boosting the margin a new explanation for the effectiveness of voting methods one of the surprising recurring phenomena observed in experiments with boosting is that the test error of the generated classifier usually does not increase as its size becomes very large and often is observed to decrease even after the training error reaches zero in this paper we show that this phenomenon is related to the distribution of margins of the training examples with respect to the generated voting classification rule where the margin of an example is simply the difference between the number of correct votes and the maximum number of votes received by any incorrect label we show that techniques used in the analysis of vapnik s support vector classifiers and of neural networks with small weights can be applied to voting methods to relate the margin distribution to the test error we also show theoretically and experimentally that boosting is especially effective at increasing the margins of the training examples finally we compare our explanation to those based on the bias variance decomposition

building forests of local trees a novel approach in the field of classifier ensembles is proposed the approach uses an ensemble of random decision trees each decision tree is trained on a different area of the input space areas can overlap and a good coverage of the input space is ensured experimental results confirm the validity of the approach ensemble methods have shown to be more effective than monolithic classifiers in particular when diversity holds among their components how to enforce diversity in classifier ensembles has received much attention from machine learning researchers yielding a variety of different techniques and algorithms in this paper a novel algorithm for ensemble classifiers is proposed in which ensemble components are trained with focus on different regions of the sample space in so doing diversity is mainly a consequence of the intention to limit the scope of base classifiers the algorithm proposed in this paper shares roots with several ensemble paradigms in particular with random forests as it generates forests of decision trees as well as decision trees are trained with focus on specific subsets of the sample space the resulting ensemble is in fact a forest of local trees comparative experimental results highlight that on average these ensembles perform better than other relevant kinds of ensemble classifiers including random forests

random subspace based ensemble sparse representation a new random subspace based joint sparse representation model is proposed the sparse representations in multiple subspaces are integrated into an ensemble sparse representation the spectral clustering algorithm with random subspace based ensemble sparse representation is shown the semi supervised classification method with random subspace based ensemble sparse representation is described in this paper a new random subspace based ensemble sparse representation rs esr algorithm is proposed where the random subspace is introduced into sparse representation model for high dimensional data the random subspace method can not only reduce dimension of data but also make full use of effective information of data it is not like traditional dimensionality reduction methods that may lose some information of original data additionally a joint sparse representation model is emloyed to obtain the sparse representation of a sample set in the low dimensional random subspace then the sparse representations in multiple random subspaces are integrated as an ensemble sparse representation moreover the obtained rs esr is applied in classical clustering and semi supervised classification the experimental results on different real world data sets show the superiority of rs esr over traditional methods

learn mf a random subspace approach for the missing feature problem we introduce learn mf an ensemble of classifiers based algorithm that employs random subspace selection to address the missing feature problem in supervised classification unlike most established approaches learn mf does not replace missing values with estimated ones and hence does not need specific assumptions on the underlying data distribution instead it trains an ensemble of classifiers each on a random subset of the available features instances with missing values are classified by the majority voting of those classifiers whose training data did not include the missing features we show that learn mf can accommodate substantial amount of missing data and with only gradual decline in performance as the amount of missing data increases we also analyze the effect of the cardinality of the random feature subsets and the ensemble size on algorithm performance finally we discuss the conditions under which the proposed approach is most effective

the algebra of weyl symmetrised polynomials and its quantum extension the algebra of weyl symmetrised polynomials in powers of hamiltonian operatorsp andq which satisfy canonical commutation relations is constructed this algebra is shown to encompass all recent infinite dimensional algebras acting on two dimensional phase space in particular the moyal bracket algebra and the poisson bracket algebra of which the moyal is the unique one parameter deformation are shown to be different aspects of this infinite algebra we propose the introduction of a second deformation by the replacement of the heisenberg algebra forp q with aq deformed commutator and construct algebras ofq symmetrised polynomials

order conditions for numerical methods for partitioned ordinary differential equations motivated by the consideration of runge kutta formulas for partitioned systems the theory of p series is studied this theory yields the general structure of the order conditions for numerical methods for partitioned systems and in addition for nystrom methods fory f y y for rosenbrock type methods with inexact jacobian w methods it is a direct generalization of the theory of butcher series 7 8 in a later publication the theory ofp series will be used for the derivation of order conditions for runge kutta type methods for volterra integral equations 1

on the deformability of heisenberg algebras based on the vanishing of the second hochschild cohomology group of the weyl algebra it is shown that differential algebras coming from quantum groups do not provide a non trivial deformation of quantum mechanics for the case of aq oscillator there exists a deforming map to the classical algebra it is shown that the differential calculus on quantum planes with involution i e if one works in position momentum realization can be mapped on aq difference calculus on a commutative real space although this calculus leads to an interesting discretization it is proved that it can be realized by generators of the undeformed algebra and does not possess a proper group of global transformations

attribute bagging improving accuracy of classifier ensembles by using random feature subsets we present attribute bagging ab a technique for improving the accuracy and stability of classifier ensembles induced using random subsets of features ab is a wrapper method that can be used with any learning algorithm it establishes an appropriate attribute subset size and then randomly selects subsets of features creating projections of the training set on which the ensemble classifiers are built the induced classifiers are then used for voting this article compares the performance of our ab method with bagging and other algorithms on a hand pose recognition dataset it is shown that ab gives consistently better results than bagging both in accuracy and stability the performance of ensemble voting in bagging and the ab method as a function of the attribute subset size and the number of voters for both weighted and unweighted voting is tested and discussed we also demonstrate that ranking the attribute subsets by their classification accuracy and voting using only the best subsets further improves the resulting performance of the ensemble

