novel graphical representation of genome sequence and its applications in similarity analysis abstract in order to compare different genome sequences an alignment free method has been proposed considering the essential property of sequence is sequentiality we define a compound transformation which transforms a genome sequence into a sparse 16 by l 1 matrix m based on 16 kinds of 2 mer dinucleotides furthermore we found the transformation above mentioned is an order preserving transformation opt based on the theory of matrix analysis we derive a 16 dimensional vector to characterize a genome sequence via singular value decomposition svd of m finally we analyze the similarities among multiple sequences from 20 eutherian species the experiment results show that our approach performs well in the field of sequence analysis

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

existence of multiple positive weak solutions and estimates for extremal values to a class of elliptic problems with hardy term and singular nonlinearity abstract this paper is devoted to the study of a class of elliptic equations of the form u x 2 u h x u q w x u p x 0 with dirichlet boundary conditions where 0 r n n 3 is a bounded domain with smooth boundary 0 is a parameter 0 n 2 2 4 0 q 1 p 2 1 n 2 n 2 h x 0 and w x is a given function with the set x w x 0 of positive measure using variational methods we establish some existence and multiplicity of positive solutions and provide uniform estimates of extremal values for the problem

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

plurality and resemblance in fmri data analysis abstract we apply nine analytic methods employed currently in imaging neuroscience to simulated and actual bold fmri signals and compare their performances under each signal type starting with baseline time series generated by a resting subject during a null hypothesis study we compare method performance with embedded focal activity in these series of three different types whose magnitudes and time courses are simple convolved with spatially varying hemodynamic responses and highly spatially interactive we then apply these same nine methods to bold fmri time series from contralateral primary motor cortex and ipsilateral cerebellum collected during a sequential finger opposition study paired comparisons of results across methods include a voxel specific concordance correlation coefficient for reproducibility and a resemblance measure that accommodates spatial autocorrelation of differences in activity surfaces receiver operating characteristic curves show considerable model differences in ranges less than 10 significance level false positives and greater than 80 power true positives concordance and resemblance measures reveal significant differences between activity surfaces in both data sets these measures can assist researchers by identifying groups of models producing similar and dissimilar results and thereby help to validate consolidate and simplify reports of statistical findings a pluralistic strategy for fmri data analysis can uncover invariant and highly interactive relationships between local activity foci and serve as a basis for further discovery of organizational principles of the brain results also suggest that a pluralistic empirical strategy coupled formally with substantive prior knowledge can help to uncover new brain behavior relationships that may remain hidden if only a single method is employed

an efficient k nearest neighbor search for multivariate time series multivariate time series mts datasets are common in various multimedia medical and financial applications in order to efficiently perform k nearest neighbor searches for mts datasets we present a similarity measure eros extended frobenius norm an index structure muse multilevel distance based index structure for eros and a feature subset selection technique ropes recursive feature elimination on common principal components for eros eros is based on principal component analysis and computes the similarity between two mts items by measuring how close the corresponding principal components are using the eigenvalues as weights muse constructs each level as a distance based index structure without using the weights up to z levels which are combined at the query time with the weights ropes utilizes both the common principal components and the weights recursively in order to select a subset of features for eros the experimental results show the superiority of our techniques as compared to earlier approaches

analysis of fmri data using improved self organizing mapping and spatio temporal metric hierarchical clustering the self organizing mapping som and hierarchical clustering hc methods are integrated to detect brain functional activation functional magnetic resonance imaging fmri data are first processed by som to obtain a primary merged neural nodes image and then by hc to obtain further brain activation patterns the conventional euclidean distance metric was replaced by the correlation distance metric in som to improve clustering and merging of neural nodes to improve the use of spatial and temporal information in fmri data a new spatial distance node coordinates in the 2 d lattice and temporal correlation correlation degree of each time course in the exemplar matrix are introduced in hc to merge the primary som results two simulation studies and two in vivo fmri data that both contained block design and event related experiments revealed that brain functional activation can be effectively detected and that different response patterns can be distinguished using these methods our results demonstrate that the improved som and hc methods are clearly superior to the statistical parametric mapping spm independent component analysis ica and conventional som methods in the block design especially in the event related experiment as revealed by their performance measured by receiver operating characteristic roc analysis our results also suggest that the proposed new integrated approach could be useful in detecting block design and event related fmri data

time series clustering with arma mixtures clustering problems are central to many knowledge discovery and data mining tasks however most existing clustering methods can only work with flxed dimensional representations of data patterns in this paper we study the clustering of data patterns that are represented as sequences or time series possibly of difierent lengths we propose a model based approach to this problem using mixtures of autoregressive moving average arma models we derive an expectation maximization em algorithm for learning the mixing coe cients as well as the parameters of the component models to address the model selection problem we use the bayesian information criterion bic to determine the number of clusters in the data experiments are conducted on a number of simulated and real datasets results from the experiments show that our method compares favorably with other methods proposed previously by others for similar time series clustering tasks

how to avoid spurious cluster validation a methodological investigation on simulated and fmri data abstract this paper presents an evaluation of a common approach that has been considered as a promising option for exploratory fmri data analyses the approach includes two stages creating from the data a sequence of partitions with increasing number of subsets clustering and selecting the one partition in this sequence that exhibits the clearest indications of an existing structure cluster validation in order to achieve that the selected partition is actually the best characterization of the data structure previous studies were directed to find the most appropriate validity function s in our analysis protocol we first optimize the sequence of partitions according to the given objective function our study showed that an insufficient optimization of the partition for one or more numbers of clusters can easily yield a spurious validation result which in turn may lead the analyst to a misleading interpretation of the fmri experiment however a sufficient optimization for each included number of clusters provided the basis for a reliable adequate characterization of the data furthermore it enabled an adequate evaluation of the validity functions these findings were obtained independently for three clustering algorithms representing the hard and fuzzy clustering variant and three up to date cluster validity functions the findings were derived from analyses of gaussian clusters simulated data sets that mimic typical fmri response signals and real fmri data based on our results we propose a number of options of how to configure improved clustering tools

