learning from partially supervised data using mixture models and belief functions this paper addresses classification problems in which the class membership of training data are only partially known each learning sample is assumed to consist of a feature vector x email protected x and an imprecise and or uncertain soft label m i defined as a dempster shafer basic belief assignment over the set of classes this framework thus generalizes many kinds of learning problems including supervised unsupervised and semi supervised learning here it is assumed that the feature vectors are generated from a mixture model using the generalized bayesian theorem an extension of bayes theorem in the belief function framework we derive a criterion generalizing the likelihood function a variant of the expectation maximization em algorithm dedicated to the optimization of this criterion is proposed allowing us to compute estimates of model parameters experimental results demonstrate the ability of this approach to exploit partial information about class labels

dissimilarity metric learning in the belief function framework the evidential k nearest neighbor ek nn method provided a global treatment of imperfect knowledge regarding the class membership of training patterns it has outperformed traditional k nn rules in many applications but still shares some of their basic limitations e g 1 classification accuracy depends heavily on how to quantify the dissimilarity between different patterns and 2 no guarantee for satisfactory performance when training patterns contain unreliable imprecise and or uncertain input features in this paper we propose to address these issues by learning a suitable metric using a low dimensional transformation of the input space so as to maximize both the accuracy and efficiency of the ek nn classification to this end a novel loss function to learn the dissimilarity metric is constructed it consists of two terms the first one quantifies the imprecision regarding the class membership of each training pattern while by means of feature selection the second one controls the influence of unreliable input features on the output linear transformation the proposed method has been compared with some other metric learning methods on several synthetic and real datasets it consistently led to comparable performance with regard to testing accuracy and class structure visualization

induction of fuzzy rules and membership functions from training examples abstract most fuzzy controllers and fuzzy expert systems must predefine membership functions and fuzzy inference rules to map numeric data into linguistic variable terms and to make fuzzy reasoning work in this paper we propose a general learning method as a framework for automatically deriving membership functions and fuzzy if then rules from a set of given training examples to rapidly build a prototype fuzzy expert system based on the membership functions and the fuzzy rules derived a corresponding fuzzy inference procedure to process inputs is also developed

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

derived localisation of algebras and modules for any dg algebra a not necessarily commutative and a subset s in h a the homology of a we construct its derived localisation l s a together with a map a l s a well defined in the homotopy category of dg algebras which possesses a universal property similar to that of the ordinary localisation but formulated in homotopy invariant terms even if a is an ordinary ring l s a may have non trivial homology unlike the commutative case the localisation functor does not commute in general with homology but instead there is a spectral sequence relating h l s a and l s h a this spectral sequence collapses when e g s is an ore set or when a is a free ring we prove that l s a could also be regarded as a bousfield localisation of a viewed as a left or right dg module over itself combined with the results of dwyer kan on simplicial localisation this leads to a simple and conceptual proof of the topological group completion theorem further applications include algebraic k theory cyclic and hochschild homology strictification of homotopy unital algebras idempotent ideals the stable homology of various mapping class groups and kontsevich s graph homology

fuzzy control rules and their natural laws abstract we consider the convergence of fuzzy controllers as the number of fuzzy rules tends to infinity we assume that the fuzzy rules are regular and show the existence of limit laws for five different fuzzy control rules

two stage orthogonal least squares methods for neural network construction a number of neural networks can be formulated as the linear in the parameters models training such networks can be transformed to a model selection problem where a compact model is selected from all the candidates using subset selection algorithms forward selection methods are popular fast subset selection approaches however they may only produce suboptimal models and can be trapped into a local minimum more recently a two stage fast recursive algorithm tsfra combining forward selection and backward model refinement has been proposed to improve the compactness and generalization performance of the model this paper proposes unified two stage orthogonal least squares methods instead of the fast recursive based methods in contrast to the tsfra this paper derives a new simplified relationship between the forward and the backward stages to avoid repetitive computations using the inherent orthogonal properties of the least squares methods furthermore a new term exchanging scheme for backward model refinement is introduced to reduce computational demand finally given the error reduction ratio criterion effective and efficient forward and backward subset selection procedures are proposed extensive examples are presented to demonstrate the improved model compactness constructed by the proposed technique in comparison with some popular methods

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

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

decision tree classifiers for evidential attribute values and class labels abstract decision trees are well known machine learning techniques for solving complex classification problems despite their great success the standard decision tree algorithms do not have the ability to process imperfect knowledge meaning uncertain imprecise and incomplete data in this paper we develop new decision tree approaches to cope with data that have uncertain attribute values and class labels more concretely we tackle the case where the uncertainty is represented and managed through the evidence theory

