research on the unbiased probability estimation of error correcting output coding supervised classification based on error correcting output codes ecoc is an efficient method to solve the problem of multi class classification and how to get the accurate probability estimation via ecoc is also an attractive research direction this paper proposed three kinds of ecoc to get unbiased probability estimates and investigated the corresponding classification performance in depth at the same time two evaluating criterions for ecoc that has better classification performance were concluded which are bayes consistence and unbiasedness of probability estimation experimental results on artificial data sets and uci data sets validate the correctness of our conclusion

multiclass data segmentation using diffuse interface methods on graphs we present two graph based algorithms for multiclass segmentation of high dimensional data on graphs the algorithms use a diffuse interface model based on the ginzburg landau functional related to total variation and graph cuts a multiclass extension is introduced using the gibbs simplex with the functional s double well potential modified to handle the multiclass case the first algorithm minimizes the functional using a convex splitting numerical scheme the second algorithm uses a graph adaptation of the classical numerical merriman bence osher mbo scheme which alternates between diffusion and thresholding we demonstrate the performance of both algorithms experimentally on synthetic data image labeling and several benchmark data sets such as mnist coil and webkb we also make use of fast numerical solvers for finding the eigenvectors and eigenvalues of the graph laplacian and take advantage of the sparsity of the matrix experiments indicate that the results are competitive with or better than the current state of the art in multiclass graph based segmentation algorithms for high dimensional data

a universal characterization of the double powerlocale the double powerlocale p x found by composing in either order the upper and lower powerlocale constructions pu and pl is shown to be isomolphic in locop set to the double exponential ssx where s is the sierpinski locale further pu x and pl x are shown to be the subobjects of p x comprising respectively the meet semilattice and join semilattice homomorphisms a key lemma shows that for any locales x and y natural transformations from sx the presheaf loc x s to sy i e loc y s are equivalent to dcpo morphisms scott continuous maps from the flame x to y it is also shown that sx has a localic reflection in locop set whose frame is the scott topology on x the reasoning is constructive in the sense of topos validity

state morphism algebras general approach we present a complete description of subdirectly irreducible state bl algebras as well as of subdirectly irreducible state morphism bl algebras in addition we present a general theory of state morphism algebras that is algebras of general type with state morphism which is a fixed idempotent endomorphism we define a diagonal state morphism algebra and we show that every subdirectly irreducible state morphism algebra can be embedded into a diagonal one we describe generators of the varieties of state morphism algebras in particular generators of state morphism bl algebras state morphism mtl algebras state morphism non associative bl algebras and state morphism pseudo mv algebras

a likelihood mpec approach to target classification in this paper we develop a method for classifying an unknown data vector as belonging to one of several classes this method is based on the statistical methods of maximum likehood and borrowed strength estimation we develop an mpec procedure for mathematical program with equilibrium constraints for the classification of a multi dimensional observation using a finite set of observed training data as the inputs to a bilevel optimization problem we present a penalty interior point method for solving the resulting mpec and report numerical results for a multispectral minefield classification application related approaches based on conventional maximum likehood estimation and a bivariate normal mixture model as well as alternative surrogate classification objective functions are described

flexible discriminant analysis by optimal scoring abstract fisher s linear discriminant analysis is a valuable tool for multigroup classification with a large number of predictors one can find a reduced number of discriminant coordinate functions that are optimal for separating the groups with two such functions one can produce a classification map that partitions the reduced space into regions that are identified with group membership and the decision boundaries are linear this article is about richer nonlinear classification schemes linear discriminant analysis is equivalent to multiresponse linear regression using optimal scorings to represent the groups in this paper we obtain nonparametric versions of discriminant analysis by replacing linear regression by any nonparametric regression method in this way any multiresponse regression technique such as mars or neural networks can be postprocessed to improve its classification performance

