feature subset selection by gravitational search algorithm optimization a new method for feature subset selection in machine learning fss mgsa feature subset selection by modified gravitational search algorithm is presented fss mgsa is an evolutionary stochastic search algorithm based on the law of gravity and mass interactions and it can be executed when domain knowledge is not available a wrapper approach over naive bayes id3 k nearest neighbor and support vector machine learning algorithms is used to evaluate the goodness of each visited solution the key to the success of the mgsa is to utilize the piecewise linear chaotic map for increasing its diversity of species and to use sequential quadratic programming for accelerating local exploitation promising results are achieved in a variety of tasks where domain knowledge is not available the experimental results show that the proposed method has the ability of selecting the discriminating input features correctly and can achieve high accuracy of classification which is comparable to or better than well known similar classifier systems furthermore the mgsa is tested on ten functions provided by cec 2005 special session and compared with various modified gravitational search algorithm particle swarm optimization and genetic algorithm the obtained results confirm the high performance of the mgsa in solving various problems in optimization

influence of model errors in optimal sensor placement abstract the paper investigates the role of model errors and parametric uncertainties in optimal or near optimal sensor placements for structural health monitoring shm and modal testing the near optimal set of measurement locations is obtained by the information entropy theory the results of placement process considerably depend on the so called covariance matrix of prediction error as well as on the definition of the correlation function a constant and an exponential correlation function depending on the distance between sensors are firstly assumed then a proposal depending on both distance and modal vectors is presented with reference to a simple case study the effect of model uncertainties on results is described and the reliability and the robustness of the proposed correlation function in the case of model errors are tested with reference to 2d and 3d benchmark case studies a measure of the quality of the obtained sensor configuration is considered through the use of independent assessment criteria in conclusion the results obtained by applying the proposed procedure on a real 5 spans steel footbridge are described the proposed method also allows to better estimate higher modes when the number of sensors is greater than the number of modes of interest in addition the results show a smaller variation in the sensor position when uncertainties occur

an iterative system equivalent reduction expansion process for extraction of high frequency response from reduced order finite element model an iterative system equivalent reduction expansion process serep is proposed for extraction of high frequency response from a reduced order model rom under frequency band limited excitation various model order reduction methods are discussed to alleviate the present drawback of the serep which requires computation of full system modal matrix an iterative method based on sturm sequence check is proposed the method uses eigenvalue separation properties on the excitation frequency band to identify the optimal number of the eigenpairs required to capture the accurate response the basic steps for numerical implementation are given numerical results are presented to validate the predicted response comparison is also made to explain the reasons for the instability of the rom based on dynamic condensation to capture the high frequency dynamics case studies are carried out to demonstrate the effect of the chosen frequency band for response extraction also it is shown that accurate results are obtained while using the proposed method when the chosen frequency band encompass the excitation frequency band

co evolutionary algorithm for structural damage identification using minimal physical testing the problem of damage identification using minimum test data is studied in this work data sparsity in damage identification applications commonly results in inverse problems that are mathematically ill posed e g non unique solutions although solution non uniqueness may be addressed by performing multiple tests on a structure it is not trivial to decide which tests to carry out given that actual physical testing is costly this problem is addressed in this work through a new co evolutionary algorithm that interactively searches for damage scenarios and optimum physical tests the algorithm is composed of two stages the estimation phase which searches for damage scenarios that can predict current physical tests and the exploration phase which searches for tests that increase the level of information about the damaged system the feasibility of the methodology is demonstrated using numerical examples copyright 2006 john wiley sons ltd

fuzzy feature selection based on min max learning rule and extension matrix in many systems such as fuzzy neural network we often adopt the language labels such as large medium small etc to split the original feature into several fuzzy features in order to reduce the computation complexity of the system after the fuzzification of features the optimal fuzzy feature subset should be selected in this paper we propose a new heuristic algorithm where the criterion is based on min max learning rule and fuzzy extension matrix is designed as the search strategy the algorithm is proved in theory and has shown its high performance over several real world benchmark data sets