analytic hierarchy process for multi sensor data fusion based on belief function theory abstract multi sensor data fusion is an evolving technology whereby data from multiple sensor inputs are processed and combined the data derived from multiple sensors can however be uncertain imperfect and conflicting the present study is undertaken to help contribute to the continuous search for viable approaches to overcome the problems associated with data conflict and imperfection sensor readings represented by belief functions have to be fused according to their corresponding weights previous studies have often estimated the weights of sensor readings based on a single criterion mono criteria approaches for the assessment of sensor reading weights are however often unreliable and inadequate for the reflection of reality accordingly this work opts for the use of a multi criteria decision aid a modified analytical hierarchy process ahp that incorporates several criteria is proposed to determine the weights of a sensor reading set the approach relies on the automation of pairwise comparisons to eliminate subjectivity and reduce inconsistency it assesses the weight of each sensor reading and fuses the weighed readings obtained using a modified average combination rule the efficiency of this approach is evaluated in a target recognition context several tests sensitivity analysis and comparisons with other approaches available in the literature are described

an efficient constraint handling method for genetic algorithms many real world search and optimization problems involve inequality and or equality constraints and are thus posed as constrained optimization problems in trying to solve constrained optimization problems using genetic algorithms gas or classical optimization methods penalty function methods have been the most popular approach because of their simplicity and ease of implementation however since the penalty function approach is generic and applicable to any type of constraint linear or nonlinear their performance is not always satisfactory thus researchers have developed sophisticated penalty functions specific to the problem at hand and the search algorithm used for optimization however the most difficult aspect of the penalty function approach is to find appropriate penalty parameters needed to guide the search towards the constrained optimum in this paper ga s population based approach and ability to make pair wise comparison in tournament selection operator are exploited to devise a penalty function approach that does not require any penalty parameter careful comparisons among feasible and infeasible solutions are made so as to provide a search direction towards the feasible region once sufficient feasible solutions are found a niching method along with a controlled mutation operator is used to maintain diversity among feasible solutions this allows a real parameter ga s crossover operator to continuously find better feasible solutions gradually leading the search near the true optimum solution gas with this constraint handling approach have been tested on nine problems commonly used in the literature including an engineering design problem in all cases the proposed approach has been able to repeatedly find solutions closer to the true optimum solution than that reported earlier

regularization theory and neural networks architectures we had previously shown that regularization principles lead to approximation schemes that are equivalent to networks with one layer of hidden units called regularization networks in particular s

use of the zero norm with linear models and kernel methods we explore the use of the so called zero norm of the parameters of linear models in learning minimization of such a quantity has many uses in a machine learning context for variable or feature selection minimizing training error and ensuring sparsity in solutions we derive a simple but practical method for achieving these goals and discuss its relationship to existing techniques of minimizing the zero norm the method boils down to implementing a simple modification of vanilla svm namely via an iterative multiplicative rescaling of the training data applications we investigate which aid our discussion include variable and feature selection on biological microarray data and multicategory classification

nested design of fuzzy controllers with partial fuzzy rule base abstract in this paper a systematic nested design approach with a partial fuzzy if then rule base is proposed to reduce the complexity of the fuzzy controllers in the design procedure the fuzzy controller is first constructed with a basic fuzzy rule base when the fuzzy rule base is not sufficient to provide the performance that meets the requirement of the fuzzy control system the fuzzy rule base contains some unsatisfactory fuzzy rules and needs to be adjusted after the unsatisfactory fuzzy rules are identified the fuzzy region controlled by each unsatisfactory fuzzy rule is further partitioned into sub regions based on the nested design procedure the partial fuzzy rule base of the fuzzy controller is modified by replacing each unsatisfactory fuzzy rule with new fuzzy rules for the corresponding sub regions each fuzzy region of the input space can be partitioned independently into fuzzy sub regions to avoid generating the redundant rules the parameters in the fuzzy mechanism are tuned by minimizing a cost function simulations are carried out to show the effectiveness of the fuzzy controllers with nested fuzzy if then rules

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

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

fuzzy flip flop and fuzzy registers abstract the concept of fuzzy flip flop has already been proposed two types of characteristic equations that are set type and reset type of fuzzy flip flop have been introduced as an extended form of that of binary j k flip flop using the concepts of fuzzy negation t norm and s norm operations the aim of this article is to present the hardware implementation of a fuzzy flip flop fuzzy negation t norm and s norm are restricted to complementation min max respectively for the sake of practical use fundamental properties of fuzzy flip flop based on complementation min and max operations are mentioned first then its characteristics are graphically shown through computer simulation experimental results of a min max type fuzzy flip flop circuit in voltage mode are presented finally an idea of a fuzzy shift register which can store and shift the membership function information defined on a finite universe of discourse is presented

conditional belief functions as lower envelopes of conditional probabilities in a finite setting the aim is to provide a characterization of full conditional measures on a finite boolean algebra obtained as lower envelope of the extensions of a full conditional probability defined on another finite boolean algebra such conditional measures are conditional belief functions defined by means of a generalized bayesian conditioning rule relying on a linearly ordered class of belief functions this notion of bayesian conditioning for belief functions is compared with other well known conditioning rules by looking for those conditional measures that can be seen as lower conditional probabilities