bayesian spatiotemporal model of fmri data this research describes a new bayesian spatiotemporal model to analyse block design bold fmri studies in the temporal dimension we parameterise the hemodynamic response function s hrf shape with a potential increase of signal and a subsequent exponential decay in the spatial dimension we use gaussian markov random fields gmrf priors on activation characteristics parameters location and magnitude that embody our prior knowledge that evoked responses are spatially contiguous and locally homogeneous the result is a spatiotemporal model with a small number of parameters all of them interpretable simulations from the model are performed in order to ascertain the performance of the sampling scheme and the ability of the posterior to estimate model parameters as well as to check the model sensitivity to signal to noise ratio results are shown on synthetic data and on real data from a block design fmri experiment

a novel dna sequence similarity calculation based on simplified pulse coupled neural network and huffman coding abstract a novel method for the calculation of dna sequence similarity is proposed based on simplified pulse coupled neural network s pcnn and huffman coding in this study we propose a coding method based on huffman coding where the triplet code was used as a code bit to transform dna sequence into numerical sequence the proposed method uses the firing characters of s pcnn neurons in dna sequence to extract features besides the proposed method can deal with different lengths of dna sequences first according to the characteristics of s pcnn and the dna primary sequence the latter is encoded using huffman coding method and then using the former the oscillation time sequence ots of the encoded dna sequence is extracted simultaneously relevant features are obtained and finally the similarities or dissimilarities of the dna sequences are determined by euclidean distance in order to verify the accuracy of this method different data sets were used for testing the experimental results show that the proposed method is effective

a novel graphical representation of proteins and its application abstract on the basis of three kinds of indices of physicochemical properties of twenty amino acids a novel 3d graphical representation of protein sequences is presented then the improved cumulative distance of the 3d graphical representations is defined in order to compare the proteins for similarity furthermore the efficiency of our approach is illustrated by performing a comparison of similarities dissimilarities among sequences of the nd5 proteins of nine different species a correlation and significance analysis is provided to compare our results on similarities dissimilarities and some other graphical representation results with the clustalw results on similarities dissimilarities the comparison results show that our approach has better correlations with clustalw for all nine species than other approaches

competitive algorithms for the clustering of noisy data abstract in this paper we consider the issue of clustering when outliers exist the outlier set is defined as the complement of the data set following this concept a specially designed fuzzy membership weighted objective function is proposed and the corresponding optimal membership is derived unlike the membership of fuzzy c means the derived fuzzy membership does not reduce with the increase of the cluster number with the suitable redefinition of the distance metric we demonstrate that the objective function could be used to extract c spherical shells a hard clustering algorithm alleviating the prototype under utilization problem is also derived artificially generated data are used for comparisons

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

3 d maps and coupling numbers for protein sequences abstract based on a five letter model of the 20 amino acids we propose a new 3 d graphical representation of protein sequence then we derive from the graphical representation numerical indices called 3 d coupling numbers to characterize protein sequences the examination of the similarities dissimilarities among the globin proteins of 15 species illustrates the utility of the approach

a new fuzzy set merging technique using inclusion based fuzzy clustering this paper proposes a new method of merging parameterized fuzzy sets based on clustering in the parameters space taking into account the degree of inclusion of each fuzzy set in the cluster prototypes the merger method is applied to fuzzy rule base simplification by automatically replacing the fuzzy sets corresponding to a given cluster with that pertaining to cluster prototype the feasibility and the performance of the proposed method are studied using an application in mobile robot navigation the results indicate that the proposed merging and rule base simplification approach leads to good navigation performance in the application considered and to fuzzy models that are interpretable by experts in this paper we concentrate mainly on fuzzy systems with gaussian membership functions but the general approach can also be applied to other parameterized fuzzy sets

statistical measures of dna sequence dissimilarity under markov chain models of base composition in molecular biology the issue of quantifying the similarity between two biological sequences is very important past research has shown that word based search tools are computationally efficient and can find some new functional similarities or dissimilarities invisible to other algorithms like fasta recently under the independent model of base composition wu burke and davison 1997 biometrics 53 1431 1439 characterized a family of word based dissimilarity measures that defined distance between two sequences by simultaneously comparing the frequencies of all subsequences of n adjacent letters i e n words in the two sequences specifically they introduced the use of mahalanobis distance and standardized euclidean distance into the study of dna sequence dissimilarity they showed that both distances had better sensitivity and selectivity than the commonly used euclidean distance the purpose of this article is to extend mahalanobis and standardized euclidean distances to markov chain models of base composition in addition a new dissimilarity measure based on kullback leibler discrepancy between frequencies of all n words in the two sequences is introduced applications to real data demonstrate that kullback leibler discrepancy gives a better performance than euclidean distance moreover under a markov chain model of order kq for base composition where kq is the estimated order based on the query sequence standardized euclidean distance performs very well under such a model it performs as well as mahalanobis distance and better than kullback leibler discrepancy and euclidean distance since standardized euclidean distance is drastically faster to compute than mahalanobis distance in a usual workstation pc computing environment the use of standardized euclidean distance under the markov chain model of order kq of base composition is generally recommended however if the user is very concerned with computational efficiency then the use of kullback leibler discrepancy which can be computed as fast as euclidean distance is recommended this can significantly enhance the current technology in comparing large datasets of dna sequences

wavelets based clustering of multivariate time series crisp and fuzzy clustering methods based on a combination of univariate and multivariate wavelet features are considered for the clustering of multivariate time series the performance of each of these methods is evaluated for stationary and variance nonstationary multivariate time series with different error correlation structures the main outcomes of the simulation studies are are as follows the superior performance of this approach for both the crisp and fuzzy cluster methods compared to some of the other approaches for clustering multivariate time series the very good performance of the fuzzy relational method overall to cluster longer time series when all of them do not appear to group exclusively into well separated clusters we consider an application to multivariate greenhouse gases time series and show that the crisp and fuzzy clustering methods considered are well validated

