extended nearest neighbor chain induced instance weights for svms prior knowledge plays an important role in increasing the performance of support vector machine svm one way to utilize prior knowledge is to assign different weight to each sample which is called weighted support vector machine wsvm in this paper a novel instance weighted method is proposed for support vector machines the weight is determined by the distances between a sequence of the nearest heterogeneous samples named the extended nearest neighbor chain the samples near the decision plane also locate near the heterogeneous samples thus the samples near the decision plane can be found by the extended nearest neighbor chain before svms training and then assigned higher weights meanwhile the samples far away from the decision plane are assigned lower weights this is consistent with the fact that the samples near the decision plane are more important for svms moreover this strategy can also assign lower weights to the samples which locate in the wrong classes the results of the experiments performed on both artificial synthetic datasets and real world benchmark datasets demonstrate that the proposed instance weighted method can further improve the performance of svms a novel instance weighted strategy is proposed for svms the samples near decision plane are assigned higher weights via the proposed method the sample near decision plane can be found by a chain named extended nearest neighbor chain the proposed method makes svm become more robust for noises

sparse ensembles using weighted combination methods based on linear programming an ensemble of multiple classifiers is widely considered to be an effective technique for improving accuracy and stability of a single classifier this paper proposes a framework of sparse ensembles and deals with new linear weighted combination methods for sparse ensembles sparse ensemble is to sparsely combine the outputs of multiple classifiers by using a sparse weight vector when the continuous outputs of multiple classifiers are provided in our methods the problem of solving sparse weight vector can be formulated as linear programming problems in which the hinge loss or and the 1 norm regularization are exploited both the hinge loss and the 1 norm regularization are techniques inducing sparsity used in machine learning we only ensemble classifiers with nonzero weight coefficients in these lp based methods the ensemble training error is minimized while the weight vector of ensemble learning is controlled which can be thought as implementing the structure risk minimization rule and naturally explains good performance of these methods the promising experimental results over uci data sets and the radar high resolution range profile data are presented

hilbert kunz density function and asymptotic hilbert kunz multiplicity for projective toric varieties abstract for a toric pair x d where x is a projective toric variety of dimension d 1 1 and d is a very ample t cartier divisor we show that the hilbert kunz density function hkd x d is the d 1 dimensional volume of p d z where p d r d is a compact d dimensional set which is a finite union of convex polytopes we also show that for k 1 the function hkd x k d can be replaced by another compactly supported continuous function k d which is linear in k this gives the formula for the associated coordinate ring r m lim k e h k r m k e 0 r m k d k d 1 e 0 r m d 1 0 d d where d see proposition 1 2 is solely determined by the shape of the polytope p d associated to the toric pair x d moreover d is a multiplicative function for segre products this yields explicit computation of d and hence the limit for smooth fano toric surfaces with respect to anticanonical divisor in general due to this formulation in terms of the polytope p d one can explicitly compute the limit for two dimensional toric pairs and their segre products we further show that theorem 6 3 the renormalized limit takes the minimum value if and only if the polytope p d tiles the space m r r d 1 with the lattice m z d 1 as a consequence one gets an algebraic formulation of the tiling property of any rational convex polytope

on the behavior of f rational rings under flat base change abstract we examine the behavior of f rationality under flat homomorphisms with geometrically f rational fibres the goal is to prove that if r s is a homomorphism with geometrically f rational fibres and r is an f rational ring then s is an f rational ring we prove a stronger version of this under a mild condition and introduce a new perspective for dealing with flat base change problems in tight closure theory

observations on the f signature of local rings of characteristic p abstract let r m k be a d dimensional noetherian reduced local ring of prime characteristic p such that r 1 p e are finite over r for all e n i e r is f finite consider the sequence a e q r d e 0 in which r log p k k p q p e and a e is the maximal rank of free r modules appearing as direct summands of r module r 1 q denote by s r and s r the liminf and limsup respectively of the above sequence as e if s r s r then the limit denoted by s r is called the f signature of r it turns out that the f signature can be defined in a way that is independent of the module finite property of r 1 q over r we show that 1 if s r 1 1 d p d then r is regular 2 if r is excellent such that r p is gorenstein for every p spec r m then s r exists 3 if r m s n is a local flat ring homomorphism then s r s s and if furthermore s m s is gorenstein s s s r s s m s

rational equivariant homotopy theory we give an algebraicization of rational s 1 equivariant homotopy theory there is an algebraic category of t systems which is equival nt to the a homotopy category of rational s 1 simply connected s 1 spaces there is is also a theory of minimal models for t systems analogous to sullivan mini nal algebras each s 1 space has an associated minimal t system whic ence des 2 all of its rational homotopy information including its rational equivariant cohomology and postnikov decomposition

behavior of test ideals under smooth and etale homomorphisms we investigate the behavior of the test ideal of an excellent reduced ring of prime characteristic under base change it is shown that if h a d is a smooth homomorphism then ad d assuming that all residue fields of a at maximal ideals are perfect and that formation of the test ideal commutes with localization it is also shown that if h a m d is a finite flat homomorphism of gorenstein normal rings etale in codimension 1 then ad d more generally this last result holds under the assumption that the closed fiber of h a m d is gorenstein provided one knows that the tight closure of zero and the finitistic tight closure of zero in the injective hulls of the residue fields of a and s are equal

