorithm that considers the geometric structures of both the sample manifold and the feature manifold simultaneously specifically multiple candidate manifolds are constructed separately to take local invariance into account then we employ multi manifold learning to approximate the optimal intrinsic manifold which better reflects the local geometrical structure by linearly combining these candidate manifolds in m3dc the candidate manifolds are obtained using various manifold based dimensionality reduction methods these methods are based on different rationales and use different metrics for data distances experimental results on several real data sets demonstrate the effectiveness of our proposed m3dc highlightswe consider the geometric structures of both sample and feature manifolds to reduces the complexity we use two low dimensional intermediate matrices we employ multi manifold learning to approximate the intrinsic manifold the intrinsic manifold is constructed by linearly combining multiple manifolds the candidate manifolds are constructed using six dimensionality reduction methods

characterizing the functional connectivity diversity of the insula cortex subregions diversity curves and behavior the connectivity of the insula cortex is diverse we present new models to characterize the resting state connectional diversity of the human insula cortex and perform model selection using high quality fmri data from the human connectome project we first attempt to parcellate the insula into distinct subregions using traditional clustering methods but find that the resulting subregions are not homogeneous and that the optimal number of subregions is substantially influenced by data smoothness we then introduce the concept of a diversity curve which we use to continuously parameterize the insula s laplacian eigenmap with respect to streamlines propagated through the eigenmap s gradient field to perform model selection we compare the insula s diversity curve to benchmark diversity curves for i two distinct regions ii a continuum of gradual change and iii an absence of any connectional diversity i e homogenous region of the three benchmarks tested we find that the insula s connectional diversity is most parsimoniously modeled as continuum of gradual change from dorsal posterior to ventral anterior we find that individuals who score high on measures of positive affect self efficacy emotion recognition motor dexterity and gustation show greater diversity within the anterior insula our findings are replicated using data from a second fmri session we conclude that the functional connectivity diversity of the insula can be characterized parsimoniously as a continuum avoiding the vexed task of determining an optimal number of insula subregions and that inter individual variation in this continuum can explain significant variation in behavior

statistical physics of language maps in the usa spatial linguistic surveys often reveal well defined geographical zones where certain linguistic forms are dominant over their alternatives it has been suggested that these patterns may be understood by analogy with coarsening in models of two dimensional physical systems here we investigate this connection by comparing data from the cambridge online survey of world englishes to the behavior of a generalized zero temperature potts model with long range interactions the relative displacements of linguistically similar population centers reveal enhanced east west affinity cluster analysis reveals three distinct linguistic zones we find that when the interaction kernel is made anisotropic by stretching along the east west axis the model can reproduce the three linguistic zones for all interaction parameters tested the model results are consistent with a view held by some linguists that in the usa language use is or has been exchanged or transmitted to a greater extent along the east west axis than the north south

least squares galerkin methods for parabolic problems iii semidiscrete case for semilinear problems this is the third part of a series of papers on least squares galerkin methods for parabolic initial boundary value problems these methods are based on the minimization of a least squares functional for an equivalent first order system over space and time with respect to suitable discrete spaces this paper presents the derivation and analysis of one step methods for semidiscretization in time from least squares principles for semilinear parabolic problems one of the most important features of the least squares methodology is a built in a posteriori estimate for the approximation error for the presentation in this paper we focus our attention on the specific combination of piecewise linear not necessarily continuous functions in time with continuous piecewise linear for the flux and scalar variables respectively for the resulting method a convergence result is shown for the scalar variable

a model selection approach for clustering a multinomial sequence with non negative factorization we consider a problem of clustering a sequence of multinomial observations by way of a model selection criterion we propose a form of a penalty term for the model selection procedure our approach subsumes both the conventional aic and bic criteria but also extends the conventional criteria in a way that it can be applicable also to a sequence of sparse multinomial observations where even within a same cluster the number of multinomial trials may be different for different observations in addition as a preliminary estimation step to maximum likelihood estimation and more generally to maximum l q estimation we propose to use reduced rank projection in combination with non negative factorization we motivate our approach by showing that our model selection criterion and preliminary estimation step yield consistent estimates under simplifying assumptions we also illustrate our approach through numerical experiments using real and simulated data

groups of lie type generated by long root elements in f4 k abstract let k be a field and g a quasi simple subgroup of the chevalley group f4 k we assume that g is generated by a class of abstract root subgroups such that there are a c with a c and any a is contained in a long root subgroup of f4 k we determine the possibilities for g and describe the embedding of g in f4 k