extracting fuzzy rules for system modeling using a hybrid of genetic algorithms and kalman filter abstract this paper proposes a hybrid algorithm for extracting important fuzzy rules from a given rule base to construct a parsimonious fuzzy model with a high generalization ability this algorithm combines the advantages of genetic algorithms strong search capacity and kalman filter s fast convergence merit each random combination of the rules in the rule base is coded into a binary string and treated as a chromosome in genetic algorithms the binary string indicates the structure of a fuzzy model the parameters of the model are then estimated using the kalman filter in order to achieve a trade off between the accuracy and the complexity of a fuzzy model the schwarz rissanen criterion is used as an evaluation function in the hybrid algorithm the practical applicability of the proposed algorithm is examined by computer simulations on a human operator modeling problem and a nonlinear system modeling problem

dynamic estimation of the discernment frame in belief function theory classification or estimation problems deal with decisions among different hypotheses in several applications the set of hypotheses may evolve with time and or with context then this work focuses on the problem of dynamic estimation and update of the discernment frame in the framework of belief function theory belief function theory is widely used in decision systems because of its ability to model both the imprecision and the uncertainty now the problem of the discernment frame estimation is even more critical as the set of handled hypotheses is the power set of the discernment frame this study describes a solution to update and adjust the discernment frame in a sequential way as new sources provide new pieces of information besides incompleteness it is assumed that the current discernment frame may contain duplicated or spurious hypotheses we thus propose new update mechanisms and we show on a practical application namely video surveillance how these mechanisms may be applied

fuzzy controller theory limit theorems for linear fuzzy control rules abstract for a general fuzzy controller employing linear fuzzy control rules it is shown that as the number of rules grow the defuzzified output becomes a linear function of the input in particular for a sufficiently large number of rules the defuzzified output is approximately the same as the pi pid controller

tuning fuzzy logic controllers using response envelope method a fuzzy logic controller flc is designed based on a human expert s knowledge of the process the performance of this initial design attempt will in general not be satisfactory in terms of certain design criteria such as steady state error the oscillatory behavior of the system etc this is due to the fact that no standard method exists for transforming human knowledge or experience into the rule base of the flc in this paper a method to tune the rule base of an initial flc design attempt is presented results of four experiments are reported and discussed

feature selection via coalitional game theory we present and study the contribution selection algorithm csa a novel algorithm for feature selection the algorithm is based on the multiperturbation shapley analysis msa a framework that relies on game theory to estimate usefulness the algorithm iteratively estimates the usefulness of features and selects them accordingly using either forward selection or backward elimination it can optimize various performance measures over unseen data such as accuracy balanced error rate and area under receiver operator characteristic curve empirical comparison with several other existing feature selection methods shows that the backward elimination variant of csa leads to the most accurate classification results on an array of data sets

fsmrank feature selection algorithm for learning to rank in recent years there has been growing interest in learning to rank the introduction of feature selection into different learning problems has been proven effective these facts motivate us to investigate the problem of feature selection for learning to rank we propose a joint convex optimization formulation which minimizes ranking errors while simultaneously conducting feature selection this optimization formulation provides a flexible framework in which we can easily incorporate various importance measures and similarity measures of the features to solve this optimization problem we use the nesterov s approach to derive an accelerated gradient algorithm with a fast convergence rate o 1 t2 we further develop a generalization bound for the proposed optimization problem using the rademacher complexities extensive experimental evaluations are conducted on the public letor benchmark datasets the results demonstrate that the proposed method shows 1 significant ranking performance gain compared to several feature selection baselines for ranking and 2 very competitive performance compared to several state of the art learning to rank algorithms

a parameterized fuzzy processor and its applications abstract in this paper a parameterized fuzzy processor pfp is presented based on a designed fuzzy instruction set of the parameterized fuzzy number pfn this pfn is presented by some parameters of the universe of the discourse instead of a series of the membership grades the algorithms of these instructions are based on the parameter operations to implement the fuzzy arithmetics and the fuzzy reasoning methods the instruction set supports the versatility of the fuzzy information e g fuzzy arithmetic operations inference operations fuzzy logic operations data translations and data exchangements based upon these the characteristics of the pfn are discussed and the architecture of the pfp outlined is constructed in this paper and its processing time is saved due to the adaptation of the parameterized fuzzy number pfn to evaluate the performance of pfn instructions and pfp structure two experiments are presented one is the speed performance evaluated for the pfn to compare with the discrete fuzzy number dfn the other is the confirmation of the feasibility and the capability of the instructions which is demonstrated by three examples relateld to human inference intuitive control and decision making

stability of the homology of the mapping class groups of orientable surfaces the mapping class group of f fgs r is f rgs wo a where a is the topological group of orientation preserving diffeomorphisms of f which are the identity on df and fix the s punctures when r 0 and 2g s 3 an important feature of f is that it acts properly discontinuously on the teichmiller space us the quotient is the moduli space f of isometry classes of complete hyperbolic metrics of finite area on f since us is homeomorphic to euclidean space and f is virtually torsion free we have