cluster significance testing using the bootstrap many of the statistical methods currently employed to analyze fmri data depend on a response template however the true form of the hemodynamic response and thereby the response template is often unknown consequently cluster analysis provides a complementary template free method for exploratory analysis of multidimensional fmri data sets clustering algorithms currently being applied to fmri data separate the data into a predefined number of clusters k a poor choice of k will result in erroneously partitioning well defined clusters although several clustering algorithms have been successfully applied to fmri data techniques for statistically testing cluster separation are still lacking to address this problem we suggest a method based on fisher s linear discriminant and the bootstrap also introduced in this paper is a measure based on the projection of multidimensional data from two clusters onto the vector maximizing the ratio of the between to the within cluster sums of squares the resulting one dimensional distribution may be readily visualized and used as a heuristic for estimating cluster homogeneity these methods are demonstrated for the self organizing maps clustering algorithm when applied to event related fmri data

some further results on a semilinear equation with concave convex nonlinearity abstract following our previous work j math anal appl 295 2004 341 we give an exact growth order near zero for positive solutions of a class of elliptic equation and use it to give the existence of multiple solutions with negative energy multiple positive solutions and sign changing solutions of the considered problem even in the particular case our results extend a previous work by ambrosetti garcia peral j funct anal 137 1996 219

analysis of fmri time series revisited again friston et al 1995 neuroimage 2 45 53 presented a method for detecting activations in fmr1 time series based on the general linear model and a heuristic analysis of the effective degrees of freedom in this communication we present corrected results that replace those of the previous paper and solve the same problem without recourse to heuristic arguments specifically we introduce a proper and unbiased estimator for the error terms and provide a more generally correct expression for the effective degrees of freedom the previous estimates of error variance were biased and in some instances could have led to a 10 20 overestimate of z values although the previous results are almost correct for the random regressors chosen for validation the present theoretical results are exact for any covariate or waveform we comment on some aspects of experimental design and data analysis in the light of the theoretical framework discussed here

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

comparison and classification of stationary multivariate time series abstract this paper presents procedures to compare and classify stationary multivariate time series the classification procedure is based on the p value of a test of hypothesis that is performed for every pair of series under consideration the test of hypothesis is based on the difference between vector autoregressive parameter estimates of the series simulation studies show that the test of hypothesis and the classification procedure perform fairly well for series of reasonable length

huffman coding with letter costs a linear time approximation scheme we give a polynomial time approximation scheme for the generalization of huffman coding in which codeword letters have nonuniform costs as in morse code where the dash is twice as long as the dot the algorithm computes a 1 epsilon approximate solution in time o n f epsilon log 3n where n is the input size

fuzzy order statistics and their application to fuzzy clustering the median and the median absolute deviation mad are robust statistics based on order statistics order statistics are extended to fuzzy sets to define a fuzzy median and a fuzzy mad the fuzzy c means fcm clustering algorithm is defined for any p norm pfcm including the l sub 1 norm 1fcm the 1fcm clustering algorithm is implemented via the alternating optimization ao method and the clustering centers are shown to be the fuzzy median the resulting ao 1fcm clustering algorithm is called the fuzzy c medians fcmed clustering algorithm an example illustrates the robustness of the fcmed

a measure of the similarity of sets of sequences not requiring sequence alignment abstract determination of first and second order markov chain homogeneity of sets of nuclear eukaryotic dna sequences both coding and noncoding finds similarities imperceptible to the standard needleman wunsch base matching or dot matrix algorithms these measures of the similarities of the distributions of adjacent pairs or triplets are in agreement with accepted evolutionary tree topologies hierarchical clustering of the distributions of doublets of 30 miscellaneous coding sequences gives clusters in reasonable agreement with accepted biological classifications in addition to similarity by homology there is also observed similarity of disparate genes in the same organism for example all three disparate yeast genes two enzymes and actin form a well distinguished cluster

a coherence based approach for the pattern recognition of time series abstract a pattern recognition approach based on the frequency domain measure of squared coherence is a useful approach to identify linearly related groupings of time series over different periods of time it is considered in an application to identify similar patterns of the yearly rates of change in the gross domestic product gdp of twenty two highly developed countries in an econophysics context the approach is also tested in simulation studies using linearly related time series and it is shown to have a very good success rate of correct pattern matching

non parametric bayesian graph models reveal community structure in resting state fmri modeling of resting state functional magnetic resonance imaging rs fmri data using network models is of increasing interest it is often desirable to group nodes into clusters to interpret the communication patterns between nodes in this study we consider three dierent nonparametric bayesian

distributional regimes for the number of k word matches between two random sequences when comparing two sequences a natural approach is to count the number of k letter words the two sequences have in common no positional information is used in the count but it has the virtue that the comparison time is linear with sequence length for this reason this statistic d2 and certain transformations of d2 are used for est sequence database searches in this paper we begin the rigorous study of the statistical distribution of d2 using an independence model of dna sequences we derive limiting distributions by means of the stein and chen stein methods and identify three asymptotic regimes including compound poisson and normal the compound poisson distribution arises when the word size k is large and word matches are rare the normal distribution arises when the word size is small and matches are common explicit expressions for what is meant by large and small word sizes are given in the paper however when word size is small and the letters are uniformly distributed the anticipated limiting normal distribution does not always occur in this situation the uniform distribution provides the exception to other letter distributions therefore a naive one distribution fits all approach to d2 statistics could easily create serious errors in estimating significance

fuzzy clustering of time series in the frequency domain traditional and fuzzy cluster analyses are applicable to variables whose values are uncorrelated hence in order to cluster time series data which are usually serially correlated one needs to extract features from the time series the values of which are uncorrelated the periodogram which is an estimator of the spectral density function of a time series is a feature that can be used in the cluster analysis of time series because its ordinates are uncorrelated additionally the normalized periodogram and the logarithm of the normalized periodogram are also features that can be used in this paper we consider a fuzzy clustering approach for time series based on the estimated cepstrum the cepstrum is the spectrum of the logarithm of the spectral density function we show in our simulation studies for the typical generating processes that have been considered fuzzy clustering based on the cepstral coefficients performs very well compared to when it is based on other features