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

multiclass semisupervised learning based upon kernel spectral clustering this paper proposes a multiclass semisupervised learning algorithm by using kernel spectral clustering ksc as a core model a regularized ksc is formulated to estimate the class memberships of data points in a semisupervised setting using the one versus all strategy while both labeled and unlabeled data points are present in the learning process the propagation of the labels to a large amount of unlabeled data points is achieved by adding the regularization terms to the cost function of the ksc formulation in other words imposing the regularization term enforces certain desired memberships the model is then obtained by solving a linear system in the dual furthermore the optimal embedding dimension is designed for semisupervised clustering this plays a key role when one deals with a large number of clusters

adaptive finite element methods for parabolic problems v long time integration we continue our previous work on adaptive finite element methods for parabolic problems now with particular emphasis on long time integration for semidefinite problems

method for determining the optimal number of clusters based on agglomerative hierarchical clustering it is crucial to determine the optimal number of clusters for the clustering quality in cluster analysis from the standpoint of sample geometry two concepts i e the sample clustering dispersion degree and the sample clustering synthesis degree are defined and a new clustering validity index is designed moreover a method for determining the optimal number of clusters based on an agglomerative hierarchical clustering ahc algorithm is proposed the new index and the method can evaluate the clustering results produced by the ahc and determine the optimal number of clusters for multiple types of datasets such as linear manifold annular and convex structures theoretical research and experimental results indicate the validity and good performance of the proposed index and the method

cluster correspondence analysis a method is proposed that combines dimension reduction and cluster analysis for categorical data by simultaneously assigning individuals to clusters and optimal scaling values to categories in such a way that a single between variance maximization objective is achieved in a unified framework a brief review of alternative methods is provided and we show that the proposed method is equivalent to groupals applied to categorical data performance of the methods is appraised by means of a simulation study the results of the joint dimension reduction and clustering methods are compared with the so called tandem approach a sequential analysis of dimension reduction followed by cluster analysis the tandem approach is conjectured to perform worse when variables are added that are unrelated to the cluster structure our simulation study confirms this conjecture moreover the results of the simulation study indicate that the proposed method also consistently outperforms alternative joint dimension reduction and clustering methods

non hierarchical clustering with masloc abstract masloc is a cluster analysis technique based on the p median model of location theory which permits for each value of p clustering the given objects into p groups each provided with a representative object both an exact and heuristic method are described along with their application range the interesting values for p are then determined along with the more interesting clusters by robustness analysis the paper includes a description of a computer program for masloc and some of the applications it was used for

fingerprint indexing based on minutiae pairs and convex core point an efficient fingerprint indexing which uses ellipse properties is proposed a new fingerprint indexing is proposed using minutiae pairs and convex core point our fingerprint representation is very robust to distortions and noise the proposed fingerprint features are invariant to rotation and translation fingerprint identification is an important issue for identifying fingerprints and plays a key role in the fingerprint recognition systems however performing a fingerprint identification over a large database can be an inefficient task due to the lack of scalability and high computing times of fingerprint matching algorithms fingerprint indexing is a key strategy in automatic fingerprint identification systems afiss which allows us to reduce the number of candidates the search space and the occurrences of false acceptance in large databases in this paper an efficient indexing algorithm is proposed using minutiae pairs and convex core point which employs k means clustering and candidate list reduction criteria to improve the identification performance our proposal can effectively reduce the search space and number of candidates for fingerprint matching and thus achieves higher efficiency and significantly improves the system retrieval performance experimental results over some of the fingerprint verification competition fvc and the national institute of standards and technology nist databases prove the superiority of the proposed approach against some of the well known indexing algorithms

adaptive finite element methods for parabolic problems ii optimal error estimates in l l 2 and l l optimal error estimates are derived for a complete discretization of linear parabolic problems using space time finite elements the discretization is done first in time using the discontinuous galerkin method and then in space using the standard galerkin method the underlying partitions in time and space need not be quasi uniform and the partition in space may be changed from time step to time step the error bounds show in particular that the error may be controlled globally in time on a given tolerance level by controlling the discretization error on each individual time step on the same given level i e without error accumulation effects the derivation of the estimates is based on the orthogonality of the galerkin procedure and the use of strong stability estimates the particular and precise form of these error estimates makes it possible to design efficient adaptive methods with reliable automatic error control for parabolic problems in the norms under consideration

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

fuzzy partitions a way to integrate expert knowledge into distance calculations this work proposes a new pseudo metric based on fuzzy partitions fps this pseudo metric allows for the introduction of expert knowledge into distance computations performed on numerical data and can be used in various types of statistical clustering or other applications the knowledge is formalized by a fp in which each fuzzy set represents a linguistic concept the pseudo metric is designed to respect the fp semantics the univariate case is first studied and the pseudo metric behavior is discussed using synthetic experiments then a multivariate version is proposed as a minkowski like combination of univariate distances or semi distances the value of the proposal is illustrated with two real world case studies in the fields of biology and precision agriculture

least squares galerkin methods for parabolic problems i semidiscretization in time this is the first part of a series of papers on least squares galerkin methods for parabolic initial boundary value problems these methods are based on the minimization of a least squares functional for an equivalent first order system over space and time with respect to suitable discrete spaces this paper presents the derivation and analysis of one step methods for semi discretization in time from least squares principles for linear parabolic problems one of the most important features of the least squares methodology is the built in a posteriori estimate for the approximation error this is a consequence of the equivalence of the least squares functional to the consistency error associated with a time step measured in an appropriate norm for the presentation in this paper we focus our attention on the specific combination of piecewise linear not necessarily continuous functions with continuous piecewise linear functions for the flux and scalar variable respectively for the resulting method a convergence result is shown for the scalar variable and the associated flux