statistical ranking and combinatorial hodge theory we propose a technique that we call hodgerank for ranking data that may be incomplete and imbalanced characteristics common in modern datasets coming from e commerce and internet applications we are primarily interested in cardinal data based on scores or ratings though our methods also give specific insights on ordinal data from raw ranking data we construct pairwise rankings represented as edge flows on an appropriate graph our statistical ranking method exploits the graph helmholtzian which is the graph theoretic analogue of the helmholtz operator or vector laplacian in much the same way the graph laplacian is an analogue of the laplace operator or scalar laplacian we shall study the graph helmholtzian using combinatorial hodge theory which provides a way to unravel ranking information from edge flows in particular we show that every edge flow representing pairwise ranking can be resolved into two orthogonal components a gradient flow that represents the l 2 optimal global ranking and a divergence free flow cyclic that measures the validity of the global ranking obtained if this is large then it indicates that the data does not have a good global ranking this divergence free flow can be further decomposed orthogonally into a curl flow locally cyclic and a harmonic flow locally acyclic but globally cyclic these provides information on whether inconsistency in the ranking data arises locally or globally when applied to statistical ranking problems hodge decomposition sheds light on whether a given dataset may be globally ranked in a meaningful way or if the data is inherently inconsistent and thus could not have any reasonable global ranking in the latter case it provides information on the nature of the inconsistencies an obvious advantage over the np hardness of kemeny optimization is that hodgerank may be easily computed via a linear least squares regression we also discuss connections with well known ordinal ranking techniques such as kemeny optimization and borda count from social choice theory

stopping criterion for boosting based data reduction techniques from binary to multiclass problem so far boosting has been used to improve the quality of moderately accurate learning algorithms by weighting and combining many of their weak hypotheses into a final classifier with theoretically high accuracy in a recent work sebban nock and lallich 2001 we have attempted to adapt boosting properties to data reduction techniques in this particular context the objective was not only to improve the success rate but also to reduce the time and space complexities due to the storage requirements of some costly learning algorithms such as nearest neighbor classifiers in that framework each weak hypothesis which is usually built and weighted from the learning set is replaced by a single learning instance the weight given by boosting defines in that case the relevance of the instance and a statistical test allows one to decide whether it can be discarded without damaging further classification tasks in sebban nock and lallich 2001 we addressed problems with two classes it is the aim of the present paper to relax the class constraint and extend our contribution to multiclass problems beyond data reduction experimental results are also provided on twenty three datasets showing the benefits that our boosting derived weighting rule brings to weighted nearest neighbor classifiers

humans in groups the importance of contextual information for understanding collective activities in this work we consider the problem of modeling and recognizing collective activities performed by groups of people sharing a common purpose for this aim we take into account the social contextual information of each person in terms of the relative orientation and spatial distribution of people groups we propose a method able to process a video stream and at each time instant associate a collective activity with each individual in the scene by representing the individual or target as a part of a group of nearby people the target group to generalize with respect to the viewpoint we associate each target with a reference frame based on his spatial orientation which we estimate automatically by semi supervised learning then we model the social context of a target by organizing a set of instantaneous descriptors capturing the essence of mutual positions and orientations within the target group in a graph structure classification of collective activities is achieved with a multi class svm endowed with a novel kernel function for graphs we report an extensive experimental analysis on benchmark datasets that validates the proposed solution and shows significant improvements with respect to state of art results

a unified view on multi class support vector classification a unified view on multi class support vector machines svms is presented covering most prominent variants including the one vs all approach and the algorithms proposed by weston watkins crammer singer lee lin wahba and liu yuan the unification leads to a template for the quadratic training problems and new multi class svm formulations within our framework we provide a comparative analysis of the various notions of multi class margin and margin based loss in particular we demonstrate limitations of the loss function considered for instance in the crammer singer machine we analyze fisher consistency of multi class loss functions and universal consistency of the various machines on the one hand we give examples of svms that are in a particular hyperparameter regime universally consistent without being based on a fisher consistent loss these include the canonical extension of svms to multiple classes as proposed by weston watkins and vapnik as well as the one vs all approach on the other hand it is demonstrated that machines based on fisher consistent loss functions can fail to identify proper decision boundaries in low dimensional feature spaces we compared the performance of nine different multi class svms in a thorough empirical study our results suggest to use the weston watkins svm which can be trained comparatively fast and gives good accuracies on benchmark functions if training time is a major concern the one vs all approach is the method of choice

multicategory support vector machines two category support vector machines svm have been very popular in the machine learning community for classification problems solving multicategory problems by a series of binary classifiers is quite common in the svm paradigm however this approach may fail under various circumstances we propose the multicategory support vector machine msvm which extends the binary svm to the multicategory case and has good theoretical properties the proposed method provides a unifying framework when there are either equal or unequal misclassification costs as a tuning criterion for the msvm an approximate leave one out cross validation function called generalized approximate cross validation is derived analogous to the binary case the effectiveness of the msvm is demonstrated through the applications to cancer classification using microarray data and cloud classification with satellite radiance profiles

