multibody structure and motion segmentation by branch and bound model selection an efficient and robust framework is proposed for two view multiple structure and motion segmentation of unknown number of rigid objects the segmentation problem has three unknowns namely the object memberships the corresponding fundamental matrices and the number of objects to handle this otherwise recursive problem hypotheses for fundamental matrices are generated through local sampling once the hypotheses are available a combinatorial selection problem is formulated to optimize a model selection cost which takes into account the hypotheses likelihoods and the model complexity an explicit model for outliers is also added for robust segmentation the model selection cost is minimized through the branch and bound technique of combinatorial optimization the proposed branch and bound approach efficiently searches the solution space and guaranties optimality over the current set of hypotheses the efficiency and the guarantee of optimality of the method is due to its ability to reject solutions without explicitly evaluating them the proposed approach was validated with synthetic data and segmentation results are presented for real images

smoothness of transition maps in singular perturbation problems with one fast variable abstract this paper deals with the smoothness of the transition map between two sections transverse to the fast flow of a singularly perturbed vector field one fast multiple slow directions orbits connecting both sections are canard orbits i e they first move rapidly towards the attracting part of a critical surface then travel a distance near this critical surface even beyond the point where the orbit enters the repelling part of the critical surface and finally repel away from the surface we prove that the transition map is smooth in a transcritical situation however where orbits from an attracting part of one critical manifold follow the repelling part of another critical manifold the smoothness of the transition map may be limited due to resonance phenomena that are revealed by blowing up the turning point we present a polynomial example in r 3

a new belief based k nearest neighbor classification method the k nearest neighbor k nn classification method originally developed in the probabilistic framework has serious difficulties to classify correctly the close data points objects originating from different classes to cope with such difficult problem and make the classification result more robust to misclassification errors we propose a new belief based k nearest neighbor bk nn method that allows each object to belong both to the specific classes and to the sets of classes with different masses of belief bk nn is able to provide a hyper credal classification on the specific classes the rejection classes and the meta classes as well thus the objects hard to classify correctly are automatically committed to a meta class or to a rejection class which can reduce the misclassification errors the basic belief assignment bba of each object is defined from the distance between the object and its neighbors and from the acceptance and rejection thresholds the bba s are combined using a new combination method specially developed for the bk nn several experiments based on simulated and real data sets have been carried out to evaluate the performances of the bk nn method with respect to several classical k nn approaches

a hybrid probabilistic framework for content based image retrieval with feature weighting in this paper we propose a probabilistic framework for efficient retrieval and indexing of image collections this framework uncovers the hierarchical structure underlying the collection from image features based on a hybrid model that combines both generative and discriminative learning we adopt the generalized dirichlet mixture and maximum likelihood for the generative learning in order to estimate accurately the statistical model of the data then the resulting model is refined by a new discriminative likelihood that enhances the power of relevant features consequently this new model is suitable for modeling high dimensional data described by both semantic and low level visual features the semantic features are defined according to a known ontology while visual features represent the visual appearance such as color shape and texture for validation purposes we propose a new visual feature which has nice invariance properties to image transformations experiments on the microsoft s collection msrcid show clearly the merits of our approach in both retrieval and indexing

a more efficient branch and bound algorithm for feature selection abstract an algorithm is presented to be able to select the globally optimal subset of d features from a larger d feature set this is a fundamental problem in statistical pattern recognition and combinatorial optimization exhaustive enumeration is computationally unfeasible in most applications this algorithm dynamically searches for the globally optimal solution on a minimum solution tree which is a subtree of the solution tree used in the traditional branch and bound algorithm the new algorithm is compared theoretically with the branch and bound algorithm the analysis and the experimental results show that it is more efficient than the traditional algorithm

learning a mahalanobis metric from equivalence constraints many learning algorithms use a metric defined over the input space as a principal tool and their performance critically depends on the quality of this metric we address the problem of learning metrics using side information in the form of equivalence constraints unlike labels we demonstrate that this type of side information can sometimes be automatically obtained without the need of human intervention we show how such side information can be used to modify the representation of the data leading to improved clustering and classification specifically we present the relevant component analysis rca algorithm which is a simple and efficient algorithm for learning a mahalanobis metric we show that rca is the solution of an interesting optimization problem founded on an information theoretic basis if dimensionality reduction is allowed within rca we show that it is optimally accomplished by a version of fisher s linear discriminant that uses constraints moreover under certain gaussian assumptions rca can be viewed as a maximum likelihood estimation of the within class covariance matrix we conclude with extensive empirical evaluations of rca showing its advantage over alternative methods

constrained large margin local projection algorithms and extensions for multimodal dimensionality reduction a constrained large margin local projection cmlp technique for multimodal dimensionality reduction is proposed we elaborate the criterion of cmlp from a pairwise constrained marginal perspective four effective cmlp solution schemes are presented and the corresponding comparative analyses are given an equivalent weighted least squares formulation for cmlp is also detailed cmlp is originated from the criterion of locality preserving projections lpp but cmlp offers a number of attractive advantages over lpp to keep the intrinsic proximity relations of inter class and intra class similarity pairs the localized pairwise cannot link and must link constraints are applied to specify the types of those neighboring pairs by utilizing the cmlp criterion margins between inter and intra class clusters are significantly enlarged as a result multimodal distributions are effectively preserved to further optimize the cmlp criterion one feasible improvement strategy is described with kernel methods we present the kernelized extensions of our approaches mathematical comparisons and analyses between this work and the related works are also detailed extensive simulations including multivariate manifold visualization and classification on the benchmark ucl orl yale umist mit cbcl and usps datasets are conducted to verify the efficiency of our techniques the presented results reveal that our methods are highly competitive with and even outperform some widely used state of the art algorithms