pareto optimal sensor locations for structural identification theoretical and computational issues arising in the selection of the optimal sensor configuration for parameter estimation in structural dynamics are addressed the objective is to optimally locate sensors in the structure such that the resulting measured data are most informative for estimating the parameters of a family of mathematical model classes used for structural modeling for a single model class the information entropy is used as the optimality criterion for selecting the best sensor configuration for multiple model classes the problem is formulated as a multi objective optimization problem of finding the pareto optimal sensor configurations that simultaneously minimize appropriately defined information entropy indices a heuristic algorithm is proposed for constructing effective pareto optimal sensor configurations that are superior in terms of computational efficiency and accuracy to the pareto sensor configurations predicted by evolutionary algorithms suitable for solving general multi objective optimisation problems the theoretical developments and the effectiveness of the proposed algorithms are illustrated for a 10 dof chain like spring mass model and a 32 dof truss structure

iterative relief for feature weighting algorithms theories and applications relief is considered one of the most successful algorithms for assessing the quality of features in this paper we propose a set of new feature weighting algorithms that perform significantly better than relief without introducing a large increase in computational complexity our work starts from a mathematical interpretation of the seemingly heuristic relief algorithm as an online method solving a convex optimization problem with a margin based objective function this interpretation explains the success of relief in real application and enables us to identify and address its following weaknesses relief makes an implicit assumption that the nearest neighbors found in the original feature space are the ones in the weighted space and relief lacks a mechanism to deal with outlier data we propose an iterative relief i relief algorithm to alleviate the deficiencies of relief by exploring the framework of the expectation maximization algorithm we extend i relief to multiclass settings by using a new multiclass margin definition to reduce computational costs an online learning algorithm is also developed convergence analysis of the proposed algorithms is presented the results of large scale experiments on the uci and microarray data sets are reported which demonstrate the effectiveness of the proposed algorithms and verify the presented theoretical results

automatic choice of measurement locations for dynamic testing this paper examines the problem of choosing an optimum set of measurement locations for experimental modal testing and suggests criteria whereby the suitability of the chosen locations can be assessed two methods of coordinate selection are used one based on guyan reduction and the other on the fisher information matrix each begins with a detailed finite element model of the structure being tested both procedures reduce this model by one degree of freedom at a time until the number of degrees of freedom in the reduced model equals the number of measurement locations required the choice of the eliminated coordinates is generally automatic and the coordinates of the reduced model are those used for modal testing

graph theoretical analysis of alzheimer s disease tools available in graph theory have been recently applied to signals recorded from the human brain where its cognitive functions are linked to topological properties of connectivity networks in this work we consider resting state electroencephalography eeg signals recorded from healthy subjects and patients suffering from alzheimer s disease ad in two conditions eyes open and eyes closed the eegs are used to construct functional brain networks in which the nodes are eeg sensor locations and edges represent functional connectivity between them the networks are then tested for a number of neurobiologically relevant graph theory metrics the analyses show that the network properties are stable across all conventional frequency bands ad brains in eyes closed condition show significantly reduced local efficiency and modularity measures p 0 05 wilcoxon s ranksum test we then use the network metrics as features for discriminating ad from healthy controls three feature selection methods genetic algorithms ga binary particle swarm optimization bpso and social impact theory based optimization sito are used to select the best feature set ga with support vector machines as classifier results in an accuracy of 83 in eyes close beta band the set of optimal features include edge betweenness centrality global efficiency modularity and synchronizability

einstein four manifolds of three nonnegative curvature operator in this paper we prove that einstein four manifolds of 3 positive curvature operator are isometric to s 4 g 0 or mathbb c p 2 g fs and einstein four manifolds of 3 nonnegative curvature operator are isometric to s 4 g 0 mathbb c p 2 g fs or s 2 times s 2 g 0 oplus g 0 up to rescaling we also prove that the first eigenvalue of the laplace operator for einstein four manifolds with mathrm ric g and nonnegative sectional curvature is bounded above by frac 4 3 4 frac 1 3 the basic idea of the proofs is to construct an integrated subharmonic function and the main ingredients of the proofs are curvature decompositions in particular berger decomposition the weitzenbock formula and the refined kato inequality along with the proofs we also discover an alternative proof for the weitzenbock formula using berger decomposition and an alternative proof for the refined kato inequality using derdzinski s argument