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

lindley s paradox 1982 lindley s paradox journal of the american statistical association vol 77 no 378 pp 325 334

modeling vague beliefs using fuzzy valued belief structures abstract this paper presents a rational approach to the representation and manipulation of imprecise degrees of belief in the framework of evidence theory we adopt as a starting point the non probabilistic interpretation of belief functions provided by smets transferable belief model as well as previous generalizations of evidence theory allowing to deal with fuzzy propositions we then introduce the concepts of interval valued and fuzzy valued belief structures defined respectively as crisp and fuzzy sets of belief structures verifying hard or elastic constraints we then proceed with a generalization of various concepts of dempster shafer theory including those of belief and plausibility functions combination rules and normalization procedures most calculations implied by the manipulation of these concepts are based on simple forms of linear programming problems for which analytical solutions exist making the whole scheme computationally tractable we discuss the application of this framework in the areas of decision making under uncertainty and classification of fuzzy data

finding relevant attributes and membership functions fuzzy systems that automatically derive fuzzy if then rules from numeric data have been developed most have to predefine membership functions in order to learn hong and lee proposed a general learning method that automatically derives fuzzy if then rules and membership functions from a set of given training examples using a decision table all available attributes were included in the decision table and the initial membership functions for each attribute were built according to the predefined smallest unit although hong and lee s method accurately derives the fuzzy if then rules and final membership functions the decision table and the initial membership functions are complex if there are many attributes or if the predefined unit is small we improve hong and lee s method by first selecting relevant attributes and building appropriate initial membership functions these attributes and membership functions are then used in a decision table to derive final fuzzy if then rules and membership functions experimental results on iris data show that the proposed method effectively induces membership functions and fuzzy if then rules

pid type fuzzy controller and parameters adaptive method abstract the authors of this paper try to analyze the dynamic behavior of the product sum crisp type fuzzy controller revealing that this type of fuzzy controller behaves approximately like a pd controller that may yield steady state error for the control system by relating to the conventional pid control theory we propose a new fuzzy controller structure namely pid type fuzzy controller which retains the characteristics similar to the conventional pid controller in order to improve further the performance of the fuzzy controller we work out a method to tune the parameters of the pid type fuzzy controller on line producing a parameter adaptive fuzzy controller simulation experiments are made to demonstrate the fine performance of these novel fuzzy controller structures

the homotopy theory of dg categories and derived morita theory the main purpose of this work is to study the homotopy theory of dg categories up to quasi equivalences our main result is a description of the mapping spaces between two dg categories c and d in terms of the nerve of a certain category of c d bimodules we also prove that the homotopy category ho dg cat possesses internal hom s relative to the derived tensor product of dg categories we use these two results in order to prove a derived version of morita theory describing the morphisms between dg categories of modules over two dg categories c and d as the dg category of c d bi modules finally we give three applications of our results the first one expresses hochschild cohomology as endomorphisms of the identity functor as well as higher homotopy groups of the classifying space of dg categories i e the nerve of the category of dg categories and quasi equivalences between them the second application is the existence of a good theory of localization for dg categories defined in terms of a natural universal property our last application states that the dg category of continuous morphisms between the dg categories of quasi coherent resp perfect complexes on two schemes resp smooth and proper schemes is quasi equivalent to the dg category of quasi coherent resp perfect complexes on their product

a recursive rule base adjustment algorithm for a fuzzy logic controller this paper introduces a recursive rule base adjustment to enhance the performance of fuzzy logic controllers here the fuzzy controller is constructed on the basis of a decision table dt relying on membership functions and fuzzy rules that incorporate heuristic knowledge and operator experience if the controller performance is not satisfactory it has previously been suggested that the rule base be altered by combined tuning of membership functions and controller scaling factors the alternative approach proposed here entails alteration of the fuzzy rule base the recursive rule base adjustment algorithm proposed in this paper has the benefit that it is computationally more efficient for the generation of a dt and advantage for online realization simulation results are presented to support this thesis

shape from silhouette using dempster shafer theory this work proposes a novel shape from silhouette sfs algorithm using the dempster shafer ds theory for dealing with inconsistent silhouettes standard sfs methods makes assumptions about consistency in the silhouettes employed however total consistency hardly ever happens in realistic scenarios because of inaccuracies in the background subtraction or occlusions thus leading to poor reconstruction outside of controlled environments our method classify voxels using the ds theory instead of the traditional intersection of all visual cones sensors reliability is modelled taking into account the positional relationships between camera pairs and voxels this information is employed to determine the degree in which a voxel belongs to a foreground object finally evidences collected from all sensors are fused to choose the best hypothesis that determines the voxel state experiments performed with synthetic and real data show that our proposal outperforms the traditional sfs method and other techniques specifically designed to deal with inconsistencies in addition our method includes a parameter for adjusting the precision of the reconstructions so that it could be adapted to the application requirements

processing individual fuzzy attributes for fuzzy rule induction fuzzy systems that can automatically derive fuzzy if then rules and membership functions from numeric data have recently been developed in this paper we propose two new fuzzy learning methods for automatically deriving membership functions and fuzzy if then rules from a set of given training examples the proposed methods first select relevant attributes and build appropriate initial membership functions they then simplify the intervals and the membership functions of each attribute before forming a decision table these attributes and membership functions are then used in a decision table to derive the final fuzzy if then rules and membership functions experimental results for the iris data show that our methods can achieve a high degree of accuracy the proposed methods are thus useful in constructing membership functions and in managing uncertainty and vagueness they can also reduce the time and effort needed to develop a fuzzy knowledge base