efficient certifiably optimal clustering with applications to latent variable graphical models motivated by the task of clustering either d variables or d points into k groups we investigate efficient algorithms to solve the peng wei p w k means semi definite programming sdp relaxation the p w sdp has been shown in the literature to have good statistical properties in a variety of settings but remains intractable to solve in practice to this end we propose force a new algorithm to solve this sdp relaxation compared to off the shelf interior point solvers our method reduces the computational complexity of solving the sdp from widetilde mathcal o d 7 log epsilon 1 to widetilde mathcal o d 6 k 2 epsilon 1 arithmetic operations for an epsilon optimal solution our method combines a primal first order method with a dual optimality certificate search which when successful allows for early termination of the primal method we show for certain variable clustering problems that with high probability force is guaranteed to find the optimal solution to the sdp relaxation and provide a certificate of exact optimality as verified by our numerical experiments this allows force to solve the p w sdp with dimensions in the hundreds in only tens of seconds for a variation of the p w sdp where k is not known a priori a slight modification of force reduces the computational complexity of solving this problem as well from widetilde mathcal o d 7 log epsilon 1 using a standard sdp solver to widetilde mathcal o d 4 epsilon 1

a new cluster validity for fuzzy clustering abstract fuzzy cluster validity criterion tends to evaluate the quality of fuzzy c partitions produced by fuzzy clustering algorithms many functions have been proposed some methods use only the properties of fuzzy membership degrees to evaluate partitions others techniques combine the properties of membership degrees and the structure of data in this paper a new heuristic method is based on the combination of two functions the search of good clustering is measured by a fuzzy compactness separation ratio the first function calculates this ratio by considering geometrical properties and membership degrees of data the second function evaluates it by using only the properties of membership degrees four numerical examples are used to illustrate its use as a validity functional its effectiveness is compared to some existing cluster validity criterion

some further results for a class of weighted nonlinear elliptic equations following our previous work m lin multiple positive solutions for a class of weighted nonlinear elliptic equations preprint 2006 we give an exact growth order near zero for positive solutions of a class of weighted elliptic equations and use it to give the existence of multiple positive solutions and sign changing solutions of the considered problem

estimation and classification of fmri hemodynamic response patterns in this paper we propose an approach to modeling functional magnetic resonance imaging fmri data that combines hierarchical polynomial models bayes estimation and clustering a cubic polynomial is used to fit the voxel time courses of event related design experiments the coefficients of the polynomials are estimated by bayes estimation in a two level hierarchical model which allows us to borrow strength from all voxels the voxel specific bayes polynomial coefficients are then transformed to the times and magnitudes of the minimum and maximum points on the hemodynamic response curve which are in turn used to classify the voxels as being activated or not the procedure is demonstrated on real data from an event related design experiment of visually guided saccades and shown to be an effective alternative to existing methods

a novel representation of dna sequence based on cmi coding abstract graphical representation of dna sequences provides a simple and intuitive way of analyzing and sorting various gene sequences it is attractive to researchers to propose much more appropriate methods in this study a new graphical representation is presented the method adopts the cmi coding to represent four nucleotides a g c and t our approach considers not only the sequences structure but also the chemical structure for dna sequence we take several sets of data to test our method the results of our experiment demonstrate that our representation is effective

robust fuzzy clustering of relational data popular relational data clustering algorithms relational dual of fuzzy c means rfcm non euclidean rfcm nerfcm both by hathaway et al and fanny by kaufman and rousseeuw are examined a new algorithm which is a generalization of fanny called the fuzzy relational data clustering frc algorithm is introduced having an identical objective functional as rfcm however the frc does not have the restriction of rfcm which is that the relational data is derived from euclidean distance as the measure of dissimilarity between the objects and it also does not have limitations of fanny including the use of a fixed membership exponent or a fuzzifier exponent m the frc algorithm is further improved by incorporating the concept of dave s object data noise clustering nc algorithm done by proposing a concept of noise dissimilarity next based on the constrained minimization which includes an inequality constraint for the memberships and corresponding kuhn tucker conditions a noise resistant frc algorithm is derived which works well for all types of non euclidean dissimilarity data thus it is shown that the extra computations for data expansion spl beta spread transformation required by the nerfcm algorithm are not necessary this new algorithm is called robust non euclidean fuzzy relational data clustering robust ne frc and its robustness is demonstrated through several numerical examples advantages of this new algorithm are faster convergence robustness against outliers and ability to handle all kinds of relational data including non euclidean the paper also presents a new and better interpretation of the noise class

clustering spatiotemporal data an augmented fuzzy c means in spatiotemporal data commonly encountered in geographical systems biomedical signals and the like each datum is composed of features comprising a spatial component and a temporal part clustering of data of this nature poses challenges especially in terms of a suitable treatment of the spatial and temporal components of the data in this study proceeding with the objective function based clustering such as e g fuzzy c means we revisit and augment the algorithm to make it applicable to spatiotemporal data an augmented distance function is discussed and the resulting clustering algorithm is provided two optimization criteria i e a reconstruction error and a prediction error are introduced and used as a vehicle to optimize the performance of the clustering method experimental results obtained for synthetic and real world data are reported

searchlight based multi voxel pattern analysis of fmri by cross validated manova abstract multi voxel pattern analysis mvpa is a fruitful and increasingly popular complement to traditional univariate methods of analyzing neuroimaging data we propose to replace the standard decoding approach to searchlight based mvpa measuring the performance of a classifier by its accuracy with a method based on the multivariate form of the general linear model following the well established methodology of multivariate analysis of variance manova we define a measure that directly characterizes the structure of multi voxel data the pattern distinctness d our measure is related to standard multivariate statistics but we apply cross validation to obtain an unbiased estimate of its population value independent of the amount of data or its partitioning into training and test sets the estimate d can therefore serve not only as a test statistic but also as an interpretable measure of multivariate effect size the pattern distinctness generalizes the mahalanobis distance to an arbitrary number of classes but also the case where there are no classes of trials because the design is described by parametric regressors it is defined for arbitrary estimable contrasts including main effects pattern differences and interactions pattern changes in this way our approach makes the full analytical power of complex factorial designs known from univariate fmri analyses available to mvpa studies moreover we show how the results of a factorial analysis can be used to obtain a measure of pattern stability the equivalent of cross decoding