einstein four manifolds of pinched sectional curvature abstract in this paper we obtain classification of four dimensional einstein manifolds with positive ricci curvature and pinched sectional curvature in particular the first result deals with an upper bound on the sectional curvature improving a theorem of e costa the second is a generalization of d yang s result assuming an upper bound on the difference between sectional curvatures

effect of rule weights in fuzzy rule based classification systems this paper examines the effect of rule weights in fuzzy rule based classification systems each fuzzy if then rule in our classification system has antecedent linguistic values and a single consequent class we use a fuzzy reasoning method based on a single winner rule in the classification phase the winner rule for a new pattern is the fuzzy if then rule that has the maximum compatibility grade with the new pattern when we use fuzzy if then rules with certainty grades the winner is determined as the rule with the maximum product of the compatibility grade and the certainty grade in this paper the effect of rule weights is illustrated by drawing classification boundaries using fuzzy if then rules with without certainty grades it is also shown that certainty grades play an important role when a fuzzy rule based classification system is a mixture of general rules and specific rules through computer simulations we show that comprehensible fuzzy rule based systems with high classification performance can be designed without modifying the membership functions of antecedent linguistic values when we use fuzzy if then rules with certainty grades

feature selection based on a modified fuzzy c means algorithm with supervision in this paper we propose a new approach to feature selection based on a modified fuzzy c means algorithm with supervision mfcms mfcms completes the unsupervised learning of classical fuzzy c means with labeled patterns the labeled patterns allow mfcms to accurately model the shape of each cluster and consequently to highlight the features which result to be particularly effective to characterize a cluster these features are distinguished by a low variance of their values for the patterns with a high membership degree to the cluster if with respect to these features the distance between the prototype of the cluster and the prototypes of the other clusters is high then these features have the property of discriminating between the cluster and the other clusters to take these two aspects into account for each cluster and each feature we introduce a purposely defined index the higher the value of the index the higher the discrimination capability of the feature for the cluster we execute mfcms on the training set considering all patterns as labeled then we retain the features which are associated at least for one cluster with an index larger than a threshold we applied mfcms to several real world pattern classification benchmarks we used the well known k nearest neighbors as learning algorithm we show that feature selection performed by mfcms achieved an improvement in generalization on all data sets

membership margin based feature selection for mixed type and high dimensional data definition of membership margin based objective function weighting the antecedents of fuzzy if then rules to improve classification performance evaluate the feature importance within membership margin framework feature selection algorithm for mixed type and high dimensional data the effectiveness of the approach is proved through an extensive experimental study the present paper describes a new feature weighting method based on a membership margin distinctive properties of the proposed method include its capability to process problems characterized by mixed type data quantitative qualitative and interval as well as a huge number of features the key idea is to map simultaneously all the features of different types into a common space the membership space once all features are represented in a homogeneous space a feature weighting task can be performed in unified way this weighting approach is integrated here within a fuzzy classifier through a fuzzy rule weighted concept in order to improve its performance each antecedent fuzzy set in the fuzzy if then rule is weighted to characterize the importance of each proposition and therefore its corresponding feature weight estimation process is based on membership margin maximization to estimate a fuzzy weight of each feature in the membership space experiments on low and high dimensional real world datasets demonstrate that the proposed approach can improve significantly the performance of the fuzzy rule based as well as other state of the art classifiers and can even outperform classical feature weighting approaches in particular we show that this approach can yield meaningful results on two real world applications for cancer prognosis and industrial process diagnosis

