damage detection from changes in curvature mode shapes abstract a damage in a structure alters its dynamic characteristics the change is characterized by changes in the eigenparameters i e natural frequency damping values and the mode shapes associated with each natural frequency considerable effort has been spent in obtaining a relationship between the changes in eigenparameters the damage location and the damage size most of the emphasis has been on using the changes in the natural frequencies and the damping values to determine the location and the size of the damage in this paper a new parameter called curvature mode shape is investigated as a possible candidate for identifying and locating damage in a structure by using a cantilever and a simply supported analytical beam model it is shown here that the absolute changes in the curvature mode shapes are localized in the region of damage and hence can be used to detect damage in a structure the changes in the curvature mode shapes increase with increasing size of damage this information can be used to obtain the amount of damage in the structure finite element analysis was used to obtain the displacement mode shapes of the two models by using a central difference approximation curvature mode shapes were then calculated from the displacement mode shapes

hessian estimates in orlicz spaces for fourth order parabolic systems in non smooth domains abstract we establish the global hessian estimate in orlicz spaces for a fourth order parabolic system with discontinuous tensor coefficients in a non smooth domain under the assumptions that the coefficients have small weak bmo semi norms the boundary of a domain is reifenberg flat for 0 small and the given young function satisfies some moderate growth condition as a corollary we obtain an optimal global w 2 p regularity for such a system

scaling up cosine interesting pattern discovery a depth first method this paper presents an efficient algorithm called cosminer t for interesting pattern discovery the widely used cosine similarity found to possess the null invariance property and the anti cross support pattern property is adopted as the interestingness measure in cosminer t cosminer t is generally an fp growth like depth first traversal algorithm that rests on an important property of the cosine similarity the conditional anti monotone property camp the combined use of camp and the depth first support ascending traversal strategy enables the pre pruning of uninteresting patterns during the mining process of cosminer t extensive experiments demonstrate the high efficiency of cosminer t in interesting pattern discovery in comparison to the breath first strategy and the post evaluation strategy in particular cosminer t shows its capability in suppressing the generation of cross support patterns and discovering rare but truly interesting patterns finally an interesting case of landmark recognition is presented to illustrate the value of cosine interesting patterns found by cosminer t in real world applications

on optimal pole assignment in a specified region in this paper the problem of pole assignment and linear quadratic design have been amalgamated a design method that has the merits of both approaches is presented and the problem of assigning the poles in a specified region is solved the characterizations for quadratic cost functions have been studied and these results used to assign poles in real schur form in a region so that the optimality is maintained designed procedures have been elaborated with examples

free vibrations and sensitivity analysis of a defective two degree of freedom system free oscillations of a two degree of freedom system with honproportional damping are analyzed by a suitable choice of parameters a family of defective systems having a noncomplete set of eigenvectors is selected free motions of underdamped and overdamped defective systems are studied in the four dimensional state space and their main characteristics are discussed in particular the rate at which the trajectories are attracted by the eigenvectors is determined small perturbations of order e of the parameters are then considered and asymptotic expressions for the modified system eigensolutions are obtained these allow qualitative discussion of the effects of modifications on the mechanical behavior of nearly defective systems marked sensitivities of order 2 or e are found these depend strongly on the damping magnitude an extensive numerical analysis is performed n structural dynamics it is by no means rare to encounter systems having multiple eigenvalues this does not pose any substantial difficulties when the system is conservative but it involves specific problems when the system is nonconservative very often indeed the geometric multiplicity of the eigenvalue is less than the algebraic multiplicity and so the system has an incomplete set of eigenvectors insufficient to form a base for the state space systems of this type are called defective the free evolution of defective systems is well known to persons working in the automatic control or system theory field moreover basic notions can be found in any good book on linear algebra however in the author s opinion the problem is not sufficiently known to the structural analyst indeed it is common practice to assume damping of proportional type so that the eigenvectors coincide with those of the corresponding undamped system always forming a complete set and defective systems cannot occur

stratified feature sampling method for ensemble clustering of high dimensional data high dimensional data with thousands of features present a big challenge to current clustering algorithms sparsity noise and correlation of features are common characteristics of such data another common phenomenon is that clusters in such high dimensional data often exist in different subspaces ensemble clustering is emerging as a prominent technique for improving robustness stability and accuracy of high dimensional data clustering in this paper we propose a stratified sampling method for generating subspace component data sets in ensemble clustering of high dimensional data instead of randomly sampling a subset of features for each component data set in this method we first cluster the features of high dimensional data into a few feature groups called feature strata using stratified sampling we randomly sample some features from each feature stratum and merge the sampled features from different feature strata to generate a component data set in this way the component data sets have better representations of the clustering structure in the original data set comparing with random sampling and random projection methods in synthetic data analysis the component clustering by stratified sampling has demonstrated that the average clustering accuracy was increased without sacrificing clustering diversity we carried out a series of experiments on eight real world data sets from microarray text and image domains to evaluate ensemble clustering methods using three subspace component data generation methods and four consensus functions the experimental results consistently showed that the stratified sampling method produced the best ensemble clustering results in all data sets the ensemble clustering with stratified sampling also outperformed three other ensemble clustering methods which generate component clusters from the entire space of the original data highlightsa new component generation approach is proposed to produce ensemble components stratified sampling is used to generate subspace component data sets the component data can well represent the characteristics of the original data the proposed method can achieve a consistent performance in ensemble clustering the proposed method is easy to implement