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

the possibilistic c means algorithm insights and recommendations recently the possibilistic c means algorithm pcm was proposed to address the drawbacks associated with the constrained memberships used in algorithms such as the fuzzy c means fcm in this issue barni et al 1996 report a difficulty they faced while applying the pcm and note that it exhibits an undesirable tendency to converge to coincidental clusters the purpose of this paper is not just to address the issues raised by barni et al but to go further and analytically examines the underlying principles of the pcm and the possibilistic approach in general we analyze the data sets used by barni et al and interpret the results reported by them in the light of our findings

a graphical representation of protein based on a novel iterated function system abstract in this article a novel family of iterated function system ifs was introduced to outline a 2d graphical representation of protein sequences which incorporates with various physicochemical properties of amino acids then a mathematical description was suggested to quantificationally compare the similarities and dissimilarities of protein sequences from their 2d curves based on this method similarities dissimilarities were compared among sequences of the nd5 proteins of nine different species as well as sequences of eight nd6 proteins the phylogenetic tree of the nine nd5 proteins was constructed according to fuzzy cluster analysis by correlation analysis the clustalw results were compared with our similarity dissimilarity results and other graphical representation results to demonstrate the effectiveness of our approach

3d graphical representation of protein sequences and their statistical characterization abstract based on three physicochemical properties of amino acid side chains we proposed a novel unique 3d graphical representation of protein sequences then we constructed two vectors of three components as mathematical objects to characterize protein sequences numerically the similarity dissimilarity analysis among nine nd5 protein sequences proved the utility of our approach a correlation and significance analysis have been provided to compare our results and the sequence homology

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

fractal landscape analysis of dna walks by mapping nucleotide sequences onto a dna walk we uncovered remarkably long range power law correlations nature 356 1992 168 that imply a new scale invariant property of dna we found such long range correlations in intron containing genes and in non transcribed regulatory dna sequences but not in cdna sequences or intron less genes in this paper we present more explicit evidences to support our findings

fuzzy c ordered means clustering fuzzy clustering helps to find natural vague boundaries in data the fuzzy c means method is one of the most popular clustering methods based on minimization of a criterion function however one of the greatest disadvantages of this method is its sensitivity to the presence of noise and outliers in data this paper introduces a new robust fuzzy clustering method named fuzzy c ordered means fcom clustering this method uses both the huber s m estimators and the yager s owa operators to obtain its robustness the proposed method is compared to many other ones e g the fuzzy c means fcm the possibilistic clustering pc the fuzzy noise clustering method ncm the l p norm clustering l p fcm 0 p 1 the l 1 norm clustering l 1 fcm the fuzzy clustering with polynomial fuzzifier pfcm and the e insensitive fuzzy c means fcm to this end experiments on synthetic data with outliers have been performed as well as on data with heavy tailed and overlapping groups of points in background noise

robust clustering methods a unified view clustering methods need to be robust if they are to be useful in practice in this paper we analyze several popular robust clustering methods and show that they have much in common we also establish a connection between fuzzy set theory and robust statistics and point out the similarities between robust clustering methods and statistical methods such as the weighted least squares technique the m estimator the minimum volume ellipsoid algorithm cooperative robust estimation minimization of probability of randomness and the epsilon contamination model by gleaning the common principles upon which the methods proposed in the literature are based we arrive at a unified view of robust clustering methods we define several general concepts that are useful in robust clustering state the robust clustering problem in terms of the defined concepts and propose generic algorithms and guidelines for clustering noisy data we also discuss why the generalized hough transform is a suboptimal solution to the robust clustering problem

classification of temporal sequences via prediction using the simple recurrent neural network abstract an approach to classify temporal sequences using the simple recurrent neural network srnn is developed in this paper a classification problem is formulated as a component prediction problem and two training methods are described to train a single srnn to predict the components of temporal sequences belonging to multiple classes issues related to the selection of the dimension of the context vector and the influence of the context vector on classification are identified and investigated the use of a different initial context vector for each class is proposed as a means to improve classification and a classification rule which incorporates the different initial context vectors is formulated a systematic method in which the srnn is trained with noisy exemplars is developed to enhance the classification performance of the network a 4 class localized object classification problem is selected to demonstrate that a a single srnn can be trained to classify real multi class sequences via component prediction b the classification accuracy can be improved by using a distinguishing initial context vector for each class and c the classification accuracy of the srnn can be improved significantly by using the distinguishing initial context vector in conjunction with the systematic re training method it is concluded that through the approach developed in this paper the srnn can robustly classify temporal sequences which may have an unequal number of components

a connectivity based method for defining regions of interest in fmri data in this paper we describe a new methodology for defining brain regions of interset rois in functional magnetic resonance imaging fmri data the rois are defined based on their functional connectivity to other rois i e rois are defined as sets of voxels with similar connectivity patterns to other rois the method relies on 1 a spatially regularized canonical correlation analysis for identifying maximally correlated signals which are not due to correlated noise 2 a test for merging rois which have similar connectivity patterns to the other rois and 3 a graph cuts optimization for assigning voxels to rois since our method is fully connectivity based the extracted rois and their corresponding time signals are ideally suited for a subsequent brain connectivity analysis

comments on a possibilistic approach to clustering in this comment we report a difficulty with the application of the possibilistic approach to fuzzy clustering pcm proposed by keller and krishnapuram 1993 in applying this algorithm we found that it has the undesirable tendency to produce coincidental clusters results illustrating this tendency are reported and a possible explanation for the pcm behavior is suggested