feature subset selection in large dimensionality domains searching for an optimal feature subset from a high dimensional feature space is known to be an np complete problem we present a hybrid algorithm saga for this task saga combines the ability to avoid being trapped in a local minimum of simulated annealing with the very high rate of convergence of the crossover operator of genetic algorithms the strong local search ability of greedy algorithms and the high computational efficiency of generalized regression neural networks we compare the performance over time of saga and well known algorithms on synthetic and real datasets the results show that saga outperforms existing algorithms

distributed representation of fuzzy rules and its application to pattern classification abstract this paper introduces the concept of distributed representation of fuzzy rules and applies it to classification problems distributed representation is implemented by superimposing many fuzzy rules corresponding to different fuzzy partitions of a pattern space this means that we simulatenously employ many fuzzy rule tables corresponding to different fuzzy partitions in fuzzy inference in order to apply distributed representation of fuzzy rules to pattern classification problems we first propose an algorithm to generate fuzzy rules from numerical data next we propose a fuzzy inference method using the generated fuzzy rules the classification power of distributed representation is compared with that of ordinary fuzzy rules which can be viewed as local representation

rule weight specification in fuzzy rule based classification systems this paper shows how the rule weight of each fuzzy rule can be specified in fuzzy rule based classification systems first we propose two heuristic methods for rule weight specification next the proposed methods are compared with existing ones through computer simulations on artificial numerical examples and real world pattern classification problems simulation results show that the proposed methods outperform the existing ones in the case of multiclass pattern classification problems with many classes

a fast feature weighting algorithm of data gravitation classification the data gravitation classification dgc model is a new classification method that has gained great research interest in recent years feature weights are the key parameters in dgc models because the classification performances of these models are very sensitive to such feature weights the available dgc models use wrapper like algorithms to obtain their optimised feature weights although such algorithms produce high classification accuracies but they contribute to the high computational complexities of the dgc models in this study we propose a fast feature weight algorithm for dgc models called ffw dgc we use the concepts of feature discrimination and redundancy to measure the importance of a feature after which two fuzzy subsets are constructed to respectively represent these concepts next we combine the two fuzzy subsets to compute the feature weights used in gravitational computing we conduct our experiments on 25 standard data sets and 22 imbalance data sets and compare ffw dgc with 11 kinds of classifiers including the swarm intelligence based dgc pso dgc model competitive results of ffw dgc demonstrate that it can obtain high classification accuracies but also hundreds of times of speedup ratios compared with pso dgc

manifolds with positive curvature operators are space forms the ricci flow was introduced by hamilton in 1982 h1 in order to prove that a compact three manifold admitting a riemannian metric of positive ricci curvature is a spherical space form in dimension four hamilton showed that compact four manifolds with positive curvature operators are spherical space forms as well h2 more generally the same conclusion holds for compact four manifolds with 2 positive curvature operators che recall that a curvature operator is called 2 positive if the sum of its two smallest eigenvalues is positive in arbitrary dimensions huisken hu described an explicit open cone in the space of curvature operators such that the normalized ricci flow evolves metrics whose curvature operators are contained in that cone into metrics of constant positive sectional curvature hamilton conjectured that in all dimensions compact riemannian manifolds with positive curvature operators must be space forms in this paper we confirm this conjecture more generally we show the following

unsupervised feature selection using feature similarity in this article we describe an unsupervised feature selection algorithm suitable for data sets large in both dimension and size the method is based on measuring similarity between features whereby redundancy therein is removed this does not need any search and therefore is fast a new feature similarity measure called maximum information compression index is introduced the algorithm is generic in nature and has the capability of multiscale representation of data sets the superiority of the algorithm in terms of speed and performance is established extensively over various real life data sets of different sizes and dimensions it is also demonstrated how redundancy and information loss in feature selection can be quantified with an entropy measure

an axiomatic approach to scalar cardinalities of fuzzy sets abstract we present an axiomatic approach to scalar cardinalities of fuzzy sets which is based on a system of three simple postulates a characterization theorem for those cardinalities is given the infinite family of possible scalar cardinalities of a fuzzy set generated by the postulates contains as particular cases all standard concepts of scalar cardinality e g the sigma count of a fuzzy set the cardinality of its core or support and the cardinality of its t level set