a generalized kernel approach to dissimilarity based classification usually objects to be classified are represented by features in this paper we discuss an alternative object representation based on dissimilarity values if such distances separate the classes well the nearest neighbor method offers a good solution however dissimilarities used in practice are usually far from ideal and the performance of the nearest neighbor rule suffers from its sensitivity to noisy examples we show that other more global classification techniques are preferable to the nearest neighbor rule in such cases for classification purposes two different ways of using generalized dissimilarity kernels are considered in the first one distances are isometrically embedded in a pseudo euclidean space and the classification task is performed there in the second approach classifiers are built directly on distance kernels both approaches are described theoretically and then compared using experiments with different dissimilarity measures and datasets including degraded data simulating the problem of missing values

second order eliptic and parabolic equations with b r2 v mo coefficients the solvability in sobolev spaces w 1 2 p is proved for nondivergence form second order parabolic equations for p 2 close to 2 the leading coefficients are assumed to be measurable in the time variable and two coordinates of space variables and almost vmo vanishing mean oscillation with respect to the other coordinates this implies the w 2 p solvability for the same p of nondivergence form elliptic equations with leading coefficients measurable in two coordinates and vmo in the others under slightly different assumptions we also obtain the solvability results when p 2

structural damage detection using active members and neural networks introduction t detection of damage in structures is a topic which has considerable interest in many fields detecting damage in space structures when subjected to the harsh environment of space could allow for the repair of the structure to occur before the damage threatens the mission objectives offshore oil platforms constantly have problems with potential member failure in the corrosive sea environment buildings and bridges where structural failure proves catastrophic would also benefit from a reliable method of detecting and pinpointing structural damage in the past many methods for detecting damage in structures have relied on finite element model refinement methods hajela and soeiro determined the damage present in a structure by updating the finite element model to match the static and dynamic characteristics of the damaged structure their method was an outgrowth of those presented in refs 2 and 3 where undamaged members section properties changed during the model update process thus smearing the damage over a wide portion of the structure and making specific damage difficult to locate hajela and soeiro also extended their damage detection techniques to composite structures where a gradient based optimization scheme was used to update the finite element model other methods of detecting damage in structures rely strictly on measured data cawley and adams used only natural frequency data pandey et al used mode shape curvature data and swamidas and chen used strain displacement and acceleration data to monitor and detect changes and damages in various structures these methods require comparing measurements of the structure in the nominal undamaged state with those at a later date where some damage is potentially present in the structure these methods have the drawback that they can only identify that the structure has changed they cannot identify the location and extent of the damage neural networks have the unique ability to be trained to recognize known patterns and classify data based on these patterns neural networks have been used with success for structural design tasks and for classification of experimental data such as sonar target classification with proper training neural networks should be able to process the dynamic response measurements taken from the structure classify the data and provide a tool for determining the location and level of damage present in a structure this note presents a structural damage methodology in which only active member transfer function data are used in conjunction with an artificial neural network to detect damage in structures specifically the method relies on training a neural network using active member transfer function pole zero information to classify damaged structure measurements and to predict the degree of damage in a structure the method differs from many of the past damage detection algorithms in that no attempt is made to update a finite element model or to match measured data with new finite element analyses of the structure in a damaged state

fast sensitivity analysis of defective system abstract sensitivity analysis of linear vibration system is of wide interest in this paper sensitivity analysis based on non defective system and defective system is summarized in all cases specially for the defective systems a fast method for the perturbation problem of state vectors is constructed in terms of the theories of generalized eigenvectors and adjoint matrices by this method the state vector derivatives can be expressed by a linear combination of generalized eigenvectors the expansion coefficients can be obtained without solving large scale equations based on eigensolutions of original system numerical results demonstrate the effectiveness and the stability of the method

eigenstructure assignment approach for structural damage detection in this work a methodology for incorporating measured modal data into an existing refined finite element model is examined with the objective of detecting and locating structural damage the algorithm is based on the partial inverse problem in that only partial spectral information is required the technique utilizes a symmetric eigenstructure assignment algorithm to perform the partial spectral assignment algorithms to enhance mode shape assignability and to preserve sparsity in the damaged fem are developed the sparsity preservation is of particular importance when considering damage detection in trusslike structures several examples are presented to highlight the key points made within the paper

elliptic equations with measurable coefficients in reifenberg domains abstract we prove w 1 p estimates for elliptic equations in divergence form under the assumption that for each point and for each sufficiently small scale there is a coordinate system so that the coefficients have small oscillation in n 1 directions we assume the boundary to be reifenberg flat and the coefficients having small oscillation in the flat direction of the boundary

lp estimates for time fractional parabolic equations in divergence form with measurable coefficients abstract in this paper we establish l p estimates and solvability for time fractional divergence form parabolic equations in the whole space when leading coefficients are merely measurable in one spatial variable and locally have small mean oscillations with respect to the other variables the corresponding results for equations on a half space are also derived

an integral equation for changes in the structural dynamics characteristics of damaged structures this paper presents a relationship between the structural dynamic characteristics of damaged and intact structures such a relationship is derived in the form of an integral equation and is used to develop a method of flaw identification the resulting flaw identification procedure uses the experimental data and relates the flaw to the observed structural dynamic response the algorithm enables one to detect the damage locations and the corresponding damage magnitude simultaneously numerical simulations and experiments are conducted to validate the theory