the simple modules of certain generalized crossed products abstract we consider a dedekind domaindand az graded ring r i z r i withr0 dand eachri dvibeing a freed module of rank 1 the structure ofris described by an automorphism ofdand a generalized 2 cocyclec z z dnot necessarily taking its values in the units ofd the aim of this paper is to classify the simpler modules say in the case wherec i j 0 for alli j z we also deal with this problem in then graded case as a consequence we obtain a description of the simple modules of some classical algebras and of generalized weyl algebras

finite dimensional irreducible modules of the universal askey wilson algebra since the introduction of askey wilson algebras by zhedanov in 1991 the classification of the finite dimensional irreducible modules of askey wilson algebras remains open a universal analog triangle q of the askey wilson algebras was recently studied in this paper we consider a family of infinite dimensional triangle q modules by the universal property of these triangle q modules we classify the finite dimensional irreducible triangle q modules when q is not a root of unity

p adic commutation relations representations of the canonical and deformed commutation relations by bounded operators on p adic banach spaces are constructed functions from the mahler basis of the space of p adic continuous functions and their multiplicative analogues are shown to be the p adic counterparts of the hermite and q hermite functions the analogue of the stone von neumann uniqueness theorem fails in the p adic case

arcing classifier with discussion and a rejoinder by the author recent work has shown that combining multiple versions of unstable classifiers such as trees or neural nets results in reduced test set error one of the more effective is bagging here modified training sets are formed by resampling from the original training set classifiers constructed using these training sets and then combined by voting freund and schapire propose an algorithm the basis of which is to adaptively resample and combine hence the acronym arcing so that the weights in the resampling are increased for those cases most often misclassified and the combining is done by weighted voting arcing is more successful than bagging in test set error reduction we explore two arcing algorithms compare them to each other and to bagging and try to understand how arcing works we introduce the definitions of bias and variance for a classifier as components of the test set error unstable classifiers can have low bias on a large range of data sets their problem is high variance combining multiple versions either through bagging or arcing reduces variance significantly

the unitary irreducible representations of the quantum heisenberg algebra the goal of this work is to describe the irreducible representations of the quantum heisenberg algebra and the unitary irreducible representation of one of its real forms the solution of this problem is obtained through the investigation of theleft spectrum of the quantum heisenberg algebra using the result about spectra of generic algebras of skew differential operators cf r

a multirate w method for electrical networks in state space formulation subunits of coupled technical systems typically behave on differing time scales which are often separated by several orders of magnitude an ordinary integration scheme is limited by the fastest changing component whereas so called multirate methods employ an inherent step size for each subsystem to exploit these settings however the realization of the coupling terms is crucial for any convergence thus the approach to return to one step methods within the multirate concept is promising this paper introduces the multirate w method for ordinary differential equations and gives a theoretical discussion in the context of partitioned rosenbrock wanner methods finally the matlab implementation of an embedded scheme of order 3 2 is tested for a multirate version of prothero robinson s equation and the inverter chain benchmark

the spectrum of the algebra of skew differential operators and the irreducible representations of the quantum heisenberg algebra the left spectrum of a wide class of the algebras of skew differential operators is described as a sequence we determine and classify all the algebraically irreducible representations of the quantum heisenberg algebra over an arbitrary field

the left spectrum the levitzki radical and noncommutative schemes this note contains a brief exposition of the basics of a noncommutative version of affine quasi affine and projective algebraic geometry in this version to any associative ring with unity a quasi affine resp affine left scheme is assigned the notion of the left spectrum of a ring plays the key role

consistency of random forests and other averaging classifiers in the last years of his life leo breiman promoted random forests for use in classification he suggested using averaging as a means of obtaining good discrimination rules the base classifiers used for averaging are simple and randomized often based on random samples from the data he left a few questions unanswered regarding the consistency of such rules in this paper we give a number of theorems that establish the universal consistency of averaging rules we also show that some popular classifiers including one suggested by breiman are not universally consistent

random rotation ensembles in machine learning ensemble methods combine the predictions of multiple base learners to construct more accurate aggregate predictions established supervised learning algorithms inject randomness into the construction of the individual base learners in an effort to promote diversity within the resulting ensembles an undesirable side effect of this approach is that it generally also reduces the accuracy of the base learners in this paper we introduce a method that is simple to implement yet general and effective in improving ensemble diversity with only modest impact on the accuracy of the individual base learners by randomly rotating the feature space prior to inducing the base learners we achieve favorable aggregate predictions on standard data sets compared to state of the art ensemble methods most notably for tree based ensembles which are particularly sensitive to rotation

stability of a multi rate method for numerical integration of ode s abstract this paper derives sufficient conditions for the absolute stability of a certain multi rate method of numerical integration of systems of first order ode s which have been separated into two subsystems the second system being made up of the faster response equation it is assumed that the subsystems are integrated with fourth order and third order runge kutta methods respectively it is shown that there will be regions of stability provided the original system is sufficiently diagonally dominant if the subsystems are weakly coupled the regions of stability are nearly as large as the classical regions

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