rigidity of einstein 4 manifolds with positive curvature an einstein metric with positive scalar curvature on a 4 manifold is said to be normalized if ric 1 a basic problem in riemannian geometry is to classify einstein 4 manifolds with positive sectional curvature in the category of either topology diffeomorphism or isometry it is shown in this paper that if the sectional curvature k of a normalized einstein 4 manifold m satisfies the lower bound k e0 e0 23 120 0 102843 or condition b of theorem 1 1 then it is isometric to either s 4 rp 4 with constant sectional curvature k 1 3 or cp 2 with the normalized fubini study metric as a consequence both the normalized moduli spaces of einstein metrics which satisfy either one of the above two conditions on s 4 and cp 2 contain only a single point in particular if m is a smooth 4 manifold which is homeomorphic to either s 4 rp 4 or cp 2 but not diffeomorphic to any of the three manifolds then it can not support any normalized einstein metric which satisfies either one of the conditions

using simulated annealing to optimize the feature selection problem in marketing applications the feature selection also specification problem is concerned with finding the most influential subset of predictors in predictive modeling from a much larger set of potential predictors that can contain hundreds of predictors the problem belongs to the realm of combinatorial optimization where the objective is to find the subset of variables that optimize the value of some goodness of fit function due to the dimensionality of the problem the feature selection problem belongs to the group of np hard problems most of the available predictors are noisy or redundant and add very little if any to the prediction power of the model using all the predictors in the model often results in strong over fitting and very poor predictions constructing a prediction model by checking out all possible subsets is impractical due to computational volume looking on the contribution of each predictor separately is not accurate because it ignores the inter correlations between predictors as a result no analytic solution is available for the feature selection problem requiring that one resorts to heuristics in this paper we employ the simulated annealing sa approach which is one of the leading stochastic search methods for specifying a large scale linear regression model the sa results are compared to the results of the more common stepwise regression swr approach for model specification the models are applied on realistic data sets in database marketing we also use simulated data sets to investigate what data characteristics make the swr approach equivalent to the supposedly more superior sa approach

a multi objective evolutionary algorithm for feature selection based on mutual information with a new redundancy measure a new feature redundancy measurement based on mutual information was proposed a multi objective evolutionary algorithm for feature selection was presented pareto optimality was used to evaluate candidate feature subsets and find compact feature subsets experiments showed that our algorithm could select compact and discriminative feature subsets feature selection is an important task in data mining and pattern recognition especially for high dimensional data it aims to select a compact feature subset with the maximal discriminative capability the discriminability of a feature subset requires that selected features have a high relevance to class labels whereas the compactness demands a low redundancy within the selected feature subset this paper defines a new feature redundancy measurement capable of accurately estimating mutual information between features with respect to the target class mifs cr based on a relevance measure and this new redundancy measure a multi objective evolutionary algorithm with class dependent redundancy for feature selection mecy fs is presented the mecy fs algorithm employs the pareto optimality to evaluate candidate feature subsets and finds compact feature subsets with both the maximal relevance and the minimal redundancy experiments on benchmark datasets are conducted to validate the effectiveness of the new redundancy measure and the mecy fs algorithm is verified to be able to generate compact feature subsets with a high predictive capability

correction to einstein four manifolds of three nonnegative curvature operator this is to acknowledge that the main results of the article 3 were first proved in a joint preprint with xiaodong cao 1