cumulative voting consensus method for partitions with variable number of clusters over the past few years there has been a renewed interest in the consensus clustering problem several new methods have been proposed for finding a consensus partition for a set of n data objects that optimally summarizes an ensemble in this paper we propose new consensus clustering algorithms with linear computational complexity in n we consider clusterings generated with a random number of clusters which we describe by categorical random variables we introduce the idea of cumulative voting as a solution for the problem of cluster label alignment where unlike the common one to one voting scheme a probabilistic mapping is computed we seek a first summary of the ensemble that minimizes the average squared distance between the mapped partitions and the optimal representation of the ensemble where the selection criterion of the reference clustering is defined based on maximizing the information content as measured by the entropy we describe cumulative vote weighting schemes and corresponding algorithms to compute an empirical probability distribution summarizing the ensemble given the arbitrary number of clusters of the input partitions we formulate the problem of extracting the optimal consensus as that of finding a compressed summary of the estimated distribution that preserves the maximum relevant information an efficient solution is obtained using an agglomerative algorithm that minimizes the average generalized jensen shannon divergence within the cluster the empirical study demonstrates significant gains in accuracy and superior performance compared to several recent consensus clustering algorithms

brief papers new results in state estimation and regulation an alternative technique to design linear state estimators and regulators is presented this technique is based on transfer matrix considerations the optimal regulator or estimator gain is obtained via spectral factorization and the solution of a simple equation in polynomial matrices this approach provides further insight displays the duality of estimation and control nicely and bridges the state space and frequency domain techniques the resulting design procedure is computationally attractive and particularly simple for system matrices in the observer or controller canonical form

controller design with regional pole constraints a design procedure is developed that combines linear quadratic optimal control with regional pole placement specifically a static and dynamic output feedback control problem is addressed in which the poles of the closed loop system are constrained to lie in specified regions of the complex plane these regional pole constraints are embedded within the optimization process by replacing the covariance lyapunov equation by a modified lyapunov equation whose solution in certain cases leads to an upper bound on the quadratic cost functional the results include necessary and sufficient conditions for characterizing static output feedback controllers with bounded performance and regional pole constraints sufficient conditions are also presented for the fixed order i e full and reduced order dynamic output feedback problem with regional pole constraints circular elliptical vertical strip parabolic and section regions are considered

cluster ensembles a knowledge reuse framework for combining multiple partitions this paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings we first identify several application scenarios for the resultant knowledge reuse framework that we call cluster ensembles the cluster ensemble problem is then formalized as a combinatorial optimization problem in terms of shared mutual information in addition to a direct maximization approach we propose three effective and efficient techniques for obtaining high quality combiners consensus functions the first combiner induces a similarity measure from the partitionings and then reclusters the objects the second combiner is based on hypergraph partitioning the third one collapses groups of clusters into meta clusters which then compete for each object to determine the combined clustering due to the low computational costs of our techniques it is quite feasible to use a supra consensus function that evaluates all three approaches against the objective function and picks the best solution for a given situation we evaluate the effectiveness of cluster ensembles in three qualitatively different application scenarios i where the original clusters were formed based on non identical sets of features ii where the original clustering algorithms worked on non identical sets of objects and iii where a common data set is used and the main purpose of combining multiple clusterings is to improve the quality and robustness of the solution promising results are obtained in all three situations for synthetic as well as real data sets

structural model updating using frequency response function and quasi linear sensitivity equation a method is presented for structural mass and stiffness estimation including damping effects and using vibration data it uses the frequency response function frf and natural frequencies data for finite element model updating the frf data are compiled using the measured displacement velocity or acceleration of the damaged structure a least square algorithm method with appropriate normalization is used for solving the over determined system of equations with noise polluted data sensitivity equation normalization and proper selection of measured frequency points improved the accuracy and convergence in finite element model updating using simulated measurements shows that this method can detect locate and quantify the severity of damage within structures

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

multiple view semi supervised dimensionality reduction multiple view data together with some domain knowledge in the form of pairwise constraints arise in various data mining applications how to learn a hidden consensus pattern in the low dimensional space is a challenging problem in this paper we propose a new method for multiple view semi supervised dimensionality reduction the pairwise constraints are used to derive embedding in each view and simultaneously the linear transformation is introduced to make different embeddings from different pattern spaces comparable hence the consensus pattern can be learned from multiple embeddings of multiple representations we derive an iterating algorithm to solve the above problem some theoretical analyses and out of sample extensions are also provided promising experiments on various data sets together with some important discussions are also presented to demonstrate the effectiveness of the proposed algorithm

eigensolutions sensitivity for nonsymmetric matrices with repeated eigenvalues a perturbation algorithm is developed for evaluating eigenvalue and eigenvector directional derivatives of nonsymmetric defective matrices some properties are recalled in particular chains of generalized right and left eigenvectors and their orthogonal properties are defined small perturbations of the matrix are then considered an asymptotic expansion of the eigensolutions of the perturbed problem is obtained in terms of noninteger powers of the perturbation parameter particular attention is devoted to the eigenvectors of the perturbed system and to the strong coupling that occurs between the chains

comments on on optimal pole assignment in a specified region in a recent paper juang and lee 1984 presented a method of optimal pole placement for linear multivariable systems the method is based on theorem 1 and corollary 1 of juang and lee 1984 unfortunately neither the theorem nor the corollary can be correct furthermore the application of corollary 1 in proposition 2 and in cases 2 3 and 4 is valid only in a special case where the number of inputs m is at most equal to the number of shifted poles one or two poles in each step

computing the local consensus of trees the inference of consensus from a set of evolutionary trees is a fundamental problem in a number of fields such as biology and historical linguistics and many models for inferring this consensus have been proposed in this paper we present a model for deriving what we call a local consensus tree t from a set of trees cal t the model we propose presumes a function f called a total local consensus function which determines for every triple a of species the form that the local consensus tree should take on a we show that all local consensus trees when they exist can be constructed in polynomial time and that many fundamental problems can be solved in linear time we also consider partial local consensus functions and study optimization problems under this model we present linear time algorithms for several variations finally we point out that the local consensus approach ties together many previous approaches to constructing consensus trees