dynamics of a predator prey model we describe the bifurcation diagram of limit cycles that appear in the first realistic quadrant of the predator prey model proposed by r m may stability and complexity in model ecosystems princeton university press princeton nj 1974 in particular we give a qualitative description of the bifurcation curve when two limit cycles collapse on a semistable limit cycle and disappear moreover we show that locally asymptotic stability of a positive equilibrium point does not imply global stability for this class of predator prey models

feature analysis through information granulation and fuzzy sets feature analysis and feature selection are fundamental pursuits in pattern recognition we revisit and generalize an issue of feature selection by introducing a mechanism of soft fuzzy feature selection the underlying idea is to consider features to be granular rather than numeric by varying the level of granularity we modify the level of contribution of the specific feature to the overall feature space we admit an interval model of the features meaning that their values assume a form of numeric intervals the intervalization of the features exhibits a clear cut interpretation moreover a contribution of the features to the formation of the feature space can be easily controlled the broader the interval the less essential contribution of the feature to the entire feature space in limit when the intervals get broad enough one may view the feature to be completely eliminated dropped from the feature space the quantification of the features in terms of their importance is realized in the setting of the clustering fcm model namely a process of the binary or fuzzy feature selection is carried out and numerically quantified in the space of membership values generated by fuzzy clusters as the focal point of this study concerns an interval like form of information granules we reveal how such feature intervalization helps approximate fuzzy sets described by any type of membership function detailed computations give rise to a detailed quantification of such granular features numerical experiments provide a comprehensive numerical illustration of the problem

credal classification rule for uncertain data based on belief functions abstract in this paper we present a new credal classification rule ccr based on belief functions to deal with the uncertain data ccr allows the objects to belong with different masses of belief not only to the specific classes but also to the sets of classes called meta classes which correspond to the disjunction of several specific classes each specific class is characterized by a class center i e prototype and consists of all the objects that are sufficiently close to the center the belief of the assignment of a given object to classify with a specific class is determined from the mahalanobis distance between the object and the center of the corresponding class the meta classes are used to capture the imprecision in the classification of the objects when they are difficult to correctly classify because of the poor quality of available attributes the selection of meta classes depends on the application and the context and a measure of the degree of indistinguishability between classes is introduced in this new ccr approach the objects assigned to a meta class should be close to the center of this meta class having similar distances to all the involved specific classes centers and the objects too far from the others will be considered as outliers noise ccr provides robust credal classification results with a relatively low computational burden several experiments using both artificial and real data sets are presented at the end of this paper to evaluate and compare the performances of this ccr method with respect to other classification methods

a grey based rough approximation model for interval data processing a new rough set model for interval data named grey rough set is proposed in this paper information system in the real world are quite complicated most of information tables record not only categorical data but also numerical data including a range of interval data the grey lattice operation in grey system theory is one of the operations for interval data that modifies endpoints non arithmetically and which is useful for interval data processing the grey rough approximation is based on an interval coincidence relation and an interval inclusion relation instead of an equivalence relation and an indiscernibility relation in pawlak s model numerical examples and four fields of practical examples decision making information retrieval knowledge discovery and kansei engineering are shown the advantages of the proposal include extending a treatable value compared with classical rough set for non deterministic information systems providing a maximum solution and minimum solution both in upper and lower approximations and not only providing mathematical support to sql but also functions for further extension in the future

multistage branch and bound merging for planar surface segmentation in disparity space an iterative split and merge framework for the segmentation of planar surfaces in the disparity space is presented disparity of a scene is modeled by approximating various surfaces in the scene to be planar in the split phase the number of planar surfaces along with the underlying plane parameters is assumed to be known from the initialization or from the previous merge phase based on these parameters planar surfaces in the disparity image are labeled to minimize the residuals between the actual disparity and the modeled disparity the labeled planar surfaces are separated into spatially continuous regions which are treated as candidates for the merging that follows the regions are merged together under a maximum variance constraint while maximizing the merged area a multistage branch and bound algorithm is proposed to carry out this optimization efficiently each stage of the branch and bound algorithm separates a planar surface from the set of spatially continuous regions the multistage merging estimates the number of planar surfaces and their labeling the splitting and the multistage merging is repeated till convergence is reached or satisfactory results are achieved experimental results are presented for variety of stereo image data

global stability for a class of predator prey systems this paper deals with the question of global stability of the positive locally asymptotically stable equilibrium in a class of predator prey systems the dulac s criterion is applied and liapunov functions are constructed to establish the global stability

feature selection for unsupervised learning in this paper we identify two issues involved in developing an automated feature subset selection algorithm for unlabeled data the need for finding the number of clusters in conjunction with feature selection and the need for normalizing the bias of feature selection criteria with respect to dimension we explore the feature selection problem and these issues through fssem feature subset selection using expectation maximization em clustering and through two different performance criteria for evaluating candidate feature subsets scatter separability and maximum likelihood we present proofs on the dimensionality biases of these feature criteria and present a cross projection normalization scheme that can be applied to any criterion to ameliorate these biases our experiments show the need for feature selection the need for addressing these two issues and the effectiveness of our proposed solutions

generalized dual hahn moment invariants in this work we introduce a generalized expression of the weighted dual hahn moment invariants up to any order and for any value of their parameters in order for the proposed invariants to be formed the weighted dual hahn moments up to any order and for any value of their parameters are expressed as a linear combination of geometric ones for this reason a formula expressing the nth degree dual hahn polynomial for any value of its parameters as a linear combination of monomials c r x r is proved in addition a recurrent relation for the fast computation of the aforementioned monomials coefficients c r is also given moreover normalization aspects of the generalized weighted dual hahn moment invariants are discussed while a modification of them is proposed in order to avoid their numerical instabilities finally experimental results and classification scenarios including datasets of natural scenes evaluate the proposed methodology