minimal two spheres and the topology of manifolds with positive curvature on totally isotropic two planes there has been much interest among differential geometers in finding relationships between curvature and topology of riemannian manifolds for the most part efforts have been directed towards understanding the implications of positive or negative sectional curvature ricci curvature or scalar curvature but there are other hypotheses on the curvature which also deserve investigation in this article we will consider the topological implications of a new curvature assumption positive curvature on totally isotropic two planes and we will prove via the sacks uhlenbeck theory of minimal two spheres that a compact simply connected riemannian manifold of dimension at least four with positive curvature on totally isotropic two planes is homeomorphic to a sphere as corollaries we will obtain a proof via minimal two spheres for riemannian manifolds of dimension at least four of the berger klingenberg rauch toponogov sphere theorem strengthened to pointwise quarter pinching as well as a proof that every simply connected compact riemannian manifold with positive curvature operators is homeomorphic to a sphere let m be an n dimensional riemannian manifold with tangent space tpm at the point p e m recall that the curvature operator at p is the self adjoint

feature selection with svd entropy some modification and extension many approaches have been developed for dimensionality reduction these approaches can broadly be categorized into supervised and unsupervised methods in case of supervised dimensionality reduction for any input vector the target value is known which can be a class label also in a supervised approach our objective is to select a subset of features that has adequate discriminating power to predict the target value this target value for an input vector is absent in case of an unsupervised approach in an unsupervised scheme we mainly try to find a subset that can capture the inherent structure of the data such as the neighborhood relation or the cluster structure in this work we first study a singular value decomposition svd based unsupervised feature selection approach proposed by varshavsky et al then we propose a modification of this method to improve its performance an svd entropy based supervised feature selection algorithm is also developed in this paper performance evaluation of the algorithms is done on altogether 13 benchmark and one synthetic data sets the quality of the selected features is assessed using three indices sammon s error se cluster preservation index cpi and misclassification error mce using a 1 nearest neighbor 1 nn classifier besides showing the improvement of the modified unsupervised scheme over the existing one we have also made a comparative study of the modified unsupervised and the proposed supervised algorithms with one well known unsupervised and two popular supervised feature selection methods respectively our results reveal the effectiveness of the proposed algorithms in selecting relevant features

optimal sensor placement methodology for parametric identification of structural systems abstract theoretical and computational issues arising in the selection of the optimal sensor configuration for parameter estimation in structural dynamics are addressed the information entropy measuring the uncertainty in the system parameters is used as the performance measure of a sensor configuration a useful asymptotic approximation for the information entropy valid for a large number of measured data is derived the asymptotic estimate is then used to rigorously justify that selections of the optimal sensor configuration can be based solely on a nominal structural model ignoring the time history details of the measured data which are not available in the experimental design stage it is further shown that the lower and upper bounds of the information entropy are decreasing functions of the number of sensors based on this result two algorithms are proposed for constructing effective sensor configurations that are superior in terms of computational efficiency and accuracy to the sensor configurations provided by genetic algorithms the theoretical developments and the effectiveness of the proposed algorithms are illustrated by designing the optimal configuration for a 10 degree of freedom d o f chain like spring mass model and a 240 d o f three dimensional truss structure

a proposed method for learning rule weights in fuzzy rule based classification systems in fuzzy rule based classification systems frbcss rule weighting has often been used as a simple mechanism to tune the classifier in past research a number of heuristic rule weight specification methods have been proposed for this purpose a learning algorithm based on reward and punishment has also been proposed to adjust the weights of each fuzzy rule in the rule base in this paper a new method of learning rule weight in frbcss is proposed the method can be used when single winner or weighted vote methods of reasoning is used compared with reward and punishment scheme the proposed method is much faster and more effective another advantage of the proposed method is that during the learning process redundant rules are removed i e by setting their weights to zero the final rule base usually contains much fewer rules than the initial one this feature is very useful since a compact rule base is usually desired from the point of efficiency and interpretability a number of uci data sets are used to assess the performance of the proposed method in comparison with reward and punishment scheme

fuzzy criteria for feature selection the presence of less relevant or highly correlated features often decrease classification accuracy feature selection in which most informative variables are selected for model generation is an important step in data driven modeling in feature selection one often tries to satisfy multiple criteria such as feature discriminating power model performance or subset cardinality therefore a multi objective formulation of the feature selection problem is more appropriate in this paper we propose to use fuzzy criteria in feature selection by using a fuzzy decision making framework this formulation allows for a more flexible definition of the goals in feature selection and avoids the problem of weighting different goals is classical multi objective optimization the optimization problem is solved using an ant colony optimization algorithm proposed in our previous work we illustrate the added value of the approach by applying our proposed fuzzy feature selection algorithm to eight benchmark problems