a multiclass classification method based on decoding of binary classifiers in this letter we present new methods of multiclass classification that combine multiple binary classifiers misclassification of each binary classifier is formulated as a bit inversion error with probabilistic models by making an analogy to the context of information transmission theory dependence between binary classifiers is incorporated into our model which makes a decoder a type of boltzmann machine we performed experimental studies using a synthetic data set data sets from the uci repository and bioinformatics data sets and the results show that the proposed methods are superior to the existing multiclass classification methods

presenting de groot duality of stably compact spaces abstract we give a constructive account of the de groot duality of stably compact spaces in the setting of strong proximity lattice a point free representation of a stably compact space to this end we introduce a notion of strong continuous entailment relation which can be thought of as a presentation of a strong proximity lattice by generators and relations the new notion allows us to identify de groot duals of stably compact spaces by analysing the duals of their presentations we carry out a number of constructions on strong proximity lattices using strong continuous entailment relations and study their de groot duals the examples include various powerlocales patch topology and the space of valuations these examples illustrate the simplicity of our approach by which we can reason about the de groot duality of stably compact spaces

lossless convexification of non convex optimal control problems for state constrained linear systems this paper analyzes a class of finite horizon optimal control problems with mixed non convex and convex control constraints and linear state constraints a convex relaxation of the problem is proposed and it is proved that a solution of the relaxed problem is also a solution of the original problem this process is called lossless convexification and its generalization for problems with state constraints is the primary contribution of the paper doing so enables the use of interior point methods of convex optimization to obtain global optimal solutions of the original non convex problem the approach is also demonstrated on example problems

combining predictions in pairwise classification an optimal adaptive voting strategy and its relation to weighted voting weighted voting is the commonly used strategy for combining predictions in pairwise classification even though it shows good classification performance in practice it is often criticized for lacking a sound theoretical justification in this paper we study the problem of combining predictions within a formal framework of label ranking and under some model assumptions derive a generalized voting strategy in which predictions are properly adapted according to the strengths of the corresponding base classifiers we call this strategy adaptive voting and show that it is optimal in the sense of yielding a map prediction of the class label of a test instance moreover we offer a theoretical justification for weighted voting by showing that it yields a good approximation of the optimal adaptive voting prediction this result is further corroborated by empirical evidence from experiments with real and synthetic data sets showing that even though adaptive voting is sometimes able to achieve consistent improvements weighted voting is in general quite competitive all the more in cases where the aforementioned model assumptions underlying adaptive voting are not met in this sense weighted voting appears to be a more robust aggregation strategy

brief paper optimal control problems with a continuous inequality constraint on the state and the control we consider an optimal control problem with a nonlinear continuous inequality constraint both the state and the control are allowed to appear explicitly in this constraint by discretizing the control space and applying a novel transformation a corresponding class of semi infinite programming problems is derived a solution of each problem in this class furnishes a suboptimal control for the original problem furthermore we show that such a solution can be computed efficiently using a penalty function method on the basis of these two ideas an algorithm that computes a sequence of suboptimal controls for the original problem is proposed our main result shows that the cost of these suboptimal controls converges to the minimum cost for illustration an example problem is solved

a stone type duality for st0 stratified alexandrov l topological spaces abstract we show that for every complete lattice a both the set of completely prime elements and the set of completely coprime elements are one to one corresponding to ch a the set of complete lattice homomorphisms from a to the two element lattice 2 a complete lattice is called completely generated a cg lattice for short if it is generated by the set of completely prime elements or equivalently by the set of completely coprime elements then we restudy the duality between the category of t 0 alexandrov topological spaces and the category of cg lattices by means of ch a with these preparations for a frame l as the truth value table we introduce s t 0 separation axiom for stratified alexandrov l topological spaces and finally establish a duality between the category of s t 0 stratified alexandrov l topological spaces and the category of completely generated complete l ordered sets we also investigate some properties of the s t 0 axiom for example it is hereditary by closed subspaces and productive