a novel graphical representation and similarity analysis of protein sequences based on physicochemical properties abstract one of popular topic in bioinformatics is protein sequence analysis the graphical representation of protein sequence is a simple and common way to visualize protein sequences in this study a numerical descriptive vector for a given protein sequence is calculated based on twelve physicochemical properties of amino acids aas and principal component analysis pca each entry of the descriptive vector corresponds to one aa in the sequence by this vector an intuitive spectrum like graphical representation of protein sequence is proposed squared correlation coefficient as well as moving window correlation coefficient as a new similarity dissimilarity measure were used to compare different sequences applicability of the proposed method is assessed by analyzing the nine nd5 proteins the results revealed the utility of the proposed method

towards a robust fuzzy clustering fuzzy clustering helps to find natural vague boundaries in data the fuzzy c means method fcm is one of the most popular clustering methods based on minimization of a criterion function however one of the greatest disadvantages of this method is its sensitivity to presence of noise and outliers in data this paper introduces a new e insensitive fuzzy c means efcm clustering algorithm as a special case this algorithm includes the well known fuzzy c medians method fcmed also methods with insensitivity control named fcm and fcm are introduced performance of the new clustering algorithm is experimentally compared with the fcm method using synthetic data with outliers and heavy tailed and overlapped groups of data in background noise

weighted measures based on maximizing deviation for alignment free sequence comparison abstract alignment free sequence comparison is becoming fairly popular in many fields of computational biology due to less requirements for sequence itself and computational efficiency for a large scale of sequence data sets especially the approaches based on k tuple like d 2 d 2 s and d 2 are used widely and effectively however these measures treat each k tuple equally without accounting for the potential importance differences among all k tuples in this paper we take advantage of maximizing deviation method proposed in multiple attribute decision making to evaluate the weights of different k tuples we modify d 2 d 2 s and d 2 with weights and test them by similarity search and evaluation on functionally related regulatory sequences the results demonstrate that the newly proposed measures are more efficient and robust compared to existing alignment free methods

correlator beware correlation has limited selectivity for fmri data analysis abstract groups of time courses created from fmri data by the frequently used correlation analysis are often highly heterogeneous this heterogeneity is due to the limited selectivity of correlation when trying to match brain time courses to an externally imposed activation paradigm thus this process unnecessarily generates many type i errors false positives furthermore as a consequence of the heterogeneity time courses identified and grouped by correlation may in fact describe different activations after demonstrating this inadequacy we give one particular approach to partition such a heterogeneous group into internally more homogeneous subgroups using kendall s coefficient of concordance w and show its applicability and application to both simulated and in vivo data such group partition and purification will help subsequent inferential methods to deal more efficiently with false positives

a least biased fuzzy clustering method a new operational definition of cluster is proposed and a fuzzy clustering algorithm with minimal biases is formulated by making use of the maximum entropy principle to maximize the entropy of the centroids with respect to the data points clustering entropy the authors make no assumptions on the number of clusters or their initial positions for each value of an adimensional scale parameter spl beta the clustering algorithm makes each data point iterate towards one of the cluster s centroids so that both hard and fuzzy partitions are obtained since the clustering algorithm can make a multiscale analysis of the given data set one can obtain both hierarchy and partitioning type clustering the relative stability with respect to spl beta of each cluster structure is defined as the measurement of cluster validity the authors determine the specific value of spl beta which corresponds to the optimal positions of cluster centroids by minimizing the entropy of the data points with respect to the centroids clustered entropy examples are given to show how this least biased method succeeds in getting perceptually correct clustering results

on clustering fmri time series analysis of fmri time series is often performed by extracting one or more parameters for the individual voxels methods based e g on various statistical tests are then used to yield parameters corresponding to probability of activation or activation strength however these methods do not indicate whether sets of voxels are activated in a similar way or in different ways typically delays between two activated signals are not identified in this article we use clustering methods to detect similarities in activation between voxels we employ a novel metric that measures the similarity between the activation stimulus and the fmri signal we present two different clustering algorithms and use them to identify regions of similar activations in an fmri experiment involving a visual stimulus

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

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

ranking fmri time courses by minimum spanning trees assessing coactivation in fmri abstract in fmri time courses with similar temporal activation patterns may belong to different brain regions i e these regions are functionally connected coactivated a group of time courses tcs corresponding to a particular type of temporal activation pattern should be maximally self consistent homogeneous we demonstrate that ordering a group of multidimensional fmri time courses by a minimum spanning tree mst may be used to investigate the temporal homogeneity of a group of tcs we show the utility of mst ranking for data driven analysis methods in investigating coactivation in fmri mst ranking is equally useful for hypothesis led methods furthermore mst ranking enables pairwise comparisons of groups clusters i e any collection of tcs no matter how derived of fmri time courses

garch based robust clustering of time series in this paper we propose different robust fuzzy clustering models for classifying heteroskedastic volatility time series following the so called model based approach to time series clustering and using a partitioning around medoids procedure the proposed models are based on a garch parametric modeling of the time series i e the unconditional volatility and the time varying volatility garch representation of the time series we first suggest a timid robustification of the fuzzy clustering then we propose three robust fuzzy clustering models belonging to the so called metric noise and trimmed approaches respectively each model neutralizes the negative effects of the outliers in the clustering process in a different manner in particular the first robust model based on the metric approach achieves its robustness with respect to outliers by taking into account a robust distance measure the second based on the noise approach achieves its robustness by introducing a noise cluster represented by a noise prototype the third based on the trimmed approach achieves its robustness by trimming away a certain fraction of outlying time series the usefulness and effectiveness of the proposed clustering models is illustrated by means of a simulation study and two applications in finance and economics