optimal sensor placement using frfs based clustering method the purpose of this work is to develop an optimal sensor placement method by selecting the most relevant degrees of freedom as actual measure position based on observation matrix of a structure s frequency response two optimal criteria are used to avoid the information redundancy of the candidate degrees of freedom by using principal component analysis the frequency response matrix can be decomposed into principal directions and their corresponding singular a relatively small number of principal directions will maintain a system s dominant response information according to the dynamic similarity of each degree of freedom the k means clustering algorithm is designed to classify the degrees of freedom and effective independence method deletes the sensors which are redundant of each cluster finally two numerical examples and a modal test are included to demonstrate the efficient of the derived method it is shown that the proposed method provides a way to extract sub optimal sets and the selected sensors are well distributed on the whole structure

structural system identification using degree of freedom based reduction and hierarchical clustering algorithm abstract a system identification method has been proposed to validate finite element models of complex structures using measured modal data finite element method is used for the system identification as well as the structural analysis in perturbation methods the perturbed system is expressed as a combination of the baseline structure and the related perturbations the changes in dynamic responses are applied to determine the structural modifications so that the equilibrium may be satisfied in the perturbed system in practical applications the dynamic measurements are carried out on a limited number of accessible nodes and associated degrees of freedom the equilibrium equation is in principle expressed in terms of the measured master primary and unmeasured slave secondary degrees of freedom only the specified degrees of freedom are included in the equation formulation for identification and the unspecified degrees of freedom are eliminated through the iterative improved reduction scheme a large number of system parameters are included as the unknown variables in the system identification of large scaled structures the identification problem with large number of system parameters requires a large amount of computation time and resources in the present study a hierarchical clustering algorithm is applied to reduce the number of system parameters effectively numerical examples demonstrate that the proposed method greatly improves the accuracy and efficiency in the inverse problem of identification

sensor and actuator placement for linear systems based on h_ 2 and h_ infty optimization sensor and actuator placement algorithms are developed for linear discrete time systems based on h 2 and h infty optimization for sensor placement we design an observer that minimizes the h 2 norm of the error dynamics and the number of sensors at the same time for actuator placement we design a state feedback controller that minimizes the h infty norm of the closed loop system and the number of actuators at the same time any other combination of actuator placement for state feedback design or sensor placement for observer design for continuous time or discrete time linear systems based on h 2 or h infty optimization can be derived from these results in both presented cases the number of sensors or actuators is formulated as the ell 0 norm of the observer or controller gain matrix this ell 0 norm is then relaxed to a weighted ell 1 norm in order to obtain an iterative convex optimization problem as an application example we use the sensor placement algorithm to place phase measurement units with maximal impact on the h 2 performance in a power grid

a new eigensolution of structures via dynamic condensation dynamic condensation or model reduction is a commonly used algorithm to fast estimate some low eigenvalues and corresponding eigenvectors of structures by reducing the order of the original structural model to a smaller one this paper proposes a new eigensolution technique via iterated dynamic condensation the technique retains all the inertia terms associated with the removed degrees of freedom in an iterated form which generates the reduced mass matrix similar to that obtained in the guyan reduction method with a frequency dependent perturbed term the corresponding eigenvalues and eigenvectors of interest are obtained as those of the guyan reduction method with perturbations by using an eigensensitivity based iterative method the effectiveness and accuracy of the proposed technique are numerically verified by using a steel frame and the garteur structure