state bck algebras and state morphism bck algebras abstract in the paper we define the notion of a state bck algebra and a state morphism bck algebra extending the language of bck algebras by adding a unary operator which models probabilistic reasoning we present a relation between state operators and state morphism operators and measures and states on bck algebras respectively we study subdirectly irreducible state morphism bck algebras we introduce the concept of an adjoint pair in bck algebras and show that there is a one to one correspondence between adjoint pairs and state morphism operators in addition we show the generators of quasivarieties of state morphism bck algebras

nonhomogeneity analysis using borrowed strength abstract this article develops a borrowed strength methodology for estimating local probability densities in a random field under a piecewise stationarity condition similarities between the densities in different regions of the field can be exploited by estimating a global mixture density and imposing the parameter space support of this borrowed strength estimate on the local estimation problems the local estimates are then used in an analysis of the homogeneity of the field which is shown to benefit from the method of borrowing strength

on nearest neighbor error correcting output codes with application to all pairs multiclass support vector machines a common way of constructing a multiclass classifier is by combining the outputs of several binary ones according to an error correcting output code ecoc scheme the combination is typically done via a simple nearest neighbor rule that finds the class that is closest in some sense to the outputs of the binary classifiers for these nearest neighbor ecocs we improve existing bounds on the error rate of the multiclass classifier given the average binary distance the new bounds provide insight into the one versus rest and all pairs matrices which are compared through experiments with standard datasets the results also show why elimination also known as dagsvm and hamming decoding often achieve the same accuracy

classification by pairwise coupling we discuss a strategy for polychotomous classification that involves estimating class probabilities for each pair of classes and then coupling the estimates together the coupling model is similar to the bradley terry method for paired comparisons we study the nature of the class probability estimates that arise and examine the performance of the procedure in real and simulated data sets classifiers used include linear discriminants nearest neighbors adaptive nonlinear methods and the support vector machine

incorporating prior probabilities into high dimensional classifiers in standard parametric classifiers or classifiers based on nonparametric methods but where there is an opportunity for estimating population densities the prior probabilities of the respective populations play a key role however those probabilities are largely ignored in the construction of high dimensional classifiers partly because there are no likelihoods to be constructed or bayes risks to be estimated nevertheless including information about prior probabilities can reduce the overall error rate particularly in cases where doing so is most important i e when the classification problem is particularly challenging and error rates are not close to zero in this paper we suggest a general approach to reducing error rate in this way by using a method derived from breiman s bagging idea the potential improvements in performance are identified in theoretical and numerical work the latter involving both applications to real data and simulations the method is simple and explicit to apply and does not involve choice of any tuning parameters

a survey of the maximum principles for optimal control problems with state constraints this paper gives a survey of the various forms of pontryagin s maximum principle for optimal control problems with state variable inequality constraints the relations between the different sets of optimality conditions arising in these forms are shown furthermore the application of these maximum principle conditions is demonstrated by solving some illustrative examples

a combinatorial graph based solution method for a class of continuous time optimal control problems the paper addresses a class of continuous time optimal control problems whose solutions are typically characterized by both bang bang and singular control regimes analytical study and numerical computation of such solutions are very difficult and far from complete when only techniques from control theory are used this paper solves optimal control problems by reducing them to the combinatorial search for the shortest path in a specially constructed graph since the nodes of the graph are weighted in a sequence dependent manner we extend the classical shortest path algorithm to our case the proposed solution method is currently limited to single state problems with multiple control functions a production planning problem and a train operation problem are optimally solved to illustrate the method

a novel technique for subpixel image classification based on support vector machine this paper presents a novel support vector machine classifier designed for subpixel image classification pixel spectral unmixing the proposed classifier generalizes the properties of svms to the identification and modeling of the abundances of classes in mixed pixels by using fuzzy logic this results in the definition of a fuzzy input fuzzy output support vector machine f2svm classifier that can 1 process fuzzy information given as input to the classification algorithm for modeling the subpixel information in the learning phase of the classifier and 2 provide a fuzzy modeling of the classification results allowing a relation many to one between classes and pixels the presented binary f2svm can address multicategory problems according to two strategies the fuzzy one against all foaa and the fuzzy one against one foao strategies these strategies generalize to the fuzzy case techniques based upon ensembles of binary classifiers used for addressing multicategory problems in crisp classification problems the effectiveness of the proposed f2svm classifier is tested on three problems related to image classification in presence of mixed pixels having different characteristics experimental results confirm the validity of the proposed subpixel classification method