pattern formation of a spatial predator prey system abstract there are random and directed movements of predator and prey populations in many natural systems which are strongly influenced and modified by spatial factors to investigate how these migration directed movement and diffusion random movement affect predator prey systems we have studied the spatiotemporal complexity in a predator prey system with holling tanner form a theoretical analysis of emerging spatial pattern is presented and wavelength and pattern speed are calculated at the same time we present the properties of pattern solutions the results of numerical simulations show that migration has prominent effect on the pattern formation of the population i e changing turing pattern into traveling pattern this study suggests that modelling by migration and diffusion in predator prey systems can account for the dynamical complexity of ecosystems

on the dempster shafer framework and new combination rules abstract we discuss the basic concepts of the dempster shafer approach basic probability assignments belief functions and probability functions we discuss how to represent various types of knowledge in this framework we discuss measures of entropy and specificity for belief structures we discuss the combination and extension of belief structures we introduce some concerns associated with the dempster rule of combination inherent in the normalization due to conflict we introduce two alternative techniques for combining belief structures the first uses dempster s rule while the second is based upon a modification of this rule we discuss the issue of credibility of a witness

modeling uncertainty in multi criteria decision analysis abstract his paper provides a review of multiple criteria decision analysis mcda for cases where attribute evaluations are uncertain the main aim is to identify different tools which can be used to represent uncertain evaluations and to broadly survey the available decision models that can be used to support uncertain decision making the review includes models using probabilities or probability like quantities explicit risk measures such as quantiles and variances fuzzy numbers and scenarios the practical assessment of uncertain outcomes and preferences associated with these outcomes is also discussed

the combination of evidence in the transferable belief model a description of the transferable belief model which is used to quantify degrees of belief based on belief functions is given the impact of open and closed world assumption on conditioning is discussed the nature of the frame of discernment on which a degree of belief will be established is discussed a set of axioms justifying dempster s rule for the combination of belief functions induced by two distinct evidences is presented

soft fuzzy rough sets for robust feature evaluation and selection the fuzzy dependency function proposed in the fuzzy rough set model is widely employed in feature evaluation and attribute reduction it is shown that this function is not robust to noisy information in this paper as datasets in real world applications are usually contaminated by noise robustness of data analysis models is very important in practice in this work we develop a new model of fuzzy rough sets called soft fuzzy rough sets which can reduce the influence of noise we discuss the properties of the model and construct a new dependence function from the model then we use the function to evaluate and select features the presented experimental results show the effectiveness of the new model

on the relation between compromise programming and ordered weighted averaging operator this paper will demonstrate a strong relationship between the compromise programming cp method and the ordered weighted averaging owa operator we will mathematically prove that the application of the cp method reflects the pessimistic view of the decision maker dm if the distance from the ideal point is minimized it will however present an optimistic dm if the distance from the nadir is maximized the owa operator may cover all of the optimistic neutral and pessimistic views a practical relationship will be developed between the power value of the cp method and the optimism degree of the dm based on fuzzy quantifiers the theoretical results will be illustrated by a real case study of a water resources management problem

using the fuzzy multi criteria decision making approach for measuring the possibility of successful knowledge management this study develops a forecasting framework based on the fuzzy multi criteria decision making fmcdm approach to help organizations build awareness of the critical influential factors on the success of knowledge management km implementation measure the success possibility of knowledge management projects as well as identify the necessary actions prior to embarking on conducting knowledge management subjectivity uncertainty and vagueness within the prediction process are dealt with using linguistic variables parameterized by triangular fuzzy numbers by multiplying the importance weights of influential factors and the possible rating of success failure predicted success failure values are determined to enable organizations to decide whether to initiate knowledge management inhibit adoption or undertake remedial improvements to increase the possibility of successful knowledge management project the proposed approach is demonstrated using a real case involving a taiwanese semiconductor engineering corporation

estimating optimal feature subsets using efficient estimation of high dimensional mutual information a novel feature selection method using the concept of mutual information mi is proposed in this paper in all mi based feature selection methods effective and efficient estimation of high dimensional mi is crucial in this paper a pruned parzen window estimator and the quadratic mutual information qmi are combined to address this problem the results show that the proposed approach can estimate the mi in an effective and efficient way with this contribution a novel feature selection method is developed to identify the salient features one by one also the appropriate feature subsets for classification can be reliably estimated the proposed methodology is thoroughly tested in four different classification applications in which the number of features ranged from less than 10 to over 15000 the presented results are very promising and corroborate the contribution of the proposed feature selection methodology

fast branch bound algorithms for optimal feature selection a novel search principle for optimal feature subset selection using the branch bound method is introduced thanks to a simple mechanism for predicting criterion values a considerable amount of time can be saved by avoiding many slow criterion evaluations we propose two implementations of the proposed prediction mechanism that are suitable for use with nonrecursive and recursive criterion forms respectively both algorithms find the optimum usually several times faster than any other known branch bound algorithm as the algorithm computational efficiency is crucial due to the exponential nature of the search problem we also investigate other factors that affect the search performance of all branch bound algorithms using a set of synthetic criteria we show that the speed of the branch bound algorithms strongly depends on the diversity among features feature stability with respect to different subsets and criterion function dependence on feature set size we identify the scenarios where the search is accelerated the most dramatically finish in linear time as well as the worst conditions we verify our conclusions experimentally on three real data sets using traditional probabilistic distance criteria

a general branch and bound formulation for understanding and synthesizing and or tree search procedures citing the confusing statements in the ai literature concerning the relationship between branch and bound b b and heuristic search procedures were present a simple and general formulation of b b which should help dispel much of the confusion we illustrate the utility of the formulation by showing that through it some apparently very different algorithms for searching and or trees reveal the specific nature of their similarities and differences in addition to giving new insights into the relationships among some ai search algorithms the general formulation also provides suggestions on how existing search procedures may be varied to obtain new algorithms