single beam analysis of damaged beams verified using a strain energy based damage measure analytical expression of a new damage measure which relates the strain energy to the damage location and magnitude is presented in this paper the strain energy expression is calculated using modes and natural frequencies of damaged beams that are derived based on single beam analysis considering both decrease in mass and stiffness decrease in mass and stiffness are a fallout of geometric discontinuity and no assumptions regarding the physical behavior of damage are made the method is applicable to beams with notch like non propagating cracks with arbitrary boundary conditions the analytical expressions derived for mode shapes curvature shapes natural frequencies and an improved strain energy based damage measure are verified using experiments the improvement in the damage measure is that it is not assumed that the bending stiffness of the damaged beam is constant and equal to that of undamaged beam when calculating the strain energy of the entire beam it is also not assumed that the bending stiffness of the element in which the damage is located is constant

bagging for path based clustering a resampling scheme for clustering with similarity to bootstrap aggregation bagging is presented bagging is used to improve the quality of path based clustering a data clustering method that can extract elongated structures from data in a noise robust way the results of an agglomerative optimization method are influenced by small fluctuations of the input data to increase the reliability of clustering solutions a stochastic resampling method is developed to infer consensus clusters a related reliability measure allows us to estimate the number of clusters based on the stability of an optimized cluster solution under resampling the quality of path based clustering with resampling is evaluated on a large image data set of human segmentations

approximate method for eigensensitivity analysis of a defective matrix based on the exact modal expansion method an arbitrary high order approximate method is developed for calculating the second order eigenvalue derivatives and the first order eigenvector derivatives of a defective matrix the numerical example shows the validity of the method if the different eigenvalues m 1 m q of the matrix are arranged so that m 1 m q and satisfy the condition that m q 1 m q 1 1 for some q 1

information theoretic measures for clusterings comparison variants properties normalization and correction for chance information theoretic measures form a fundamental class of measures for comparing clusterings and have recently received increasing interest nevertheless a number of questions concerning their properties and inter relationships remain unresolved in this paper we perform an organized study of information theoretic measures for clustering comparison including several existing popular measures in the literature as well as some newly proposed ones we discuss and prove their important properties such as the metric property and the normalization property we then highlight to the clustering community the importance of correcting information theoretic measures for chance especially when the data size is small compared to the number of clusters present therein of the available information theoretic based measures we advocate the normalized information distance nid as a general measure of choice for it possesses concurrently several important properties such as being both a metric and a normalized measure admitting an exact analytical adjusted for chance form and using the nominal 0 1 range better than other normalized variants

stability based validation of clustering solutions data clustering describes a set of frequently employed techniques in exploratory data analysis to extract natural group structure in data such groupings need to be validated to separate the signal in the data from spurious structure in this context finding an appropriate number of clusters is a particularly important model selection question we introduce a measure of cluster stability to assess the validity of a cluster model this stability measure quantifies the reproducibility of clustering solutions on a second sample and it can be interpreted as a classification risk with regard to class labels produced by a clustering algorithm the preferred number of clusters is determined by minimizing this classification risk as a function of the number of clusters convincing results are achieved on simulated as well as gene expression data sets comparisons to other methods demonstrate the competitive performance of our method and its suitability as a general validation tool for clustering solutions in real world problems

the inverse problem of linear optimal control for constant disturbance this paper presents the solution to the inverse problem of linear optimal control systems to achieve pole placement and at the same time minimize the cost function and accommodate a constant but unknown disturbance the sufficient conditions for an optimal feedback law to have a positive r and positive semi definite q are found the relationships between the open loop poles and the closed loop poles that guarantee a positive r and q 0 are also obtained these relations offer a rule for selection of the appropriate closed loop poles which will guarantee the required feedback properties

stiffness matrix adjustment using mode data a procedure is introduced that uses in addition to mode data structural connectivity information to optimally adjust deficient stiffness matrices the adjustments performed are such that the percentage change to each stiffness coefficient is minimized the physical configuration of the analytical model is preserved and the adjusted model will exactly reproduce the modes used in the identification the theoretical development is presented and the procedure is demonstrated by numerical simulation of a test problem

structural control using inverse h2 optimal theory the piezoelectric transducers embedded in structures offer distributed sensor and actuator architectures for structural control a process that involves health monitoring and control of local structural degrees of freedom the design steps demand sensor and actuator management schemes so that the response of a structural component in question is monitored and then tailored to the design requirements kalman s inverse theory is used to determine sensor and sensor actuator combinations for optimal observers and controllers the riccati equations for each combination are derived to formulate the linear quadratic gaussian theory for a reconfigurable architecture an oscillator model with two inputs is considered to illustrate the underlying structural control principles

combining multiple clusterings using evidence accumulation we explore the idea of evidence accumulation eac for combining the results of multiple clusterings first a clustering ensemble a set of object partitions is produced given a data set n objects or patterns in d dimensions different ways of producing data partitions are 1 applying different clustering algorithms and 2 applying the same clustering algorithm with different values of parameters or initializations further combinations of different data representations feature spaces and clustering algorithms can also provide a multitude of significantly different data partitionings we propose a simple framework for extracting a consistent clustering given the various partitions in a clustering ensemble according to the eac concept each partition is viewed as an independent evidence of data organization individual data partitions being combined based on a voting mechanism to generate a new n times n similarity matrix between the n patterns the final data partition of the n patterns is obtained by applying a hierarchical agglomerative clustering algorithm on this matrix we have developed a theoretical framework for the analysis of the proposed clustering combination strategy and its evaluation based on the concept of mutual information between data partitions stability of the results is evaluated using bootstrapping techniques a detailed discussion of an evidence accumulation based clustering algorithm using a split and merge strategy based on the k means clustering algorithm is presented experimental results of the proposed method on several synthetic and real data sets are compared with other combination strategies and with individual clustering results produced by well known clustering algorithms