comparing methods of analyzing fmri statistical parametric maps approaches for the analysis of statistical parametric maps spms can be crudely grouped into three main categories in which different philosophies are applied to delineate activated regions these being type i error control thresholding false discovery rate fdr control thresholding and posterior probability thresholding to better understand the properties of these main approaches we carried out a simulation study to compare the approaches as they would be used on real data sets using default settings we find that posterior probability thresholding is the most powerful approach and type i error control thresholding provides the lowest levels of type i error false discovery rate control thresholding performs in between the other approaches for both these criteria although for some parameter settings this approach can approximate the performance of posterior probability thresholding based on these results we discuss the relative merits of the three approaches in an attempt to decide upon an optimal approach we conclude that viewing the problem of delineating areas of activation as a classification problem provides a highly interpretable framework for comparing the methods within this framework we highlight the role of the loss function which explicitly penalizes the types of errors that may occur in a given analysis

a new graphical coding of dna sequence and its similarity calculation abstract the dna primary sequence is translated into structure graph based on classification of its four bases then the invariants such as topological indices are extracted from those graphic representations of dna primary sequences and used to calculate the similarities among the eleven species from these similarities dissimilarities the homologies can be revealed that they are in agreement with evolutionary relation satisfactorily

a similarity based robust clustering method this paper presents an alternating optimization clustering procedure called a similarity based clustering method scm it is an effective and robust approach to clustering on the basis of a total similarity objective function related to the approximate density shape estimation we show that the data points in scm can self organize local optimal cluster number and volumes without using cluster validity functions or a variance covariance matrix the proposed clustering method is also robust to noise and outliers based on the influence function and gross error sensitivity analysis therefore scm exhibits three robust clustering characteristics 1 robust to the initialization cluster number and initial guesses 2 robust to cluster volumes ability to detect different volumes of clusters and 3 robust to noise and outliers several numerical data sets and actual data are used in the scm to show these good aspects the computational complexity of scm is also analyzed some experimental results of comparing the proposed scm with the existing methods show the superiority of the scm method

ts fuzzy system based support vector regression this paper proposes a new regression model the takagi sugeno fuzzy system based support vector regression tsfs svr the tsfs svr is motivated by ts type fuzzy rules and its parameters are learned by a combination of fuzzy clustering and linear svr in contrast to a kernel based svr the tsfs svr has a smaller number of parameters while retaining the svr s good generalization ability in tsfs svr a one pass clustering algorithm clusters the input training data a new ts kernel which corresponds to a ts type fuzzy rule is then constructed by the product of a cluster output and a linear combination of input variables the tsfs svr output is a linear weighted sum of the ts kernels to achieve high generalization ability tsfs svr weights are learned through linear svr this paper demonstrates the capabilities of tsfs svr by conducting simulations in clean and noisy function approximations and signal prediction this paper also compares simulation results from the tsfs svr with gaussian kernel based svr and other learning models

a metric for arma processes autoregressive moving average arma models seek to express a system function of a discretely sampled process as a rational function in the z domain treating an arma model as a complex rational function we discuss a metric defined on the set of complex rational functions we give a natural measure of the distance between two arma processes the paper concentrates on the mathematics behind the problem and shows that the various algebraic structures endow the choice of metric with some interesting and remarkable properties which we discuss we suggest that the metric can be used in at least two circumstances i in which we have signals arising from various models that are unknown so we construct the distance matrix and perform cluster analysis and ii where there are several possible models m sub i all of which are known and we wish to find which of these is closest to an observed data sequence modeled as m

piecewise two dimensional normal cloud representation for time series data mining many high level dimensionality reduction approaches for mining time series have been proposed e g sax pwca and feature based due to the rapid performance degradation of time series data mining in much lower dimensionality and the continuously increasing amount of time series data with uncertainty there remains a burning need to develop new time series representations that can retain good performance in much lower reduced space and address uncertainty efficiently in this work we propose a novel time series representation namely two dimensional normal cloud representation 2d ncr based on cloud model theory the representation achieves dimensionality reduction by transforming the raw time series into a sequence of two dimensional normal cloud models moreover a new similarity measure between the transformed time series is presented the proposed method can reflect the characteristic data distribution of the time series and capture the variation with time we validate the performance of our representation on the various data mining tasks of classification clustering and query by content the experimental results demonstrate that 2d ncr is an effective and competitive representation for time series data mining

using cluster analysis to classify time series abstract we promote the idea of using the statistical technique of cluster analysis in nonlinear data analysis the technique is illustrated by using it to help identify local oscillators in the wake of the flow past a cylinder

cluster analysis in kinetic modelling of the brain a noninvasive alternative to arterial sampling in emission tomography quantification of brain tracer uptake metabolism or binding requires knowledge of the cerebral input function traditionally this is achieved with arterial blood sampling we propose a noninvasive alternative via the use of a blood vessel time activity curve tac extracted directly from dynamic positron emission tomography pet scans by cluster analysis five healthy subjects were injected with the 5ht 2a receptor ligand 18 f altanserin and blood samples were subsequently taken from the radial artery and cubital vein eight regions of interest roi tacs were extracted from the pet data set hierarchical k means cluster analysis was performed on the pet time series to extract a cerebral vasculature roi the number of clusters was varied from k 1 to 10 for the second of the two stage method determination of the correct number of clusters was performed by the within variance measure and by 3d visual inspection of the homogeneity of the determined clusters the cluster determined input curve was then used in logan plot analysis and compared with the arterial and venous blood samples and additionally with one of the currently used alternatives to arterial blood sampling the simplified reference tissue model srtm and logan analysis with cerebellar tac as an input there was a good agreement p 0 05 between the values of distribution volume dv obtained from the k means clustered input function and those from the arterial blood samples this work acts as a proof of principle that the use of cluster analysis on a pet data set could obviate the requirement for arterial cannulation when determining the input function for kinetic modelling of ligand binding and that this may be a superior approach as compared to the other noninvasive alternatives

clustering for sparsely sampled functional data we develop a flexible model based procedure for clustering functional data the technique can be applied to all types of curve data but is particularly useful when individuals are observed at a sparse set of time points in addition to producing final cluster assignments the procedure generates predictions and confidence intervals for missing portions of curves our approach also provides many useful tools for evaluating the resulting models clustering can be assessed visually via low dimensional representations of the curves and the regions of greatest separation between clusters can be determined using a discriminant function finally we extend the model to handle multiple functional and finite dimensional covariates and show how it can be applied to standard finite dimensional clustering problems involving missing data

discrimination and clustering for multivariate time series abstract minimum discrimination information provides a useful generalization of likelihood methodology for classification and clustering of multivariate time series discrimination between different classes of multivariate time series that can be characterized by differing covariance or spectral structures is of importance in applications occurring in the analysis of geophysical and medical time series data for discrimination between such multivariate series kullback leibler discrimination information and the chernoff information measure are developed for the multivariate non gaussian case asymptotic error rates and limiting distributions are given for a generalized spectral disparity measure that includes the foregoing criteria as special cases applications to problems of clustering and classifying earthquakes and mining explosions are given