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

invariant optimal feature selection a distance discriminant and feature ranking based solution the goal of feature selection is to find the optimal subset consisting of m features chosen from the total n features one critical problem for many feature selection methods is that an exhaustive search strategy has to be applied to seek the best subset among all the possible nm feature subsets which usually results in a considerably high computational complexity the alternative suboptimal feature selection methods provide more practical solutions in terms of computational complexity but they cannot promise that the finally selected feature subset is globally optimal we propose a new feature selection algorithm based on a distance discriminant fsdd which not only solves the problem of the high computational costs but also overcomes the drawbacks of the suboptimal methods the proposed method is able to find the optimal feature subset without exhaustive search or branch and bound algorithm the most difficult problem for optimal feature selection the search problem is converted into a feature ranking problem following rigorous theoretical proof such that the computational complexity can be greatly reduced the proposed method is invariant to the linear transformation of data when a diagonal transformation matrix is applied fsdd was compared with relieff and mrmrmid based on mutual information on 8 data sets the experiment results show that fsdd outperforms the other two methods and is highly efficient

a comparative study of suboptimal branch and bound algorithms abstract the branch and bound algorithm is widely known as an efficient approach for selecting optimal feature subsets if the optimality of the solution is allowed to be compromised it is possible to further improve the search speed of the branch and bound algorithm this paper studies the look ahead search strategy which can eliminate many solutions deemed to be suboptimal early in the branch and bound search we propose ways to incorporate the look ahead search scheme into four major branch and bound algorithms namely the basic branch and bound algorithm the ordered branch and bound algorithm the fast branch and bound algorithm and the adaptive branch and bound algorithm a comparative study of the look ahead scheme in terms of the computational cost and the solution quality on these suboptimal branch and bound algorithms is carried out on real data sets furthermore we test the feasible use of suboptimal branch and bound algorithms on a high dimensional data set and compare its performance with other well known suboptimal feature selection algorithms

socp relaxation bounds for the optimal subset selection problem applied to robust linear regression abstract this paper deals with the problem of finding the globally optimal subset of h elements from a larger set of n elements in d space dimensions so as to minimize a quadratic criterion with an special emphasis on applications to computing the least trimmed squares estimator ltse for robust regression the computation of the ltse is a challenging subset selection problem involving a nonlinear program with continuous and binary variables linked in a highly nonlinear fashion the selection of a globally optimal subset using the branch and bound bb algorithm is limited to problems in very low dimension typically d 5 as the complexity of the problem increases exponentially with d we introduce a bold pruning strategy in the bb algorithm that results in a significant reduction in computing time at the price of a negligeable accuracy lost the novelty of our algorithm is that the bounds at nodes of the bb tree come from pseudo convexifications derived using a linearization technique with approximate bounds for the nonlinear terms the approximate bounds are computed solving an auxiliary semidefinite optimization problem we show through a computational study that our algorithm performs well in a wide set of the most difficult instances of the ltse problem

an improvement on floating search algorithms for feature subset selection a new improved forward floating selection iffs algorithm for selecting a subset of features is presented our proposed algorithm improves the state of the art sequential forward floating selection algorithm the improvement is to add an additional search step called replacing the weak feature to check whether removing any feature in the currently selected feature subset and adding a new one at each sequential step can improve the current feature subset our method provides the optimal or quasi optimal close to optimal solutions for many selected subsets and requires significantly less computational load than optimal feature selection algorithms our experimental results for four different databases demonstrate that our algorithm consistently selects better subsets than other suboptimal feature selection algorithms do especially when the original number of features of the database is large

making use of partial knowledge about hidden states in hmms an approach based on belief functions this paper addresses the problem of parameter estimation and state prediction in hidden markov models hmms based on observed outputs and partial knowledge of hidden states expressed in the belief function framework the usual hmm model is recovered when the belief functions are vacuous parameters are learned using the evidential expectation maximization algorithm a recently introduced variant of the expectation maximization algorithm for maximum likelihood estimation based on uncertain data the inference problem i e finding the most probable sequence of states based on observed outputs and partial knowledge of states is also addressed experimental results demonstrate that partial information about hidden states when available may substantially improve the estimation and prediction performances

feature subset selection using separability index matrix effective feature subset selection fss is an important step when designing engineering systems that classify complex data in real time the electromyographic emg signal based walking assistance system is a typical system that requires an efficient computational architecture for classification the performance of such a system depends largely on a criterion function that assesses the quality of selected feature subsets however many well known conventional criterion functions use less relevant features for classification or they have a high computational cost here we propose a new criterion function that provides more effective fss the proposed criterion function known as a separability index matrix sim provides features pertinent to the classification task and a very low computational cost this new function produces to a simple feature selection algorithm when combined with the forward search paradigm we performed extensive experimental comparisons in terms of classification accuracy and computational costs to confirm that the proposed algorithm outperformed other filter type feature selection methods that are based on various distance measures including inter intra euclidean mahalanobis and bhattacharyya distances we then applied the proposed method to a gait phase recognition problem in our emg signal based walking assistance system we demonstrated that the proposed method performed competitively when compared with other wrapper type feature selection methods in terms of class separability and recognition rate

constraint score a new filter method for feature selection with pairwise constraints feature selection is an important preprocessing step in mining high dimensional data generally supervised feature selection methods with supervision information are superior to unsupervised ones without supervision information in the literature nearly all existing supervised feature selection methods use class labels as supervision information in this paper we propose to use another form of supervision information for feature selection i e pairwise constraints which specifies whether a pair of data samples belong to the same class must link constraints or different classes cannot link constraints pairwise constraints arise naturally in many tasks and are more practical and inexpensive than class labels this topic has not yet been addressed in feature selection research we call our pairwise constraints guided feature selection algorithm as constraint score and compare it with the well known fisher score and laplacian score algorithms experiments are carried out on several high dimensional uci and face data sets experimental results show that with very few pairwise constraints constraint score achieves similar or even higher performance than fisher score with full class labels on the whole training data and significantly outperforms laplacian score