can a semi simple eigenvalue admit fractional sensitivities we perform high order sensitivity analysis of eigenvalues and eigenvectors of linear systems depending on parameters attention is focused on double not semi simple and semi simple eigenvalues undergoing perturbations either of regular or singular type the use of integer taylor or fractional puiseux series expansions is discussed and the analysis carried out both on the characteristic polynomial and on the eigenvalue problem it is shown that semi simple eigenvalues can admit fractional sensitivities when the perturbations are singular conversely to the not semi simple case however such occurrence only manifests itself when a second order perturbation analysis is carried out as a main result it is found that such over degenerate case spontaneously emerges in bifurcation analysis when one looks for the boundaries of the stability domain of circulatory mechanical systems possessing symmetries a four degree of freedom system under a follower force is studied as an illustrative example

solvability of parabolic equations in divergence form with partially bmo coefficients abstract we prove the h p 1 solvability of second order parabolic equations in divergence form with leading coefficients a i j measurable in t x 1 and having small bmo bounded mean oscillation semi norms in the other variables additionally we assume a 11 is measurable in x 1 and has small bmo semi norms in the other variables the corresponding results for the cauchy problem are also established parabolic equations in sobolev spaces h q p 1 with mixed norms are also considered under the same conditions of the coefficients

gradient estimates for a class of parabolic systems we establish local calderon zygmund type estimates for a class of parabolic problems whose model is the nonhomogeneous degenerate singular parabolic p laplacian system ut div du p 2du div f p 2f proving that f lqloc du lqloc q p we also treat systems with discontinuous coefficients of vanishing mean oscillation vmo type

a parameter free community detection method based on centrality and dispersion of nodes in complex networks abstract k means is a simple and efficient clustering algorithm to detect communities in networks however it may suffer from a bad choice of initial seeds also called centers that seriously affect the clustering accuracy and the convergence rate additionally in k means the number of communities should be specified in advance till now it is still an open problem on how to select initial seeds and how to determine the number of communities in this study a new parameter free community detection method named k rank d was proposed first based on the fact that good initial seeds usually have high importance and are dispersedly located in a network we proposed a modified pagerank centrality to evaluate the importance of a node and drew a decision graph to depict the importance and the dispersion of nodes then the initial seeds and the number of communities were selected from the decision graph actively and intuitively as the start parameter of k means experimental results on synthetic and real world networks demonstrate the superior performance of our approach over competing methods for community detection

joint image clustering and labeling by matrix factorization we propose a novel algorithm to cluster and annotate a set of input images jointly where the images are clustered into several discriminative groups and each group is identified with representative labels automatically for these purposes each input image is first represented by a distribution of candidate labels based on its similarity to images in a labeled reference image database a set of these label based representations are then refined collectively through a non negative matrix factorization with sparsity and orthogonality constraints the refined representations are employed to cluster and annotate the input images jointly the proposed approach demonstrates performance improvements in image clustering over existing techniques and illustrates competitive image labeling accuracy in both quantitative and qualitative evaluation in addition we extend our joint clustering and labeling framework to solving the weakly supervised image classification problem and obtain promising results

eigensensitivity analysis of a defective matrix with zero first order eigenvalue derivatives a direct method is developed for calculating the first to third order eigenvalue derivatives and first to second order eigenvector derivatives of a defective matrix with a zero first order eigenvalue derivative associated with jordan blocks of order higher than the lowest it is found under some conditions that the corresponding eigen solution of the perturbed problem has a distinct structure that in the fractional power series of the perturbation parameter the denominator of the power can not only he the orders of jordan blocks as in the normal cases but also can be the sum of two successive orders of jordan blocks the solution method is composed of three parts one of them is simular to known work and the other two are very different numerical example show the correctness of the method

reliability based fuzzy clustering ensemble abstract in the clustering ensemble the quality of base clusterings influences the consensus clustering although some researches have been devoted to weighting the base clustering fuzzy cluster level weighting has been ignored more specifically they did not pay attention to the role of cluster reliability in the fuzzy clustering ensemble in this paper we propose a new fuzzy clustering ensemble framework without access to the features of data objects based on fuzzy cluster level weighting the reliability of each fuzzy cluster is computed based on estimation of its unreliability and is considered as its weight in the ensemble the unreliability of fuzzy clusters is estimated by applying the similarity between fuzzy clusters in the ensemble based on an entropic criterion in our framework the final clustering is produced by two types of consensus functions 1 a reliability based weighted fuzzy co association matrix is constructed from the base clusterings and then a single traditional clustering such as hierarchical agglomerative clustering or k means is applied over the matrix to produce the final clustering 2 a new graph based fuzzy consensuses function the graph based consensus function has linear time complexity in the number of data objects experimental results on various standard datasets demonstrated the effectiveness of the proposed approach compared to the state of the art methods in terms of evaluation criteria and clustering robustness

generalized morrey estimates for the gradient of divergence form parabolic operators with discontinuous coefficients abstract we consider the cauchy dirichlet problem for linear divergence form parabolic operators in bounded reifenberg flat domains the coefficients are supposed to be only measurable in one of the space variables and small bmo with respect to the others we obtain boundedness of the hardy littlewood maximal operator in the generalized morrey spaces w p p 1 and weight satisfying certain supremum condition this permits us to obtain calderon zygmund type estimate for the gradient of the weak solution of the problem