a grouped ranking model for item preference parameter given a set of rating data for a set of items determining preference levels of items is a matter of importance various probability models have been proposed to solve this task one such model is the plackett luce model which parameterizes the preference level of each item by a real value in this letter the plackett luce model is generalized to cope with grouped ranking observations such as movie or restaurant ratings since it is difficult to maximize the likelihood of the proposed model directly a feasible approximation is derived and the em algorithm is adopted to find the model parameter by maximizing the approximate likelihood which is easily evaluated the proposed model is extended to a mixture model and two applications are proposed to show the effectiveness of the proposed model numerical experiments with real world data are carried out

characterizing the scale dimension of a high dimensional classification problem classi cation of high dimensional data is inherently di1cult we present an exploratory data analysis methodology for characterizing the scale dimension of a classi cation problem the idea is to characterize the support of one distinguished target class as a collection of balls covering the class with each ball centeredat an observation in that class such that the radius is maximal without containing observations from the other classes the scale dimension is de ned to be the number of distinct radii ball sizes required to cover the class without covering observations from the other class a greedy algorithm is used to t the balls the balls then provide a description of the support of the target class with information about the complexity of the classi cation problem implicit in the number radii adjacency and position of the balls clustering the balls by radius and pruning the cluster tree yields an estimate of the scale dimension for the problem we illustrate the methodology with pedagogical simulations anda chemical sensor data analysis application publishedby elsevier science ltdon behalf of pattern recognition society

design of reject rules for ecoc classification systems ecoc is a widely used and successful technique which implements a multi class classification system by decomposing the original problem into several two class problems in this paper we study the possibility to provide ecoc systems with a tailored reject option carried out through different schemes that can be grouped under two different categories an external and an internal approach the first one is based on the reliability of the entire system output and does not require any change in its structure the second scheme instead estimates the reliability of the internal dichotomizers and implies a slight modification in the decoding stage experimental results on popular benchmark data sets are reported to show the behavior of the different schemes

information systems for continuous posets abstract the method of information systems is extended from algebraic posets to continuous posets by taking a set of tokens with an ordering that is transitive and interpolative but not necessarily reflexive this develops the results of raney on completely distributive lattices and of hoofman on continuous scott domains and also generalizes smyth s r structures various constructions on continuous posets have neat descriptions in terms of these continuous information systems here we describe hoffmann lawson duality which could not be done easily with r structures and vietoris power locales we also use the method to give a partial answer to a question of johnstone s in the context of continuous posets vietoris algebras are the same as localic semilattices

risk sensitive loss functions for sparse multi category classification problems in this paper we propose two risk sensitive loss functions to solve the multi category classification problems where the number of training samples is small and or there is a high imbalance in the number of samples per class such problems are common in the bio informatics medical diagnosis areas the most commonly used loss functions in the literature do not perform well in these problems as they minimize only the approximation error and neglect the estimation error due to imbalance in the training set the proposed risk sensitive loss functions minimize both the approximation and estimation error we present an error analysis for the risk sensitive loss functions along with other well known loss functions using a neural architecture classifiers incorporating these risk sensitive loss functions have been developed and their performance evaluated for two real world multi class classification problems viz a satellite image classification problem and a micro array gene expression based cancer classification problem to study the effectiveness of the proposed loss functions we have deliberately imbalanced the training samples in the satellite image problem and compared the performance of our neural classifiers with those developed using other well known loss functions the results indicate the superior performance of the neural classifier using the proposed loss functions both in terms of the overall and per class classification accuracy performance comparisons have also been carried out on a number of benchmark problems where the data is normal i e not sparse or imbalanced results indicate similar or better performance of the proposed loss functions compared to the well known loss functions

brief paper optimal control problems with multiple characteristic time points in the objective and constraints in this paper we develop a computational method for a class of optimal control problems where the objective and constraint functionals depend on two or more discrete time points these time points can be either fixed or variable using the control parametrization technique and a time scaling transformation this type of optimal control problem is approximated by a sequence of approximate optimal parameter selection problems each of these approximate problems can be viewed as a finite dimensional optimization problem new gradient formulae for the cost and constraint functions are derived with these gradient formulae standard gradient based optimization methods can be applied to solve each approximate optimal parameter selection problem for illustration two numerical examples are solved