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

contextual clustering for analysis of functional mri data presents a contextual clustering procedure for statistical parametric maps spm calculated from time varying three dimensional images the algorithm can be used for the detection of neural activations from functional magnetic resonance images fmri an important characteristic of spm is that the intensity distribution of background nonactive area is known whereas the distributions of activation areas are not the developed contextual clustering algorithm divides an spm into background and activation areas so that the probability of detecting false activations by chance is controlled i e hypothesis testing is performed unlike the much used voxel by voxel testing neighborhood information is utilized an important difference this is achieved by using a markov random field prior and iterated conditional modes icm algorithm however unlike in the conventional use of icm algorithm the classification is based only on the distribution of background the results from the authors simulations and human fmri experiments using visual stimulation demonstrate that a better sensitivity is achieved with a given specificity in comparison to the voxel by voxel thresholding technique the algorithm is computationally efficient and can be used to detect and delineate objects from a noisy background in other applications

functional linear discriminant analysis for irregularly sampled curves we introduce a technique for extending the classical method of linear discriminant analysis lda to data sets where the predictor variables are curves or functions this procedure which we call functional linear discriminant analysis flda is particularly useful when only fragments of the curves are observed all the techniques associated with lda can be extended for use with flda in particular flda can be used to produce classifications on new test curves give an estimate of the discriminant function between classes and provide a one or two dimensional pictorial representation of a set of curves we also extend this procedure to provide generalizations of quadratic and regularized discriminant analysis

ellipsoidal support vector clustering for functional mri analysis as an exploratory approach the clustering of fmri time series has proved its effectiveness in analyzing the functional mri especially in the detection of activated regions due to the arbitrary distribution of fmri time series in the temporal domain imposing simple assumption on the data structure usually could be misleading and limit the detector s performance therefore a true data driven clustering algorithm that adapts to the data structure is preferred and only high level control over the clustering procedure is desired support vector clustering svc is a suitable one in some extent because of its advantages such as no cluster shape restriction no need to explicitly specify the number of clusters and the mechanism in outlier elimination in this work we propose an extension of the svc to step further toward a data sensitive detector this approach is named as ellipsoidal support vector clustering esvc to be robust to noise the clustering is performed on features extracted from the fmri time series via fourier transform experimental results on simulated and real data sets demonstrate the effectiveness of incorporating data structure in clustering fmri time series

fuzzy c ordered medoids clustering for interval valued data fuzzy clustering for interval valued data helps us to find natural vague boundaries in such data the fuzzy c medoids clustering fcmdc method is one of the most popular clustering methods based on a partitioning around medoids approach however one of the greatest disadvantages of this method is its sensitivity to the presence of outliers in data this paper introduces a new robust fuzzy clustering method named fuzzy c ordered medoids clustering for interval valued data fcomdc id the huber s m estimators and the yager s ordered weighted averaging owa operators are used in the method proposed to make it robust to outliers the described algorithm is compared with the fuzzy c medoids method in the experiments performed on synthetic data with different types of outliers a real application of the fcomdc id is also provided highlightsfuzzy clustering for interval valued data helps us to find natural vague boundaries in such data a new robust fuzzy clustering method named fuzzy c ordered medoids clustering for interval valued data fcomdc id is proposedthe method uses both the huber s m estimators and the yager s owa operators to obtain its robustness experiments performed on synthetic data with different types of outliers and a real application are provided

phylogenetic analysis of dna sequences based on k word and rough set theory among alignment free methods for sequence comparison the model of k word frequencies is a well developed one however most existing word based methods neglect relationships among k word frequencies while a few others focus on the correlation of k words but ignore the word frequency itself in this paper we propose a new k word method which succeeds in conquering the two problems by means of characteristic sequences of a dna sequence we construct a 3 2k dimensional complete word based vector then we present a feature selection scheme based on rough set theory rst to extract the most informative k words and use only these selected features to represent the dna sequence to evaluate the effectiveness of our method we test it by phylogenetic analysis on three datasets the first one is used as a training set by which 869 top ranked k words are selected the other two are used as the testing set the results demonstrate that the proposed method can capture more important information and is more efficient for molecular phylogenetic analysis

a new graphical representation of protein sequences and its applications abstract sequence analysis is one of the foundations in bioinformatics for the abundant information hidden in the sequences it is helpful for scientists study on the function of dna proteins and cells in this paper we outline a novel method for protein sequences similarity analysis based on the physical chemical properties of amino acids we consider the protein sequence as a rigid body with mass then we introduce the moment of inertia to the calculation of similarity of sequences and the sequences are transformed into vectors by the tensor for moment of inertia the euclidean distance is employed as a measurement of the similarities at last the comparison with other references results shows our approach is reasonable and effective

l 1 norm based fuzzy clustering abstract the paper presents the l1 version of the well known fuzzy clustering method namely fuzzy isodata proposed by bezdek and dunn due to their robustness l1 norm based methods gained much attention in statistics the presented fuzzy clustering problem uses the distance between observations and location parameter vectors which is based on the l1 norm instead of the inner product induced norm used in classical fuzzy isodata two alternative methods to solve the l1 fuzzy clustering problem are derived in practice both membership grades and location parameter vectors are unknown the paper presents two iterative algorithms each the implementation of the derived method finally numerical examples are presented one of them refers to famous iris data