positional and confidence voting based consensus functions for fuzzy cluster ensembles consensus clustering i e the task of combining the outcomes of several clustering systems into a single partition has lately attracted the attention of researchers in the unsupervised classification field as it allows the creation of clustering committees that can be applied with multiple interesting purposes such as knowledge reuse or distributed clustering however little attention has been paid to the development of algorithms known as consensus functions especially designed for consolidating the outcomes of multiple fuzzy or soft clustering systems into a single fuzzy partition despite the fact that fuzzy clustering is far more informative than its crisp counterpart as it provides information regarding the degree of association between objects and clusters that can be helpful for deriving richer descriptive data models for this reason this paper presents a set of fuzzy consensus functions capable of creating soft consensus partitions by fusing a collection of fuzzy clusterings our proposals base clustering combination on a cluster disambiguation process followed by the application of positional and confidence voting techniques the modular design of these algorithms makes it possible to sequence their constituting steps in different manners which allows to derive versions of the proposed consensus functions optimized from a computational standpoint the proposed consensus functions have been evaluated in terms of the quality of the consensus partitions they deliver and in terms of their running time on multiple benchmark data sets a comparison against several representative state of the art consensus functions reveals that our proposals constitute an appealing alternative for conducting fuzzy consensus clustering as they are capable of yielding high quality consensus partitions at a low computational cost

on w1 p estimates for elliptic equations in divergence form first we will apply the method to study w 1 p regularity for a nonlinear elliptic operator in divergence form we would like to point out that in the particular case of a linear elliptic equation this method gives an alternative proof to the classical one which uses the general theory of singular integrals the utility of the method that we describe below is that hypotheses a and b are obtained directly by studying the deviation of the coefficients of a from the coefficients of a0 and this is usually not a difficult task a more interesting application of this kind of approximation method is to elliptic homogenization problems for which we obtain results that give w 1 p estimates with a weak hypothesis of regularity in the coefficients for instance we are able to study the following cases

eigensensitivity analysis of a defective matrix the formulas for calculating the first to third order perturbation coefficients of the eigenvalues and the first order perturbation coefficients of eigenvectors of a defective matrix are derived by use of the direct perturbation method for the case where the eigenvalue problem for the first order perturbation coefficients of the eigenvalues of the defective matrix has repeated eigenvalues associated with th order jordan blocks of the matrix the perturbation equations are derived by expanding the perturbed eigenvalues and eigenvectors in power series of 1 where is the small parameter of the problem substituting the series into the perturbed eigenvalue problem and comparing the powers of the kth order perturbation equations for k 1 1 can be solved formally the solutions contain some undetermined quantities by use of the solvability conditions of the kth order equations for k v 1 the undetermined quantities in the solutions can be calculated in turns when we run all orders of the jordan blocks the problem is solved the numerical example shows the validity of the method

higher order eigensensitivity analysis of a defective matrix under the assumption that all of the eigenvalues of the eigenproblem for the first order perturbation coefficients of the eigenvalues are simple and nonzero a direct method is given for calculating the first to third order perturbation coefficients of the eigenvalues and the first to second order perturbation coefficients of the eigenvectors of a defective matrix the method is extended to the case where one of the first order perturbation coefficients of the eigenvalues associated with the lowest order jordan blocks is zero numerical examples show the validity of the method

community mining with new node similarity by incorporating both global and local topological knowledge in a constrained random walk abstract detection of community is a crucial step to understand the structure and dynamics of complex networks most of conventional community detection methods focus on optimizing a certain objective function or on clustering nodes based on their similarities which leads to a phenomenon that they have preference for specific types of networks but are not general using constrained random walk we exploit global and local topology structures of network to propose a modified transition matrix and further to define a new similarity metric named isim between two nodes in contrast to the existing similarities isim does not work directly on the observed data but in a convergent stable space this feature makes isim robust to the observed noisy data in real world networks isim not only measures node s distance but also captures node s topology structure in network experiments on synthetic and real world networks demonstrate that isim can be successfully applied to community detection in broader types of networks and outperforms other community detection methods

construction of the similarity matrix for the spectral clustering method numerical experiments abstract spectral clustering is a powerful method for finding structure in a dataset through the eigenvectors of a similarity matrix it often outperforms traditional clustering algorithms such as k means when the structure of the individual clusters is highly non convex its accuracy depends on how the similarity between pairs of data points is defined two important items contribute to the construction of the similarity matrix the sparsity of the underlying weighted graph which depends mainly on the distances among data points and the similarity function when a gaussian similarity function is used the choice of the scale parameter can be critical in this paper we examine both items the sparsity and the selection of suitable s based either directly on the graph associated to the dataset or on the minimal spanning tree mst of the graph an extensive numerical experimentation on artificial and real world datasets has been carried out to compare the performances of the methods

fuzzy consensus clustering with applications on big data consensus clustering aims to find a single partition of data that agrees as much as possible with existing basic partitions given its robustness and generalizability consensus clustering has emerged as a promising solution to find cluster structures inside heterogeneous big data rising from various application domains in the area of fuzzy systems however research along this line is still in its initial stage with some unsystematic algorithmic studies finding a fuzzy consensus partition from multiple fuzzy basic partitions in an efficient flexible and robust way is still an exciting open problem calling for further investigation in light of this this paper provides a systematic study of fuzzy consensus clustering fcc from a utility perspective specifically we first define the objective function of fcc clearly using the novel fuzzified contingency matrix we then derive a family of fcc utility functions termed as fccu that can transform fcc to a weighted piecewise fuzzy c means clustering pifcm problem this helps us to establish an algorithmic framework for fcc with flexible choice of utility functions and speeds fcc significantly with a fcm like iterative process of pifcm to meet the big data challenge we further parallelize fcc on the spark platform with both vertical and horizontal segmentation schemes extensive experiments on various real world datasets demonstrate the excellent performance of fcc even with a majority of poor basic partitions in particular our method exhibits interesting potential for big data clustering in two real life applications concerned with online event detection and overlapping community detection respectively