a transitivity analysis of bipartite rankings in pairwise multi class classification many multi class classification algorithms in statistics and machine learning typically combine several binary classifiers in order to construct an overall classifier in the popular pairwise ensemble one classifier is built for each pair of classes resulting in pairwise bipartite rankings in contrast ordinal regression algorithms consider a single ranking function for several ordered classes it is known in the literature that pairwise ensembles can be useful for ordinal regression however can single ranking models make a contribution to multi class classification the answer to this question should be affirmative as supported by theoretical results presented in this article we conduct a formal analysis of the consistency of pairwise bipartite rankings by uncovering the conditions under which they can be equivalently expressed in terms of a single ranking similar to the utility representability of pairwise preference relations it turns out that transitivity plays a crucial role in the characterization of the ranking representability of pairwise bipartite rankings to this end we introduce the new concepts of strict ranking representability a restrictive condition that can be verified easily and auc ranking representability a practically more useful condition that is more difficult to verify however the link between pairwise bipartite rankings and dice games allows us to formulate necessary transitivity conditions for auc ranking representability a sufficient condition on the other hand is obtained by introducing a new type of transitivity that can be verified by solving an integer quadratic program

method of evolving junctions a new approach to optimal control with constraints abstract we propose a new strategy called method of evolving junctions mej to compute the solutions for a class of optimal control problems with constraints on both state and control variables our main idea is that by leveraging the geometric structures of the optimal solutions we recast the infinite dimensional optimal control problem into an optimization problem depending on a finite number of points called junctions then using a modified gradient flow method whose dimension can change dynamically we find local solutions for the optimal control problem we also employ intermittent diffusion a global optimization method based on stochastic differential equations to obtain the global optimal solution we demonstrate via a numerical example that mej can effectively solve path planning problems in dynamical environments

posterior probability based ensemble strategy using optimizing decision directed acyclic graph for multi class classification ensemble strategy is important to develop a decomposition and ensemble method for multi class classification problems most existing ensemble strategies use predetermined and heuristic decision rules in this work we build up the decision rules by optimizing decision directed acyclic graph oddag with classical and fuzzy decision trees to ensemble the posterior probabilities of binary classifiers from one vs one ovo or one vs all ova decomposition strategies for multi class classification problems four widely used extensible algorithms and ten decomposition and ensemble methods incorporating four binary classifiers bcs have been tested on 25 data sets the empirical results show that the methods based on ensemble strategies using oddag are among the top methods that achieve the best performance in terms of two different measures

probability estimation for multi class classification using adaboost abstract it is a general viewpoint that adaboost classifier has excellent performance on classification problems but could not produce good probability estimations in this paper we put forward a theoretical analysis of probability estimation model and present some verification experiments which indicate that adaboost can be used for probability estimation with the theory we suggest some useful measures for using adaboost algorithms properly and then we deduce a probability estimation model for multi class classification by pairwise coupling unlike previous approximate methods we provide an analytical solution instead of a special iterative procedure moreover a new problem that how to get a robust prediction with classifier scores is proposed experiments show that the traditional predict framework which chooses one with the highest score from all classes as the prediction is not always good while our model performs well

brief paper lossless convexification of a class of optimal control problems with non convex control constraints we consider a class of finite time horizon optimal control problems for continuous time linear systems with a convex cost convex state constraints and non convex control constraints we propose a convex relaxation of the non convex control constraints and prove that the optimal solution of the relaxed problem is also an optimal solution for the original problem which is referred to as the lossless convexification of the optimal control problem the lossless convexification enables the use of interior point methods of convex optimization to obtain globally optimal solutions of the original non convex optimal control problem the solution approach is demonstrated on a number of planetary soft landing optimal control problems

solving multi class problems with linguistic fuzzy rule based classification systems based on pairwise learning and preference relations this paper deals with multi class classification for linguistic fuzzy rule based classification systems the idea is to decompose the original data set into binary classification problems using the pairwise learning approach confronting all pair of classes and to obtain an independent fuzzy system for each one of them along the inference process each fuzzy rule based classification system generates an association degree for both of its corresponding classes and these values are encoded into a fuzzy preference relation our analysis is focused on the final step that returns the predicted class label specifically we propose to manage the fuzzy preference relation using a non dominance criterion on the different alternatives contrasting the behaviour of this model with both the classical weighted voting scheme and a decision rule that combines the fuzzy relations of preference conflict and ignorance by means of a voting strategy our experimental study is carried out using two different linguistic fuzzy rule learning methods for which we show that the non dominance criterion is a good alternative in comparison with the previously mentioned aggregation mechanisms this empirical analysis is supported through the corresponding statistical analysis using non parametrical tests

