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

exploiting coding theory for classification we propose a multiclass to binary decomposition strategy founded on coding theory we use low density parity check codes a very effective family of binary block codes exploiting the algebraic properties of the code we handle both coding and decoding two decoding rules are proposed that provide many advantages over known strategies several experiments are performed that show significant performance improvements a powerful strategy for the classification of multiple classes is to create a classifier ensemble that decomposes the polychotomy into several dichotomies the central issue when designing a multiclass to binary decomposition scheme is the definition of both the coding matrix and the decoding algorithm in this study we propose a new classification system based on low density parity check codes which is a very effective class of binary block codes the main idea is to exploit the algebraic properties of the codes to generate the codewords for the coding matrix and to define two decoding approaches which allow us to detect and recover possible errors or rejects produced by the dichotomizers experiments based on benchmark datasets demonstrated that the proposed approach provides a statistically significant improvement in terms of the classification performance compared with state of the art decomposition strategies

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

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

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

some results on the statistical properties of an inequality constrained least squares estimator in a linear model with two regressors abstract the inequality constrained least squares estimator in this paper is from the regression model y x 1 1 x 2 2 e where both of the regression coefficients are subject to non negative inequality constraints the first and second moments of this estimator are derived the regressors are permitted to be non orthogonal a number of conclusions are drawn from comparisons of the inequality constrained least squares estimator with the ordinary least squares and equality constrained least squares estimators

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

on inequality constrained generalized least squares estimation abstract the inequality constrained generalized least squares icgls estimator is considered based on results of the powerful theory of generalized inversion a nice method for obtaining the estimator is given and it is shown how this method leads to closed form expressions the paper is concluded with some remarks on the so called two step estimator

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

on the nielsen type and the classification for the mapping class group let s be a compact surface of genus g with n boundary components with 2g 2 n 0 and let m s be its mapping class group also known as the teichmiiller modular group using measurd foliations thurston 15 has shown that m s contains three different types of elements bers has shown this decomposition can be obtained using teichmiiller distance 3 subdividing one of the classes further he obtains four classes nielsen has a series of papers 7 8 parts i iii in which he develops an elaborate theory of fixed points of mapping classes if t is any homeomorphism of s and h a lift of t or of a power of 1 to the upper half plane nielsen s theory involves the assignment of a pair of integers to h called the nielsen type of h the purpose of this paper is to show how the thurston classes and the bers classes can be defined in terms of the nielsen types of the lifts of

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 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

reducing multiclass to binary a unifying approach for margin classifiers we present a unifying framework for studying the solution of multiclass categorization problems by reducing them to multiple binary problems that are then solved using a margin based binary learning algorithm the proposed framework unifies some of the most popular approaches in which each class is compared against all others or in which all pairs of classes are compared to each other or in which output codes with error correcting properties are used we propose a general method for combining the classifiers generated on the binary problems and we prove a general empirical multiclass loss bound given the empirical loss of the individual binary learning algorithms the scheme and the corresponding bounds apply to many popular classification learning algorithms including support vector machines adaboost regression logistic regression and decision tree algorithms we also give a multiclass generalization error analysis for general output codes with adaboost as the binary learner experimental results with svm and adaboost show that our scheme provides a viable alternative to the most commonly used multiclass algorithms

multiclass from binary expanding one versus all one versus one and ecoc based approaches recently there has been a lot of success in the development of effective binary classifiers although many statistical classification techniques have natural multiclass extensions some such as the support vector machines do not the existing techniques for mapping multiclass problems onto a set of simpler binary classification problems run into serious efficiency problems when there are hundreds or even thousands of classes and these are the scenarios where this paper s contributions shine we introduce the concept of correlation and joint probability of base binary learners we learn these properties during the training stage group the binary leaner s based on their independence and with a bayesian approach combine the results to predict the class of a new instance finally we also discuss two additional strategies one to reduce the number of required base learners in the multiclass classification and another to find new base learners that might best complement the existing set we use these two new procedures iteratively to complement the initial solution and improve the overall performance this paper has two goals finding the most discriminative binary classifiers to solve a multiclass problem and keeping up the efficiency i e small number of base learners we validate and compare the method with a diverse set of methods of the literature in several public available datasets that range from small 10 to 26 classes to large multiclass problems 1000 classes always using simple reproducible scenarios