fuzzy rule base ensemble generated from data by linguistic associations mining as there are many various methods for time series prediction developed but none of them generally outperforms all the others there always exists a danger of choosing a method that is inappropriate for a given time series to overcome such a problem distinct ensemble techniques that combine several individual forecasts are being proposed in this contribution we employ the so called fuzzy rule based ensemble this method is constructed as a linear combination of a small number of forecasting methods where the weights of the combination are determined by fuzzy rule bases based on time series features such as trend seasonality or stationarity for identification of fuzzy rule bases we use the linguistic association mining a huge experimental justification is provided

calculation of eigenvalue and eigenvector derivatives of a defective matrix based on puiseux expansions of perturbation parameter for the solution of the perturbed problem a modal expansion method for the eigensensitivity analysis of a defective matrix is developed in which any of eigenvector derivatives is expressed as a linear combination of all the eigenvectors and principal vectors of the matrix first an eigenvalue problem related to the differentiable eigenvectors and the first order eigenvalue derivatives associated with the same order jordan blocks corresponding to a concerned eigenvalue of the matrix is formulated then under the condition that all of the eigenvalues of the derived eigenvalue problem are simple the formulas for calculating the differentiable eigenvectors the first to third order eigenvalue derivatives and the first to second order eigenvector derivatives are derived two numerical examples show the validity of the method and how to program based on the mathematical derivations

bagging constraint score for feature selection with pairwise constraints constraint score is a recently proposed method for feature selection by using pairwise constraints which specify whether a pair of instances belongs to the same class or not it has been shown that the constraint score with only a small amount of pairwise constraints achieves comparable performance to those fully supervised feature selection methods such as fisher score however one major disadvantage of the constraint score is that its performance is dependent on a good selection on the composition and cardinality of constraint set which is very challenging in practice in this work we address the problem by importing bagging into constraint score and a new method called bagging constraint score bcs is proposed instead of seeking one appropriate constraint set for single constraint score in bcs we perform multiple constraint score each of which uses a bootstrapped subset of original given constraint set diversity analysis on individuals of ensemble shows that resampling pairwise constraints is helpful for simultaneously improving accuracy and diversity of individuals we conduct extensive experiments on a series of high dimensional datasets from uci repository and gene databases and the experimental results validate the effectiveness of the proposed method

lp regularity for fourth order parabolic systems with measurable coefficients we treat fourth order parabolic systems in divergence form with bounded measurable coefficients we establish hessian estimates for such parabolic systems by proving that the lp regularity of the inhomogeneous terms exactly reflects in the regularity of the hessian of the solutions for every p in 1 infty the assumptions are that the coefficients are allowed to be merely measurable in one of spatial variables but averaged in the other spatial variables and time variable

a development of modal expansion method for eigensensitivity analysis of a defective matrix abstract in zhang and zhang 2006 z y zhang h s zhang calculation of eigenvalue and eigenvector derivatives of a defective matrix applied mathematics and computation 176 2006 7 26 a modal expansion method for eigensensitivity analysis of a defective matrix was developed where all of the eigenvalues of the derived eigenvalue problem for the first order eigenvalues derivatives are simple in this paper the work is extended to the case where the derived eigenvalue problem has repeated eigenvalues the formulas for calculating the differentiable eigenvectors the first to third order eigenvalue derivatives and the first order eigenvector derivatives are derived a numerical example shows the validity of the method

the exact explicit dynamic stiffness matrix of multi cracked euler bernoulli beam and applications to damaged frame structures abstract in this paper the closed form expression of the exact dynamic stiffness matrix of an euler bernoulli beam in the presence of an arbitrary number of concentrated cracks is derived the procedure adopted for the evaluation of the dynamic stiffness matrix is based on the availability of the exact closed form solution of the vibration modes of the multi cracked beam derived by the same authors in a previous paper the knowledge of the exact explicit dynamic stiffness matrix of the multi cracked beam makes the direct evaluation of the exact global dynamic stiffness matrix of damaged frame structures possible furthermore it allows the exact evaluation of the frequencies and the corresponding vibration modes consistent with the distributed parameter model through the application of the well known wittrick williams algorithm some numerical applications relative to the evaluation of frequencies and the corresponding mode shapes of multi cracked framed structure are reported furthermore the closed form solution has been validated by comparing with some exact results available in the literature for a simple single cracked frame finally further new results for a multi cracked frame have been compared with those obtained by a finite element simulation

discriminative metric learning for multi view graph partitioning we propose discriminative metric learning for multi view graph partitioning we envision the multi view graph as an adaptive dynamic system the intra view connections and the inter view couplings are interplayed extensive experiments have been conducted to show the effectiveness in recent years multi view graph partitioning has attracted more and more attention but most efforts have been made to develop graph partitioning approaches directly in the original topological structure in many real world applications graph may contain noisy links and the distance metric may not be so discriminative for revealing cluster structure this paper addresses the problem of discriminative metric learning for multi view graph partitioning in particular we propose a novel method called multi view dml abbr of multi view discriminative metric learning to transform the metric space in the original graph into a more discriminative metric space in which better graph partitioning results will be obtained we envision the multi view graph as an adaptive dynamic system where both the intra view connections and the inter view couplings are interplayed to gradually update the relation metric among nodes on the one hand the inter view coupling will be influenced by the intra view connection between two nodes on the other hand the inter view coupling will also affect the intra view connection such interplay eventually makes the whole graph reach a steady state which has a stronger cluster structure than the original graph extensive experiments are conducted on both synthetic and real world graphs to confirm that the proposed method is able to learn more discriminative metric