online learning of complex prediction problems using simultaneous projections we describe and analyze an algorithmic framework for online classification where each online trial consists of multiple prediction tasks that are tied together we tackle the problem of updating the online predictor by defining a projection problem in which each prediction task corresponds to a single linear constraint these constraints are tied together through a single slack parameter we then introduce a general method for approximately solving the problem by projecting simultaneously and independently on each constraint which corresponds to a prediction sub problem and then averaging the individual solutions we show that this approach constitutes a feasible albeit not necessarily optimal solution of the original projection problem we derive concrete simultaneous projection schemes and analyze them in the mistake bound model we demonstrate the power of the proposed algorithm in experiments with synthetic data and with multiclass text categorization tasks

continuous information system abstract in this paper we generalise the notion of algebraic information system to continuous information system just as algebraic information systems are concrete representations of scott domains continuous information systems are concrete representations of continuous scott domains the class of continuous information systems can be generated from the subclass of qualitative information systems in the sense that the category of continuous information systems is equivalent to the karoubi envelope of the category of qualitative information systems because qualitative information systems correspond to the qualitative domains of girard theoret comput sci 45 159 192 1986 this implies that the category of continuous scott domains is equivalent to the karoubi envelope of the category of qualitative domains we show how constructions on qualitative information systems such as product and function space can be translated to constructions on continuous information systems among other things we prove that the category of qualitative information systems is weak cartesian closed finally we define two universal information systems

information systems revisited the general continuous case in this paper a new notion of continuous information system is introduced it is shown that the information systems of this kind generate exactly the continuous domains the new information systems are of the same logic oriented style as the information systems first introduced by scott in 1982 they consist of a set of tokens a consistency predicate and an entailment relation satisfying a set of natural axioms it is shown that continuous information systems are closely related to abstract bases indeed both categories are equivalent since it is known that the categories of abstract bases and or continuous domains are equivalent it follows that the category of continuous information systems is also equivalent to that of continuous domains in applications mostly subclasses of continuous domains are considered for example the domains have to be pointed algebraic bounded complete or fs conditions are presented that when fulfilled by a continuous information system force the generated domain to belong to the required subclass in most cases the requirements are not only sufficient but also necessary

re visiting axioms of information systems based on the investigation of the axioms used in the theory of information system the notion of simplified continuous information system is introduced which is considered as a generalization of continuous information systems just like the continuous information system it is also a concrete representation of continuous domains and categorically equivalent to the category of continuous domains and scott continuous functions what is more all types of information systems studied in the literature so far turn out to be special cases of the new type by defining linear information systems and their entailment functions we show that the states of a scott style information system are exactly the fixpoints of its entailment function some axioms about an entailment relation can be characterized by the properties of the corresponding entailment function and in particular the simplified continuous information systems are solely determined by the idempotence of entailment functions

probability estimates for multi class classification by pairwise coupling pairwise coupling is a popular multi class classification method that combines all comparisons for each pair of classes this paper presents two approaches for obtaining class probabilities both methods can be reduced to linear systems and are easy to implement we show conceptually and experimentally that the proposed approaches are more stable than the two existing popular methods voting and the method by hastie and tibshirani 1998

entailment systems for stably locally compact locales the category scfru of stably continuous frames and preframe homomorphisms preserving finite meets and directed joins is dual to the karoubi envelope of a category ent whose objects are sets and whose morphisms x y are upper closed relations between the finite powersets fx and fy composition of these morphisms is the cut composition of jung et al that interfaces disjunction in the codomains with conjunctions in the domains and thereby relates to their multi lingual sequent calculus thus stably locally compact locales are represented by entailment systems x in which a generalization of entailment relations is idempotent for cut composition some constructions on stably locally compact locales are represented in terms of entailment systems products duality and powerlocales relational converse provides ent with an involution and this gives a simple treatment of the duality of stably locally compact locales if a and b are stably continuous frames then the internal preframe hom a b is isomorphic to a b where a is the hofmann lawson dual for a stably locally compact locale x the lower powerlocale of x is shown to be the dual of the upper powerlocale of the dual of x