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

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

on the algorithmic implementation of multiclass kernel based vector machines in this paper we describe the algorithmic implementation of multiclass kernel based vector machines our starting point is a generalized notion of the margin to multiclass problems using this notion we cast multiclass categorization problems as a constrained optimization problem with a quadratic objective function unlike most of previous approaches which typically decompose a multiclass problem into multiple independent binary classification tasks our notion of margin yields a direct method for training multiclass predictors by using the dual of the optimization problem we are able to incorporate kernels with a compact set of constraints and decompose the dual problem into multiple optimization problems of reduced size we describe an efficient fixed point algorithm for solving the reduced optimization problems and prove its convergence we then discuss technical details that yield significant running time improvements for large datasets finally we describe various experiments with our approach comparing it to previously studied kernel based methods our experiments indicate that for multiclass problems we attain state of the art accuracy

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

pseudo periodic homeomorphisms and degeneration of riemann surfaces the authors classify all topological types of degenerate central fibers appearing in holomorphic families of closed riemann surfaces of genus g 2 over the unit disc a degenerating family of genus g is a triple m d consisting of a 2 dimensional complex manifold m an open unit disk d in the complex plane and a surjective proper holomorphic map such that all fibers of are connected and 1 d 1 d d is a smooth fiber bundle with fiber g where g is an oriented closed surface of genus g and d d 0 the monodromy homeomorphism f g g of m d is determined as usual up to isotopy and conjugation it is known that f is a pseudo periodic homeomorphism of negative twist that is its mapping class f is either of finite order or reducible and in the latter case all component mapping classes are of finite order and its screw numbers are all negative a family is said to be minimal if it is free of 1 curves two families mi d i i 1 2 are topologically equivalent if there exist homeomorphisms h m1 m2 and h d d satisfying h 0 0 and h 1 2 h let sg minimal degenerating families of genus g modulo topological equivalence denote by p g the set of all pseudo periodic mapping classes of negative twist of g then we have a well defined map monodromy sg p g the main result is the following theorem for g 2 sg p g is bijective the most essential part of the proof of this theorem is to construct the inverse map of that is for a given pseudo periodic homeomorphism f of negative twist the authors construct a degenerating family m d of genus g with monodromy homeomorphism f in the second part of this paper the authors give a complete set of conjugacy invariants for the pseudo periodic homeomorphisms of negative twist which shows that nielsen s set of invariants is not complete

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

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

enhancing directed binary trees for multi class classification one approach to multi class classification consists in decomposing the original problem into a collection of binary classification tasks the outputs of these binary classifiers are combined to produce a single prediction winner takes all max wins and tree voting schemes are the most popular methods for this purpose however tree schemes can deliver faster predictions because they need to evaluate less binary models despite previous conclusions reported in the literature this paper shows that their performance depends on the organization of the tree scheme i e the positions where each pairwise classifier is placed on the graph different metrics are studied for this purpose proposing a new one that considers the precision and the complexity of each pairwise model what makes the method to be classifier dependent the study is performed using support vector machines svms as base classifiers but it could be extended to other kind of binary classifiers the proposed method tested on benchmark data sets and on one real world application is able to improve the accuracy of other decomposition multi class classifiers producing even faster predictions

modified lagrange multiplier tests for problems with one sided alternatives abstract a modified lagrange multiplier test statistic is proposed which takes explicit account of the one sided nature of the alternative in problems where the null hypothesis specifies that the true value of the parameter vector lies on the boundary of the parameter space computation of this statistic requires only the constrained maximum likelihood estimator conditions for the consistency of tests based on this statistic are examined and it is shown that the distribution of the statistic is not affected of nuisance parameters are allowed to lie on the boundary of the parameter space

meyer s signature cocycle and hyperelliptic fibrations we show that the cohomology class represented by meyer s signature cocycle is of order 2g 1 in the 2 dimensional cohomology group of the hyperelliptic mapping class group of genus g by using the 1 cochain cobounding the signature cocycle we extend the local signature for singular fibers of genus 2 fibrations due to y matsumoto 18 to that for singular fibers of hyperelliptic fibrations of arbitrary genus g and calculate its values on lefschetz singular fibers finally we compare our local signature with another local signature which arises from algebraic geometry

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