additive logistic regression a statistical view of boosting boosting is one of the most important recent developments in classification methodology boosting works by sequentially applying a classification algorithm to reweighted versions of the training data and then taking a weighted majority vote of the sequence of classifiers thus produced for many classification algorithms this simple strategy results in dramatic improvements in performance we show that this seemingly mysterious phenomenon can be understood in terms of well known statistical principles namely additive modeling and maximum likelihood for the two class problem boosting can be viewed as an approximation to additive modeling on the logistic scale using maximum bernoulli likelihood as a criterion we develop more direct approximations and show that they exhibit nearly identical results to boosting direct multiclass generalizations based on multinomial likelihood are derived that exhibit performance comparable to other recently proposed multiclass generalizations of boosting in most situations and far superior in some we suggest a minor modification to boosting that can reduce computation often by factors of 10 to 50 finally we apply these insights to produce an alternative formulation of boosting decision trees this approach based on best first truncated tree induction often leads to better performance and can provide interpretable descriptions of the aggregate decision rule it is also much faster computationally making it more suitable to large scale data mining applications

ecmdd evidential c medoids clustering with multiple prototypes in this work a new prototype based clustering method named evidential c medoids ecmdd which belongs to the family of medoid based clustering for proximity data is proposed as an extension of fuzzy c medoids fcmdd on the theoretical framework of belief functions in the application of fcmdd and original ecmdd a single medoid prototype which is supposed to belong to the object set is utilized to represent one class for the sake of clarity this kind of ecmdd using a single medoid is denoted by secmdd in real clustering applications using only one pattern to capture or interpret a class may not adequately model different types of group structure and hence limits the clustering performance in order to address this problem a variation of ecmdd using multiple weighted medoids denoted by wecmdd is presented unlike secmdd in wecmdd objects in each cluster carry various weights describing their degree of representativeness for that class this mechanism enables each class to be represented by more than one object experimental results in synthetic and real data sets clearly demonstrate the superiority of secmdd and wecmdd moreover the clustering results by wecmdd can provide richer information for the inner structure of the detected classes with the help of prototype weights

algebras and modules in monoidal model categories in recent years the theory of structured ring spectra formerly known as a infty and e infty ring spectra has been simplified by the discovery of categories of spectra with strictly associative and commutative smash products now a ring spectrum can simply be defined as a monoid with respect to the smash product in one of these new categories of spectra in this paper we provide a general method for constructing model category structures for categories of ring algebra and module spectra this provides the necessary input for obtaining model categories of symmetric ring spectra functors with smash product gamma rings and diagram ring spectra algebraic examples to which our methods apply include the stable module category over the group algebra of a finite group and unbounded chain complexes over a differential graded algebra 1991 mathematics subject classification primary 55u35 secondary 18d10

complete modules and torsion modules suppose that r is a ring and that a is a chain complex over r inside the derived category of differential graded a modules there are naturally defined subcategories of a torsion objects and of a complete objects under a finiteness condition on a we develop a morita theory for these subcat egories find conceptual interpretations for some associated algebraic functors and in appropriate commutative situations identify the associated functors as local homology or local cohomology some of the results are suprising even in the case r z and a z p 1 introduction let r be a ring and r mod the derived category of chain complexes of left modules see section 1 2 we choose a fixed complex a which is perfect in other words isomorphic in mod to a complex of finite length in which the entries are finitely generated projective modules we de clare another complex n to be a trivial if hom a a0 0 where hom denotes the chain complex of morphisms in r mod going further we say that x is a torsion if hom x at 0 for all a trivial n9 and that x is a complete if homr n9x 0 for all a trivial n we then study the category ators of a torsion complexes and the category acomp of a complete complexes both of these are triangulated full subcategories of r mod it turns out that these categories are equivalent to one another and also equivalent to the derived category of dif ferential graded modules over the endomorphism complex of a we construct approximation functors celu r mod at0rs and a r mod acomp for an object m of r mod9 the complex celu m is a kind of a cellular approxi mation to m in the sense that it is the best approximation to m which can be cobbled together from a and its suspensions the complex ma is the bousfield localization of m with respect to a homology theory on r mod derived from a we provide algebraic formulas for the functors and find that the functors are related in interesting ways one of which involves an arithmetic square we also show that if cciia r has certain finite dimensionality properties then an object m of r mod is a torsion or a complete if and only if the homology groups 77 m individually satisfy appropriate torsion or completeness conditions suppose now that r is a commutative ring that 7 c r is a finitely generated ideal that a r i9 and that k is the associated koszul complex the complex a