the three semantics of fuzzy sets abstract three main semantics for membership functions seem to exist in the literature similarity preference and uncertainty each semantics underlies a particular class of applications similarity notions are exploited in clustering analysis and fuzzy controllers uncertainty is captured by fuzzy sets in the framework of possibility theory the membership function of a fuzzy set is also sometimes a kind of utility function that represents flexible constraints in decision problems this paper advocates the claim that progress in operational semantics of membership functions presupposes that these distinct semantics be acknowledged and related to more basic measurement issues in terms of distance cost and frequency on which scientific traditions exist

weighted fuzzy pattern matching the fuzzy pattern matching technique has been developed in the framework of fuzzy set and possibility theory in order to take into account the imprecision and the uncertainty pervading values which have to be compared in a matching process this technique has proved very useful for implementing patterns of approximate reasoning in expert system inference engines and for designing retrieval systems capable of managing incomplete and fuzzy information data bases and vague queries in this paper the fuzzy pattern matching procedure is improved by introducing weights assessing the relative importance of atoms in the pattern matching indices are obtained using weighted versions of the minimum and maximum operations of fuzzy set theory this approach is extended to the case of variable weights and is related to aggregation schemes proposed by yager when modeling soft quantified statements such as most of the criteria must be met a notion of soft partial matching is thus modelled

fuzzy rough sets assisted attribute selection attribute selection as refers to the problem of selecting those input attributes or features that are most predictive of a given outcome a problem encountered in many areas such as machine learning pattern recognition and signal processing unlike other dimensionality reduction methods attribute selectors preserve the original meaning of the attributes after reduction this has found application in tasks that involve datasets containing huge numbers of attributes in the order of tens of thousands which for some learning algorithms might be impossible to process further recent examples include text processing and web content classification as techniques have also been applied to small and medium sized datasets in order to locate the most informative attributes for later use one of the many successful applications of rough set theory has been to this area the rough set ideology of using only the supplied data and no other information has many benefits in as where most other methods require supplementary knowledge however the main limitation of rough set based attribute selection in the literature is the restrictive requirement that all data is discrete in classical rough set theory it is not possible to consider real valued or noisy data this paper investigates a novel approach based on fuzzy rough sets fuzzy rough feature selection frfs that addresses these problems and retains dataset semantics frfs is applied to two challenging domains where a feature reducing step is important namely web content classification and complex systems monitoring the utility of this approach is demonstrated and is compared empirically with several dimensionality reducers in the experimental studies frfs is shown to equal or improve classification accuracy when compared to the results from unreduced data classifiers that use a lower dimensional set of attributes which are retained by fuzzy rough reduction outperform those that employ more attributes returned by the existing crisp rough reduction method in addition it is shown that frfs is more powerful than the other as techniques in the comparative study

refined kato inequalities and conformal weights in riemannian geometry abstract we establish refinements of the classical kato inequality for sections of a vector bundle which lie in the kernel of a natural injectively elliptic first order linear differential operator our main result is a general expression which gives the value of the constants appearing in the refined inequalities these constants are shown to be optimal and are computed explicitly in most practical cases

cultured differential evolution for constrained optimization a cultural algorithm with a differential evolution population is proposed in this paper this cultural algorithm uses different knowledge sources to influence the variation operator of the differential evolution algorithm in order to reduce the number of fitness function evaluations required to obtain competitive results comparisons are provided with respect to three techniques that are representative of the state of the art in the area the results obtained by our algorithm are similar in quality to those obtained by the other approaches with respect to which it was compared however our approach requires a lower number of fitness function evaluations than the others

dynamic condensation approach for nonclassically damped structures an iterative dynamic condensation procedure for calculating the elgenproperties of damped dynamic systems is presented the kept and reduced degrees of freedom of the systems are related through dynamic condensation matrices the formulation to define the condensation matrices is developed the procedure starts with a classical static condensation scheme but iteratively improves the results the complex eigenproperties calculated in an iteration step are used to construct an updated condensation matrix for the following iteration step which in turn is utilized to form a revised condensed system a few iterations can provide accurate values of the eigenproperties the iterative process can be expedited initially by a proper selection of the kept and reduced coordinates numerical results are presented to demonstrate the accuracy and convergence characteristics of the proposed condensation scheme