weak algebraic information systems and a new equivalent category of dom of domains abstract in this paper concepts of generalized algebraic information system in short ga inf and weak algebraic information system in short wa inf are introduced relationships among several algebraicities of information systems are explored main results are 1 a dcpo d is an algebraic domain iff d is represented by an algebraic information system in short a inf and iff d is represented by a ga inf 2 every a inf is a ga inf and a wa inf 3 every c inf s d b induced by a domain with a basis b is a wa inf 4 the category wainf of wa infs and approximable mappings is equivalent to the category dom of domains and scott continuous functions 5 every wa inf s satisfying condition mt is a retract of w s the information structure induced by s in category wainf of wa infs and approximable mappings particularly c inf s d b induced by a domain d with a basis b is a retract of a inf w s d b in category wainf

presenting locale pullback via directed complete posets this paper shows how to describe the pullbacks of directed complete posets dcpos along geometric morphisms this extends joyal and tierney s original results on the pullbacks of suplattices it is then shown how to treat every frame as a dcpo and so locale pullback is described in this way applications are given describing triquotient assignments in terms of internal dcpo maps leading to pullback stability results for triquotient maps the main application here shows how dcpo maps between frames can be described in terms of certain external natural transformations

a representation of stably compact spaces and patch topology this note presents a concrete representation of stably compact spaces this is used to give a simple and predicative description of the patch topology of a stably compact space j pure appl algebra to appear

on the relationship between compact regularity and gentzen s cut rule the patch topology on a stably compact space generalizing the lawson topology on a domain is a coreflection of stably compact spaces in compact regular spaces this paper investigates compact regularity and the patch coreflection in multilingual sequent calculus mls which can be regarded as a category of predicative representations of stably compact spaces an object of mls is a certain sort of generalization of the positive fragment of gentzen s sequent calculus we show that an object of mls represents a compact regular space if and only if every sequent arises as an instance of gentzen s cut rule with complete freedom to choose the placement of the cut formula the relationship between compact regularity and gentzen s cut rule is further explicated by the patch coreflection in mls the construction is a universal solution up to a certain equivalence of tokens to the problem of adding opposites to a logic i e tokens that obey gentzen s rules for negation in the spectral case this is equivalent to adding boolean complements the paper closes by considering the full subcategory of mls consisting of objects with opposites by taking contrapositives of sequents we obtain an anti involution on morphisms making this category equivalent to the freyd scedrov allegory of compact regular spaces and closed binary relations moreover the category of maps of this allegory is predicatively equivalent to the image of the patch functor

a representation of l domains by information systems in this paper we propose the notion of l information systems which provides a concrete representation of l domains in particular we prove that the category of l information systems with approximable mappings as morphisms is equivalent to that of l domains with scott continuous functions as morphisms

a new approach for imbalanced data classification based on data gravitation imbalanced classification is an important machine learning research topic that troubles most general classification models because of the imbalanced class distribution a newly developed physical inspired classification method i e the data gravitation based classification dgc model performs well in many general classification problems however like other general classifiers the performance of dgc suffers in imbalanced tasks in this study we develop a specific dgc model namely imbalanced dgc idgc model for imbalanced problems the amplified gravitation coefficient agc is introduced for gravitation computing agc is a type of coefficient that contains class imbalance information which can strengthen and weaken the gravitational field of the minority and majority classes we also design a fitness evaluation function in the weight optimization procedure of the data distribution to ensure that the model parameters adapt to the imbalanced class distributions a total of 44 binary class data sets and 15 multiclass imbalanced data sets are used to test the performance of the proposed method experimental results show that the adapted dgc model is effective for imbalanced problems

composite multiclass losses we consider loss functions for multiclass prediction problems we show when a multiclass loss can be expressed as a proper composite loss which is the composition of a proper loss and a link function we extend existing results for binary losses to multiclass losses we subsume results on classification calibration by relating it to properness we determine the stationarity condition bregman representation order sensitivity and quasi convexity of multiclass proper losses we then characterise the existence and uniqueness of the composite representation for multiclass losses we show how the composite representation is related to other core properties of a loss mixability admissibility and strong convexity of multiclass losses which we characterise in terms of the hessian of the bayes risk we show that the simple integral representation for binary proper losses can not be extended to multiclass losses but offer concrete guidance regarding how to design different loss functions the conclusion drawn from these results is that the proper composite representation is a natural and convenient tool for the design of multiclass loss functions