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

adaptive imputation of missing values for incomplete pattern classification in classification of incomplete pattern the missing values can either play a crucial role in the class determination or have only little influence or eventually none on the classification results according to the context we propose a credal classification method for incomplete pattern with adaptive imputation of missing values based on belief function theory at first we try to classify the object incomplete pattern based only on the available attribute values as underlying principle we assume that the missing information is not crucial for the classification if a specific class for the object can be found using only the available information in this case the object is committed to this particular class however if the object cannot be classified without ambiguity it means that the missing values play a main role for achieving an accurate classification in this case the missing values will be imputed based on the k nearest neighbor k nn and self organizing map som techniques and the edited pattern with the imputation is then classified the original or edited pattern is classified according to each training class and the classification results represented by basic belief assignments are fused with proper combination rules for making the credal classification the object is allowed to belong with different masses of belief to the specific classes and meta classes which are particular disjunctions of several single classes the credal classification captures well the uncertainty and imprecision of classification and reduces effectively the rate of misclassifications thanks to the introduction of meta classes the effectiveness of the proposed method with respect to other classical methods is demonstrated based on several experiments using artificial and real data sets highlightsmissing values are adaptively imputed in classification according to context som and k nn are used for the imputation with admissible computation burden ensemble classifier is introduced for credal classification the imprecision of classification can be well captured using belief functions the proposed method has been tested by artificial and real data sets

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

computational complexity of general fuzzy logic control and its simplification for a loop controller this paper analyzes the number of operations and parameters of general fuzzy logic control algorithms and limitations of loop controllers to implement the fuzzy logic control are investigated in terms of computation time and required memory using analysis of general fuzzy logic control algorithms it is shown that general fuzzy logic control algorithms are not suitable for loop controllers a simplified fuzzy logic control for loop controllers is presented using a fixed control table with mapping parameters this simplified fuzzy logic control is shown to be suitable for a loop controller with regard to the computation time and the required memory for easy programming of the simplified fuzzy logic control a fuzzy logic control block is suggested as a specific block for general graphical block diagram editors experiments show that the simplified fuzzy logic control overcomes the limitations of loop controllers and provides good performance

generalized jeffrey s rule of conditioning and evidence combining rule for a priori probabilistic knowledge in conditional evidence theory in bayesian probabilistic approach for uncertain reasoning one basic assumption is that a priori knowledge about the uncertain variable is modeled by a probability distribution when new evidence representable by a constant set is available the bayesian conditioning is used to update a priori knowledge in the conventional d s evidence theory all bodies of evidence about the uncertain variable are imprecise and uncertain all bodies of evidence are combined by so called dempster s rule of combination to achieve a combined body of evidence without considering a priori knowledge from our point of view when identifying the true value of an uncertain variable bayesian approach and evidence theory can cooperate to deal with uncertain reasoning firstly all imprecise and uncertain bodies of evidence about the uncertain variable are fused to achieve a combined evidence based on a priori knowledge then the a posteriori probability distribution is achieved from a priori probability distribution by conditioning on the combined evidence in this paper we firstly deal with the knowledge updating problem where a priori knowledge is represented by a probability distribution and new evidence is represented by a random set then we review the conditional evidence theory which resolves the knowledge combining problem based on a priori probabilistic knowledge finally we discuss the close relationship between knowledge updating procedure and knowledge combining procedure presented in this paper we show that a posteriori probability conditioned on fused body of evidence satisfies the bayesian parallel combination rule

the combination of multiple classifiers using an evidential reasoning approach in many domains when we have several competing classifiers available we want to synthesize them or some of them to get a more accurate classifier by a combination function in this paper we propose a class indifferent method for combining classifier decisions represented by evidential structures called triplet and quartet using dempster s rule of combination this method is unique in that it distinguishes important elements from the trivial ones in representing classifier decisions makes use of more information than others in calculating the support for class labels and provides a practical way to apply the theoretically appealing dempster shafer theory of evidence to the problem of ensemble learning we present a formalism for modelling classifier decisions as triplet mass functions and we establish a range of formulae for combining these mass functions in order to arrive at a consensus decision in addition we carry out a comparative study with the alternatives of simplet and dichotomous structure and also compare two combination methods dempster s rule and majority voting over the uci benchmark data to demonstrate the advantage our approach offers

medical diagnosis fuzzy sets and degrees of belief abstract a model simulating the medical diagnostic process is presented diagnostic groups are considered as fuzzy sets partial knowledge is quantified by belief functions the process is considered as the evaluation by the clinician of his degree of belief concerning the belonging of his patient to a fuzzy set given fuzzy and partial informations

representation and fusion of heterogeneous fuzzy information in the 3d space for model based structural recognition application to 3d brain imaging we present a novel approach to model based pattern recognition where structural information and spatial relationships have a most important role it is illustrated in the domain of 3d brain structure recognition using an anatomical atlas our approach performs segmentation and recognition of the scene simultaneously the solution of the recognition task is progressive processing successively different objects and using different pieces of knowledge about the object and about relationships between objects therefore the core of the approach is the knowledge representation part and constitutes the main contribution of this paper we make use of a spatial representation of each piece of information as a spatial fuzzy set representing a constraint to be satisfied by the searched object thanks in particular to fuzzy mathematical morphology operations fusion of these constraints allows us to select segment and recognize the desired object