input feature selection by mutual information based on parzen window mutual information is a good indicator of relevance between variables and have been used as a measure in several feature selection algorithms however calculating the mutual information is difficult and the performance of a feature selection algorithm depends on the accuracy of the mutual information in this paper we propose a new method of calculating mutual information between input and class variables based on the parzen window and we apply this to a feature selection algorithm for classification problems

novel moment invariants for improved classification performance in computer vision applications a novel set of moment invariants based on the krawtchouk moments are introduced in this paper these moment invariants are computed over a finite number of image intensity slices extracted by applying an innovative image representation scheme the image slice representation isr method based on this technique an image is decomposed to a several non overlapped intensity slices which can be considered as binary slices of certain intensity this image representation gives the advantage to accelerate the computation of image s moments since the image can be described in a number of homogenous rectangular blocks which permits the simplification of the computation formulas the moments computed over the extracted slices seem to be more efficient than the corresponding moments of the same order that describe the whole image in recognizing the pattern under processing the proposed moment invariants are exhaustively tested in several well known computer vision datasets regarding their rotation scaling and translation rst invariant recognition performance by resulting to remarkable outcomes

relaxation oscillation and canard explosion abstract we give a geometric analysis of relaxation oscillations and canard cycles in singularly perturbed planar vector fields the transition from small hopf type cycles to large relaxation cycles which occurs in an exponentially thin parameter interval is described as a perturbation of a family of singular cycles the results are obtained by means of two blow up transformations combined with standard tools of dynamical systems theory the efficient use of various charts is emphasized the results are applied to the van der pol equation

traveling waves for a generalized holling tanner predator prey model abstract we study traveling wave solutions for holling tanner type predator prey models where the predator equation has a singularity at zero prey population the traveling wave solutions here connect the prey only equilibrium 1 0 with the unique constant coexistence equilibrium u v first we give a sharp existence result on weak traveling wave solutions for a rather general class of predator prey systems with minimal speed explicitly determined such a weak traveling wave u v connects 1 0 at but needs not connect u v at next we modify the holling tanner model to remove its singularity and apply the general result to obtain a weak traveling wave solution for the modified model and show that the prey component in this weak traveling wave solution has a positive lower bound and thus is a weak traveling wave solution of the original model these results for weak traveling wave solutions hold under rather general conditions then we use two methods a squeeze method and a lyapunov function method to prove that under additional conditions the weak traveling wave solutions are actually traveling wave solutions namely they converge to the coexistence equilibrium as

a fuzzy mcdm method for solving marine transshipment container port selection problems abstract transshipment is a very popular and important issue in the present international trade container transportation market in order to reduce the international trade container transportation operation cost it is very important for shipping companies to choose the best transshipment container port the aim of this paper is to present a new fuzzy multiple criteria decision making method fmcdm for solving the transshipment container port selection problem under fuzzy environment in this paper we present first the canonical representation of multiplication operation on three fuzzy numbers and then this canonical representation is applied to the selection of transshipment container port based on the canonical representation the decision maker of shipping company can determine quickly the ranking order of all candidate transshipment container ports and select easily the best one

travelling waves in the holling tanner model with weak diffusion for a wide range of parameters we study travelling waves in a diffusive version of the holling tanner predator prey model from population dynamics fronts are constructed using geometric singular perturbation theory and the theory of rotated vector fields we focus on the appearance of the fronts in various singular limits in addition periodic travelling waves of relaxation oscillation type are constructed using a recent generalization of the entry exit function

grafting fast incremental feature selection by gradient descent in function space we present a novel and flexible approach to the problem of feature selection called grafting rather than considering feature selection as separate from learning grafting treats the selection of suitable features as an integral part of learning a predictor in a regularized learning framework to make this regularized learning process sufficiently fast for large scale problems grafting operates in an incremental iterative fashion gradually building up a feature set while training a predictor model using gradient descent at each iteration a fast gradient based heuristic is used to quickly assess which feature is most likely to improve the existing model that feature is then added to the model and the model is incrementally optimized using gradient descent the algorithm scales linearly with the number of data points and at most quadratically with the number of features grafting can be used with a variety of predictor model classes both linear and non linear and can be used for both classification and regression experiments are reported here on a variant of grafting for classification using both linear and non linear models and using a logistic regression inspired loss function results on a variety of synthetic and real world data sets are presented finally the relationship between grafting stagewise additive modelling and boosting is explored

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

the random subspace method for constructing decision forests much of previous attention on decision trees focuses on the splitting criteria and optimization of tree sizes the dilemma between overfitting and achieving maximum accuracy is seldom resolved a method to construct a decision tree based classifier is proposed that maintains highest accuracy on training data and improves on generalization accuracy as it grows in complexity the classifier consists of multiple trees constructed systematically by pseudorandomly selecting subsets of components of the feature vector that is trees constructed in randomly chosen subspaces the subspace method is compared to single tree classifiers and other forest construction methods by experiments on publicly available datasets where the method s superiority is demonstrated we also discuss independence between trees in a forest and relate that to the combined classification accuracy

a method for group decision making with multi granularity linguistic assessment information this paper proposes a method to solve the group decision making gdm problems with multi granularity linguistic assessment information in the method the multi granularity linguistic information provided by experts is firstly expressed in the form of fuzzy numbers in order to make the collective opinion close to each expert s opinion a linear goal programming model is constructed to integrate the fuzzy assessment information and to directly compute the collective ranking values of alternatives without the need of information transformation then a fuzzy preference relation on the pairwise comparisons of the collective ranking values of alternatives is constructed using the dominance possibility degree of the comparison between the fuzzy numbers by applying a non dominance choice degree to this fuzzy preference relation the ranking of alternatives is determined and the most desirable alternative s is selected an example is used to illustrate the applicability of the proposed method and its advantages