on successive pole assignment by linear quadratic optimal feedbacks abstract this paper studies a method of shifting poles of linear constant systems via lq optimal feedback by making use of a solution to the so called inverse regulator problem this method enables us to shift poles successively by pairs while maintaining the well known advantages of lq regulators polynomial fractional representation is effectively used both to characterize the maximal pole assignable area which clarifies the theoretical bound of the lq optimal pole shifting and to derive an algorithm a numerical example is given to illustrate the results

d stability analysis for discrete systems with a time delay this paper first discusses the d pole placement problem of discrete time delay systems some criteria are proposed to ensure that all the closed loop eigenvalues of discrete systems with a time delay are located inside a specific disk d r centered at 0 with radius r then several sufficient conditions for guaranteeing the d stability of discrete time delay systems subjected to parametric perturbations are presented both unstructured and highly structured parametric perturbations are considered by these sufficient conditions the tolerable parametric perturbation bounds that ensure all the closed loop poles of discrete time delay perturbed systems to remain inside the desired disk d r can be estimated finally illustrative examples are given for demonstration

a schur method for pole assignment in this paper a new numerical algorithm for pole assignment of linear time invariant systems is presented the proposed algorithm uses reliable numerical techniques based on the schur form of the state matrix and on the use of orthogonal transformations only the bad eigenvalues of the system are modified by a sequential pole shifting procedure and the resulted gains in the feedback matrix are minimized

an extension on statistical comparisons of classifiers over multiple data sets for all pairwise comparisons in a recently published paper in jmlr dem sar 2006 recommends a set of non parametric statistical tests and procedures which can be safely used for comparing the performance of classifiers over multiple data sets after studying the paper we realize that the paper correctly introduces the basic procedures and some of the most advanced ones when comparing a control method however it does not deal with some advanced topics in depth regarding these topics we focus on more powerful proposals of statistical procedures for comparing n n classifiers moreover we illustrate an easy way of obtaining adjusted and comparable p values in multiple comparison procedures

a frequency domain method of structural damage identification formulated from the dynamic stiffness equation of motion this paper introduces a frequency domain method of structural damage identification it is formulated in a general form from the dynamic stiffness equation of motion for a structure and then applied to a beam structure only the dynamic stiffness matrix for the intact state appears in the final form of the damage identification algorithm as the structure model the appealing features of the present damage identification method are 1 it requires only the frequency response functions experimentally measured from the damaged structure as the input data and 2 it can locate and quantify many local damages at the same time the feasibility of the present damage identification method is tested through some numerically simulated damage identification analyses and then experimental verification is conducted for a cantilevered beam with damage caused by introducing three slots

smoothness of linear laminates linearly elastic laminates are examples of materials whose equilibrium equations may have only bounded measurable coefficients yet whose solutions may be fairly smooth this is quite different from general experience where regularity of solutions is determined by the closeness of the system to a diagonal one a particular situation where a laminate may appear is a highly twinned elastic or ferroelectric crystal and there are questions related to these materials which make it useful to know some properties of these special systems of equations

fourth order parabolic equations with weak bmo coefficients in reifenberg domains abstract we study optimal w 2 p regularity for fourth order parabolic equations with discontinuous coefficients in general domains we obtain the global w 2 p regularity for each 1 p under the assumption that the coefficients have suitably small bmo semi norm of weak type and the boundary of the domain is reifenberg flat the situation of our main theorem arises when the conductivity on fractals is controlled by a random variable in the time direction

hessian estimates for fourth order elliptic systems with singular bmo coefficients in composite reifenberg domains abstract we consider fourth order elliptic systems in divergence form with greatly discontinuous coefficients in a nonsmooth domain our domain is composed of a finite number of disjoint subdomains with r reifenberg flat boundaries and the coefficients which are allowed to have great discontinuity across the boundaries of subdomains have small bmo semi norms on each subdomain our main result is deriving the global w 2 p 1 p regularity with the estimates independent of the distance between the subdomains

from cluster ensemble to structure ensemble this paper investigates the problem of integrating multiple structures which are extracted from different sets of data points into a single unified structure we first propose a new generalized concept called structure ensemble for the fusion of multiple structures unlike traditional cluster ensemble approaches the main objective of which is to align individual labels obtained from different clustering solutions the structure ensemble approach focuses on how to unify the structures obtained from different data sources based on this framework a new structure ensemble approach called the probabilistic bagging based structure ensemble approach bsea is designed which integrates the bagging technique the force based self organizing map fbsom and the normalized cut algorithm into the proposed framework bsea views structures obtained from different datasets generated by the bagging technique as nodes in a graph and adopts graph theory to find the most representative structure in addition the force based self organizing map fbsom which is a generalized form of som is proposed to serve as the basic clustering algorithm in the structure ensemble framework finally a new external index called correlation index ci which considers the correlation relationship of both the similarity and dissimilarity between the predicted solution and the true solution is proposed to evaluate the performance of bsea the experiments show that i the performance of bsea outperforms most of the state of the art clustering approaches and ii bsea performs well on datasets from the uci repository and real cancer gene expression profiles

linear quadratic regulators with eigenvalue placement in a vertical strip a computational method is presented for finding the linear quadratic regulator such that the optimal closed loop system has eigenvalues lying within a vertical strip in the complex plane the proposed method is suitable for the two stage optimal design of two time scale systems

gradient estimates for the p x laplacean system we prove calderon and zygmund type estimates for a class of elliptic problems whose model is the non homogeneous p x laplacean system div jduj p x 2 du div jf j p x 2 f