k order additive discrete fuzzy measures and their representation abstract in order to face with the complexity of discrete fuzzy measures we propose the concept of k orderadditive fuzzy measure including usual additive measures and fuzzy measures every discrete fuzzy measure is a k order additive fuzzy measure for a unique k a related topic of the paper is to introduce an alternative representation of fuzzy measures called the interaction representation which sets and extends in a common framework the shapley value and the interaction index proposed by murofushi and soneda

a self tuning fuzzy controller abstract the aim of a fuzzy controller is to compensate the dynamic characteristics of the controlled system it is the same purpose as for the fuzzy logic controller flc now the best design of the flc is required for achievement of this purpose but such a controller has not yet been completely designed because the fuzzy controller is constructed of control rules which are ambiguously described by conventional controller strategies and expert knowledge and because its structure theory is not well established yet that is in order to construct the best rules a highly skilled technique and a tuning technique using trial and error are required as a way to easily design a flc a method which improves a given standard flc is considered in this paper we propose a self tuning algorithm of the flc it has two functions in adjusting the scaling factors which are the parameters of the flc and in improving the control rules of flc by evaluating the control response at real time and the control results after operations we add these functions to the flc and design the self tuning fuzzy controller stfc this makes the flc a good controller

conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence dempster s rule plays a central role in the theory of belief functions however it assumes the combined bodies of evidence to be distinct an assumption which is not always verified in practice in this paper a new operator the cautious rule of combination is introduced this operator is commutative associative and idempotent this latter property makes it suitable to combine belief functions induced by reliable but possibly overlapping bodies of evidence a dual operator the bold disjunctive rule is also introduced this operator is also commutative associative and idempotent and can be used to combine belief functions issues from possibly overlapping and unreliable sources finally the cautious and bold rules are shown to be particular members of infinite families of conjunctive and disjunctive combination rules based on triangular norms and conorms

the stable moduli space of riemann surfaces mumford s conjecture d mumford conjectured in 30 that the rational cohomology of the stable moduli space of riemann surfaces is a polynomial algebra generated by certain classes i of di mension 2i for the purpose of calculating rational cohomology one may replace the stable moduli space of riemann surfaces by b 1 where 1 is the group of isotopy classes of automorphisms of a smooth oriented connected surface of large genus tillmann s insight 41 that the plus construction makes b 1 into an infinite loop space led to a stable homo topy version of mumford s conjecture stronger than the original 22 we prove the stronger version relying on harer s stability theorem 15 vassiliev s theorem concerning spaces of functions with moderate singularities 43 42 and methods from homotopy theory

switching based filter based on dempster s combination rule for image processing in this work a two pass switching rank ordered arithmetic mean tsram filter that preserves image details while effectively suppressing impulse noise is proposed to improve the performance of switching based median filters the proposed filter mechanism includes an efficient impulse detector based on the dempster shafer d s evidence theory and a rank ordered arithmetic mean filter that works by estimating the noise free ordered mean values excluding the current pixel a modified dempster s combination rule is applied to the impulse detector to improve filtering performance a simple switching median filter is included to perform second pass filtering experimental results show that the proposed filter outperforms many well accepted switching based median filters in terms of both noise suppression and detail preservation providing excellent robustness at various percentages of impulse noise

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

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

a pd like self tuning fuzzy controller without steady state error abstract this paper presents a pd like self tuning fuzzy controller stfc based on the tuning of scaling factors a two stage tuning method including a direct tuning stage and indirect tuning stage is proposed for most linear controlled plants application of the direct tuning stage alone is enough to yield satisfactory system responses the proposed stfc can automatically detect the operating ranges of input variables and then adjust the scaling factors in the indirect tuning stage the back propagation algorithm can be directly applied to fine tune the scaling factors when a more complicated plant is controlled furthermore a simple but efficient method for fully compensating for steady state error which is the main problem in a pd like fuzzy logic control system is proposed so that tuning for fuzzy logic rule bases is unnecessary simulation results with linear time invariant systems and a nonlinear unstable system as the controlled plants show that the proposed technique yields zero steady state error responses very quickly without overshoot or oscillatory behavior

evaluating and comparing soft partitions an approach based on dempster shafer theory in evidential clustering cluster membership uncertainty is represented by dempster shafer mass functions the notion of evidential partition generalizes other soft clustering structures such as fuzzy possibilistic or rough partitions in this paper we propose two extensions of the rand index for evaluating and comparing evidential partitions called similarity and consistency indices the similarity index is suitable for measuring the closeness of two soft partitions whereas the consistency index allows one to assess the agreement or lack of conflict between a soft partition and the true hard partition simulation experiments illustrate some applications of these indices

representation and use of imprecise temporal knowledge in dynamic systems abstract in this paper the importance of representation and use of imprecise temporal knowledge for problem solving in industrial dynamic systems is emphasized first a representation of imprecise temporal knowledge is then given for describing the dynamic behavior of systems a novel problem on on line temporal matching and numeric matching is presented and a method for solving this problem is proposed a method for fuzzy proposition reasoning and temporal reasoning is put forward finally as two application examples the fault diagnosis of a fluidized catalytic cracking unit is taken up to illustrate the usefulness of the proposed knowledge representation and methods