matrixized learning machine with modified pairwise constraints matrix pattern oriented classifier design matcd has been demonstrated to be effective in terms of the classification performance since it utilizes two sided weight vectors to constrain the matrix based patterns however the existing matcd might not be able to acquire the prior distribution knowledge such as the relationship between two patterns inspired by the pairwise constraints pc method i e must links and cannot links between the patterns this paper introduces a new regularization term named rp with a modified pc method into matcd the new classifier design strategy is expected to not only learn the structural information of each pattern itself but also acquire the prior distribution knowledge about each constrained pair with both the discrimination metric from the traditional pc and the spatial distance measure from the heat kernel method in practice this paper selects one typical matrixized classifier named matmhks as the basic building block and introduces the term rp into it the newly proposed classifier is named mlmmpc and the subsequent experiments validate the effectiveness of it two major contributions of this paper can be concluded as 1 improving the existing matrix pattern oriented classifier design techniques and 2 modifying the traditional pc method by combining the discrimination metric and the distance measure together highlightsa novel matrix oriented classification algorithm named mlmmpc is proposed to improve the original matrix learning framework by a new regularization term r p to combine pairwise constraints and spatial measure together in r p implementability is demonstrated on both image and vector based datasets

a fitting model for feature selection with fuzzy rough sets a fuzzy rough set is an important rough set model used for feature selection it uses the fuzzy rough dependency as a criterion for feature selection however this model can merely maintain a maximal dependency function it does not fit a given dataset well and cannot ideally describe the differences in sample classification therefore in this study we introduce a new model for handling this problem first we define the fuzzy decision of a sample using the concept of fuzzy neighborhood then a parameterized fuzzy relation is introduced to characterize the fuzzy information granules using which the fuzzy lower and upper approximations of a decision are reconstructed and a new fuzzy rough set model is introduced this can guarantee that the membership degree of a sample to its own category reaches the maximal value furthermore this approach can fit a given dataset and effectively prevents samples from being misclassified finally we define the significance measure of a candidate attribute and design a greedy forward algorithm for feature selection twelve datasets selected from public data sources are used to compare the proposed algorithm with certain existing algorithms and the experimental results show that the proposed reduction algorithm is more effective than classical fuzzy rough sets especially for those datasets for which different categories exhibit a large degree of overlap

efficient and robust feature extraction by maximum margin criterion in pattern recognition feature extraction techniques are widely employed to reduce the dimensionality of data and to enhance the discriminatory information principal component analysis pca and linear discriminant analysis lda are the two most popular linear dimensionality reduction methods however pca is not very effective for the extraction of the most discriminant features and lda is not stable due to the small sample size problem in this paper we propose some new linear and nonlinear feature extractors based on maximum margin criterion mmc geometrically feature extractors based on mmc maximize the average margin between classes after dimensionality reduction it is shown that mmc can represent class separability better than pca as a connection to lda we may also derive lda from mmc by incorporating some constraints by using some other constraints we establish a new linear feature extractor that does not suffer from the small sample size problem which is known to cause serious stability problems for lda the kernelized nonlinear counterpart of this linear feature extractor is also established in the paper our extensive experiments demonstrate that the new feature extractors are effective stable and efficient

a multilevel tabu search algorithm for the feature selection problem in biomedical data the automated analysis of patients biomedical data can be used to derive diagnostic and prognostic inferences about the observed patients many noninvasive techniques for acquiring biomedical samples generate data that are characterized by a large number of distinct attributes i e features and a small number of observed patients i e samples using these biomedical data to derive reliable inferences such as classifying a given patient as either cancerous or noncancerous requires that the ratio r of the number of samples to the number of features be within the range 5

u curve a branch and bound optimization algorithm for u shaped cost functions on boolean lattices applied to the feature selection problem this paper presents the formulation of a combinatorial optimization problem with the following characteristics i the search space is the power set of a finite set structured as a boolean lattice ii the cost function forms a u shaped curve when applied to any lattice chain this formulation applies for feature selection in the context of pattern recognition the known approaches for this problem are branch and bound algorithms and heuristics that explore partially the search space branch and bound algorithms are equivalent to the full search while heuristics are not this paper presents a branch and bound algorithm that differs from the others known by exploring the lattice structure and the u shaped chain curves of the search space the main contribution of this paper is the architecture of this algorithm that is based on the representation and exploration of the search space by new lattice properties proven here several experiments with well known public data indicate the superiority of the proposed method to the sequential floating forward selection sffs which is a popular heuristic that gives good results in very short computational time in all experiments the proposed method got better or equal results in similar or even smaller computational time

compromise solution by mcdm methods a comparative analysis of vikor and topsis the multiple criteria decision making mcdm methods vikor and topsis are based on an aggregating function representing closeness to the ideal which originated in the compromise programming method in vikor linear normalization and in topsis vector normalization is used to eliminate the units of criterion functions the vikor method of compromise ranking determines a compromise solution providing a maximum group utility for the majority and a minimum of an individual regret for the opponent the topsis method determines a solution with the shortest distance to the ideal solution and the greatest distance from the negative ideal solution but it does not consider the relative importance of these distances a comparative analysis of these two methods is illustrated with a numerical example showing their similarity and some differences 2003 elsevier b v all rights reserved

evidential reasoning rule for evidence combination this paper aims to establish a unique evidential reasoning er rule to combine multiple pieces of independent evidence conjunctively with weights and reliabilities the novel concept of weighted belief distribution wbd is proposed and extended to wbd with reliability wbdr to characterise evidence in complement of belief distribution bd introduced in dempster shafer d s theory of evidence the implementation of the orthogonal sum operation on wbds and wbdrs leads to the establishment of the new er rule the most important property of the new er rule is that it constitutes a generic conjunctive probabilistic reasoning process or a generalised bayesian inference process it is shown that the original er algorithm is a special case of the er rule when the reliability of evidence is equal to its weight and the weights of all pieces of evidence are normalised it is proven that email protected s rule is also a special case of the er rule when each piece of evidence is fully reliable the er rule completes and enhances email protected s rule by identifying how to combine pieces of fully reliable evidence that are highly or completely conflicting through a new reliability perturbation analysis the main properties of the er rule are explored to facilitate its applications several existing rules are discussed and compared with the er rule numerical and simulation studies are conducted to show the features of the er rule

the transferable belief model abstract we describe the transferable belief model a model for representing quantified beliefs based on belief functions beliefs can be held at two levels 1 a credal level where beliefs are entertained and quantified by belief functions 2 a pignistic level where beliefs can be used to make decisions and are quantified by probability functions the relation between the belief function and the probability function when decisions must be made is derived and justified four paradigms are analyzed in order to compare bayesian upper and lower probability and the transferable belief approaches

fuzzy measures and integrals in evaluation of strategies artificial intelligence ai techniques have been applied to games for a long time in this paper we will explore the use of fuzzy measures and integrals to evaluate strategies in games we will show their use in decision making when modeling auctions the paper describes the role of fuzzy measures and integrals in decision making and reviews some computational aspects which are important for building real applications

a method to improve integer linear programming problem with branch and bound procedure abstract integer linear programming ilp problems are harder to solve than linear programming lp problems it doesn t work if try to round off the results of lp problems and claim they are the optimum solution the branch and bound b b is the popular method to solve ilp problems in this paper we propose a revised b b which is demonstrated to be more efficient most of time this method is extraordinarily useful when facing ilp problems with large differences between constraints and variables it could reduce the number of constraint and work efficiently when handling ilp problems with many constraints and less variables even if the ilp problems have fewer constraints but many variables we suggest using duality concept to interchange variables with constraints then the revised b b could be used to compute results very quickly

a real coded genetic algorithm for solving integer and mixed integer optimization problems in this paper a real coded genetic algorithm named mi lxpm is proposed for solving integer and mixed integer constrained optimization problems the proposed algorithm is a suitably modified and extended version of the real coded genetic algorithm lxpm of deep and thakur k deep m thakur a new crossover operator for real coded genetic algorithms applied mathematics and computation 188 2007 895 912 k deep m thakur a new mutation operator for real coded genetic algorithms applied mathematics and computation 193 2007 211 230 the algorithm incorporates a special truncation procedure to handle integer restrictions on decision variables along with a parameter free penalty approach for handling constraints performance of the algorithm is tested on a set of twenty test problems selected from different sources in literature and compared with the performance of an earlier application of genetic algorithm and also with random search based algorithm rst2anu incorporating annealing concept the proposed mi lxpm outperforms both the algorithms in most of the cases which are considered

feature selection for monotonic classification monotonic classification is a kind of special task in machine learning and pattern recognition monotonicity constraints between features and decision should be taken into account in these tasks however most existing techniques are not able to discover and represent the ordinal structures in monotonic datasets thus they are inapplicable to monotonic classification feature selection has been proven effective in improving classification performance and avoiding overfitting to the best of our knowledge no technique has been specially designed to select features in monotonic classification until now in this paper we introduce a function which is called rank mutual information to evaluate monotonic consistency between features and decision in monotonic tasks this function combines the advantages of dominance rough sets in reflecting ordinal structures and mutual information in terms of robustness then rank mutual information is integrated with the search strategy of min redundancy and max relevance to compute optimal subsets of features a collection of numerical experiments are given to show the effectiveness of the proposed technique

semi supervised local multi manifold isomap by linear embedding for feature extraction we explore the discriminative feature extraction problem a semisupervised local multimanifold isomap by linear embedding is proposed our model can use labeled and unlabeled data to deliver manifold features our model aims to minimize pairwise intraclass distances in the same manifold our model aims to maximize the distances between different manifolds in this paper we mainly propose a semi supervised local multi manifold isomap learning framework by linear embedding termed ssmm isomap that can apply the labeled and unlabeled training samples to perform the joint learning of neighborhood preserving local nonlinear manifold features and a linear feature extractor the formulation of ssmm isomap aims at minimizing pairwise distances of intra class points in the same manifold and maximizing the distances over different manifolds to enhance the performance of nonlinear manifold feature learning we also incorporate the neighborhood reconstruction error to preserve local topology structures between both labeled and unlabeled samples to enable our ssmm isomap to extract local manifold features from the outside new data we also add a feature approximation error that correlates manifold features with embedded features by the jointly learnt feature extractor thus the learnt linear extractor can extract the local manifold features from the new data efficiently by direct embedding to optimize the proposed objective function two effective schemes are presented i e scaling by majorizing a complicated function and eigen decomposition notice that the comparison of the proposed two solvers is also described we mainly evaluate ssmm isomap for manifold feature learning data clustering and classification extensive simulation results verify the effectiveness of our ssmm isomap algorithm compared with other related feature learning techniques

method of multi criteria group decision making based on cloud aggregation operators with linguistic information abstract the cloud model which can synthetically describe the randomness and fuzziness of qualitative concepts and implement uncertain transformations between a qualitative concept and its quantitative instantiations has attracted considerable attention from researchers studying multi criteria group decision making problems involving linguistic information in this paper some operations of clouds and several new aggregation operators are proposed these include the cloud weighted arithmetic averaging cwaa operator cloud ordered weighted arithmetic averaging cowa operator and cloud hybrid arithmetic cha operator the conversion between linguistic variables and clouds is introduced based on this conversion a linguistic multi criteria group decision making method is developed in this method linguistic variables are first converted into clouds and then aggregated using cloud aggregation operators the proposed method is then compared to the existing methods to confirm its feasibility and rationality