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

ecm an evidential version of the fuzzy c means algorithm a new clustering method for object data called ecm evidential c means is introduced in the theoretical framework of belief functions it is based on the concept of credal partition extending those of hard fuzzy and possibilistic ones to derive such a structure a suitable objective function is minimized using an fcm like algorithm a validity index allowing the determination of the proper number of clusters is also proposed experiments with synthetic and real data sets show that the proposed algorithm can be considered as a promising tool in the field of exploratory statistics

belief functions and parametric models the theory of belief functions assesses evidence by fitting it to a scale of canonical examples in which the meaning of a message depends on chance in order to analyse parametric statistical problems within the framework of this theory we must specify the evidence on which the parametric model is based this article gives several examples to show how the nature of this evidence affects the analysis these examples also illustrate how the theory of belief functions can deal with problems where the evidence is too weak to support a parametric model

evaluating stability and comparing output of feature selectors that optimize feature subset cardinality stability robustness of feature selection methods is a topic of recent interest yet often neglected importance with direct impact on the reliability of machine learning systems we investigate the problem of evaluating the stability of feature selection processes yielding subsets of varying size we introduce several novel feature selection stability measures and adjust some existing measures in a unifying framework that offers broad insight into the stability problem we study in detail the properties of considered measures and demonstrate on various examples what information about the feature selection process can be gained we also introduce an alternative approach to feature selection evaluation in the form of measures that enable comparing the similarity of two feature selection processes these measures enable comparing e g the output of two feature selection methods or two runs of one method with different parameters the information obtained using the considered stability and similarity measures is shown to be usable for assessing feature selection methods or criteria as such

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

dg quotients of dg categories abstract keller introduced a notion of quotient of a differential graded category modulo a full differential graded subcategory which agrees with verdier s notion of quotient of a triangulated category modulo a triangulated subcategory this work is an attempt to further develop his theory

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

reduction of fuzzy control rules by means of premise learning method and case study rule number reduction is important for fuzzy control of complex processes with high dimensionality it is stated in the paper that this issue can be treated effectively by means of learning premises with general structure since conditions of rules are generalised by a genetic algorithm ga rather than enumerated according to every and connection of input fuzzy sets a parsimonious knowledge base with a reduced number of rules can be expected on the other hand to give a numerical evaluation of possible conflicts among rules a consistency index of the rule set is established this index is integrated into the fitness function of the ga to search for a set of optimal rule premises yielding not only good control performance but also little or no inconsistency in the fuzzy knowledge base the advantage of the proposed method is demonstrated by the case study of development of a compact fuzzy controller to balance an inverted pendulum in the laboratory

the homology of the mapping class group 1 2 h btg a h mg q in this paper we will show that m g btg and b i l sg get more and more complicated as the genus g tends to infinity more precisely we will prove theorem 1 1 let q z2 z4 z6 denote the polynomial algebra of generators z2n in dimension in n 1 2 3 there are classes y2 y4 y2n with y2n in the 2nth cohomology group h 2n b i sg z such that the homomorphism of algebras sending z2n toy2n

the telescope conjecture for hereditary rings via ext orthogonal pairs abstract for the module category of a hereditary ring the ext orthogonal pairs of subcategories are studied for each ext orthogonal pair that is generated by a single module a 5 term exact sequence is constructed the pairs of finite type are characterized and two consequences for the class of hereditary rings are established homological epimorphisms and universal localizations coincide and the telescope conjecture for the derived category holds true however we present examples showing that neither of these two statements is true in general for rings of global dimension 2

on the homotopy of the stable mapping class group by considering all surfaces and their mapping class groups at once it is shown that the classifying space of the stable mapping class group after plus construction b has the homotopy type of an infinite loop space the main new tool is a generalized group completion theorem for simplicial categories the first deloop of b coincides with that of miller m induced by the pairs of pants multiplication the classical representation of the mapping class group onto siegel s modular group is shown to induce a map of infinite loop spaces from b to k theory it is then a direct consequence of a theorem by charney and cohen cc that there is a space y such that b im j 1 2 y where im j 1 2 is the image of j localized away from the prime 2

an information fusion approach by combining multigranulation rough sets and evidence theory multigranulation rough set mgrs theory provides two kinds of qualitative combination rules that are generated by optimistic and pessimistic multigranulation fusion functions they are used to aggregate multiple granular structures from a set theoretic standpoint however the two combination rules seem to lack robustness because one is too relaxed and the other too restrictive to solve some practical problems dempster s combination rule in the evidence theory has been employed to aggregate information coming from multiple sources however it fails to deal with conflict evidence to overcome these limitations we focus on the combination of granular structures with both reliability and conflict from multiple sources which has been a challenging task in the field of granular computing we first address the connection between multigranulation rough set theory and the evidence theory then a two grade fusion approach involved in the evidence theory and multigranulation rough set theory is proposed which is based on a well defined distance function among granulation structures finally an illustrative example is given to show the effectiveness of the proposed fusion method the results of this study will be useful for pooling the uncertain data from different sources and significant for establishing a new direction of granular computing