kernel quadratic discriminant analysis for small sample size problem it is generally believed that quadratic discriminant analysis qda can better fit the data in practical pattern recognition applications compared to linear discriminant analysis lda method this is due to the fact that qda relaxes the assumption made by lda based methods that the covariance matrix for each class is identical however it still assumes that the class conditional distribution is gaussian which is usually not the case in many real world applications in this paper a novel kernel based qda method is proposed to further relax the gaussian assumption by using the kernel machine technique the proposed method solves the complex pattern recognition problem by combining the qda solution and the kernel machine technique and at the same time tackles the so called small sample size problem through a regularized estimation of the covariance matrix extensive experimental results indicate that the proposed method is a more sophisticated solution outperforming many traditional kernel based learning algorithms

clustering ensembles models of consensus and weak partitions clustering ensembles have emerged as a powerful method for improving both the robustness as well as the stability of unsupervised classification solutions however finding a consensus clustering from multiple partitions is a difficult problem that can be approached from graph based combinatorial or statistical perspectives this study extends previous research on clustering ensembles in several respects first we introduce a unified representation for multiple clusterings and formulate the corresponding categorical clustering problem second we propose a probabilistic model of consensus using a finite mixture of multinomial distributions in a space of clusterings a combined partition is found as a solution to the corresponding maximum likelihood problem using the em algorithm third we define a new consensus function that is related to the classical intraclass variance criterion using the generalized mutual information definition finally we demonstrate the efficacy of combining partitions generated by weak clustering algorithms that use data projections and random data splits a simple explanatory model is offered for the behavior of combinations of such weak clustering components combination accuracy is analyzed as a function of several parameters that control the power and resolution of component partitions as well as the number of partitions we also analyze clustering ensembles with incomplete information and the effect of missing cluster labels on the quality of overall consensus experimental results demonstrate the effectiveness of the proposed methods on several real world data sets

exploring the boundary region of tolerance rough sets for feature selection of all of the challenges which face the effective application of computational intelligence technologies for pattern recognition dataset dimensionality is undoubtedly one of the primary impediments in order for pattern classifiers to be efficient a dimensionality reduction stage is usually performed prior to classification much use has been made of rough set theory for this purpose as it is completely data driven and no other information is required most other methods require some additional knowledge however traditional rough set based methods in the literature are restricted to the requirement that all data must be discrete it is therefore not possible to consider real valued or noisy data this is usually addressed by employing a discretisation method which can result in information loss this paper proposes a new approach based on the tolerance rough set model which has the ability to deal with real valued data whilst simultaneously retaining dataset semantics more significantly this paper describes the underlying mechanism for this new approach to utilise the information contained within the boundary region or region of uncertainty the use of this information can result in the discovery of more compact feature subsets and improved classification accuracy these results are supported by an experimental evaluation which compares the proposed approach with a number of existing feature selection techniques

an evidential classifier based on feature selection and two step classification strategy in this paper we investigate ways to learn efficiently from uncertain data using belief functions in order to extract more knowledge from imperfect and insufficient information and to improve classification accuracy we propose a supervised learning method composed of a feature selection procedure and a two step classification strategy using training information the proposed feature selection procedure automatically determines the most informative feature subset by minimizing an objective function the proposed two step classification strategy further improves the decision making accuracy by using complementary information obtained during the classification process the performance of the proposed method was evaluated on various synthetic and real datasets a comparison with other classification methods is also presented highlightsa classifier is based on belief functions to tackle uncertain data the classifier composed by feature selection and a two step classification a new combination rule to better represent data uncertainty a new feature selection is based on minimizing uncertainty with sparse constraint two step classification improving accuracy of decision making

the basins of attraction in a modified may holling tanner predator prey model with allee affect abstract i analyse a modified may holling tanner predator prey model considering an allee effect in the prey and alternative food sources for predator additionally the predation functional response or predation consumption rate is linear the extended model exhibits rich dynamics and we prove the existence of separatrices in the phase plane separating basins of attraction related to oscillation co existence and extinction of the predator prey population we also show the existence of a homoclinic curve that degenerates to form a limit cycle and discuss numerous potential bifurcations such as saddle node hopf and bogdanov takens bifurcations we use simulations to illustrate the behaviour of the model

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

a fast branch and bound algorithm for u curve feature selection abstract we introduce a fast branch and bound algorithm for optimal feature selection based on a u curve assumption for the cost function the u curve assumption which is based on the peaking phenomenon of the classification error postulates that the cost over the chains of the boolean lattice that represents the search space describes a u shaped curve the proposed algorithm is an improvement over the original algorithm for u curve feature selection introduced recently extensive simulation experiments are carried out to assess the performance of the proposed algorithm iubb comparing it to the original algorithm ubb as well as exhaustive search and generalized sequential forward search the results show that the iubb algorithm makes fewer evaluations and achieves better solutions under a fixed computational budget we also show that the iubb algorithm is robust with respect to violations of the u curve assumption we investigate the application of the iubb algorithm in the design of imaging w operators and in classification feature selection using the average mean conditional entropy mce as the cost function for the search

a discrete particle swarm optimization method for feature selection in binary classification problems abstract this paper investigates the feature subset selection problem for the binary classification problem using logistic regression model we developed a modified discrete particle swarm optimization pso algorithm for the feature subset selection problem this approach embodies an adaptive feature selection procedure which dynamically accounts for the relevance and dependence of the features included the feature subset we compare the proposed methodology with the tabu search and scatter search algorithms using publicly available datasets the results show that the proposed discrete pso algorithm is competitive in terms of both classification accuracy and computational performance