semistable sheaves in positive characteristic we prove maruyama s conjecture on the boundedness of slope semistable sheaves on a projective variety defined over a noetherian ring our approach also gives a new proof of the boundedness for varieties defined over a characteristic zero field this result implies that in mixed characteristic the moduli spaces of gieseker semistable sheaves are projective schemes of finite type the proof uses a new inequality bounding slopes of the restriction of a sheaf to a hypersurface in terms of its slope and the discriminant this inequality also leads to effective restriction theorems in all characteristics improving earlier results in characteristic zero

optimizing the data dependent kernel under a unified kernel optimization framework the kernel functions play a central role in kernel methods accordingly over the years the optimization of kernel functions has been a promising research area ideally fisher discriminant criteria can be used as an objective function to optimize the kernel function to augment the margin between different classes unfortunately fisher criteria are optimal only in the case that all the classes are generated from underlying multivariate normal distributions of common covariance matrix but different means and each class is expressed by a single cluster due to the assumptions fisher criteria obviously are not a suitable choice as a kernel optimization rule in some applications such as the multimodally distributed data in order to solve this problem recently many improved discriminant criteria dc have been also developed therefore to apply these discriminant criteria to kernel optimization in this paper based on a data dependent kernel function we propose a unified kernel optimization framework which can use any discriminant criteria formulated in a pairwise manner as the objective functions under the kernel optimization framework to employ different discriminant criteria one has to only change the corresponding affinity matrices without having to resort to any complex derivations in feature space experimental results based on some benchmark data demonstrate the efficiency of our method

fisher regularized support vector machine this paper proposes fisher regularized support vector machine fishersvm fishersvm is a graph based supervised learning method fishersvm has two regularization terms maximum margin and fisher regularizations fishersvm aims to maximize the margin and minimize the within class scatter support vector machine svm and fisher discriminant analysis fda are two commonly used methods in machine learning and pattern recognition a combined method of the linear svm and fda called svm lda linear discriminant analysis has been proposed only for the linear case this paper generalizes this combined method to the nonlinear case from the view of regularization a fisher regularization is defined and incorporated into svm to obtain a fisher regularized support vector machine fishersvm in fishersvm there are two regularization terms the maximum margin regularization and fisher regularization which allow fishersvm to maximize the classification margin and minimize the within class scatter roughly speaking fishersvm can approximatively fulfill the fisher criterion and obtain good statistical separability this paper also discusses the connections of fishersvm to graph based regularization methods and the mathematical programming method to kernel fisher discriminant analysis kfda it shows that fishersvm can be thought of as a graph based supervised learning method or a robust kfda experimental results on artificial and real world data show that fishersvm has a promising generalization performance

reductions and special parts of closures abstract we provide an axiomatic framework for working with a wide variety of closure operations on ideals and submodules in commutative algebra including notions of reduction independence spread and special parts of closures this framework is applied to tight frobenius and integral closures applications are given to evolutions and special briancon skoda theorems

rapid and brief communication improving support vector data description using local density degree we propose a new support vector data description svdd incorporating the local density of a training data set by introducing a local density degree for each data point by using a density induced distance measure based on the degree we reformulate a conventional svdd experiments with various real data sets show that the proposed method more accurately describes training data sets than the conventional svdd in all tested cases

extension of weakly and strongly f regular rings by flat maps this is a preprint of an article published in the journal of algebra vol 241 2001 no 2 799 807

drops in joint hilbert kunz multiplicities and projective equivalence abstract given two m primary ideals a and i in a noetherian local or graded ring we introduce the level ideals of i with respect to a as a measure of the asymptotic growth of the drop in the joint hilbert kunz multiplicity e hk a t i e hk a t i x we study the properties that must hold for two ideals a b to determine the same level ideals for all i and we show that this is related to projective equivalence

density induced margin support vector machines this paper proposes a new classifier called density induced margin support vector machines dmsvms dmsvms belong to a family of svm like classifiers thus dmsvms inherit good properties from support vector machines svms e g unique and global solution and sparse representation for the decision function for a given data set dmsvms require to extract relative density degrees for all training data points these density degrees can be taken as relative margins of corresponding training data points moreover we propose a method for estimating relative density degrees by using the k nearest neighbor method we also show the upper bound on the leave out one error of dmsvms for a binary classification problem and prove it promising results are obtained on toy as well as real world data sets

f regularity does not deform we show that the property of f regularity does not deform and thereby settle a long standing open question in the theory of tight closure specifically we construct a three dimensional graded domain r which is not f regular or even f pure but has a quotient r tr which is f regular examples are constructed over fields of characteristic p 0 as well as over fields of characteristic zero 1 introduction throughout this paper all rings are commutative noethe rian and have an identity element the theory of tight closure was developed by melvin hochster and craig huneke in hh2 and draws attention to rings which have the property that all their ideals are tightly closed called weakly f regular rings the term f regular is reserved for rings all of whose localizations are weakly f regular a natural question that arose with the development of the the ory was whether the property of f regularity deforms i e if r m k is a local ring such that r tr is f regular for some nonzerodivisor t m m ustr be f regular see the epilogue of ho hochster and huneke showed that this is indeed true if the ring r is gorenstein hh3 and their work has been followed by various attempts at extending this result see akm si sm3 our pri mary goal here is to settle this question by constructing a family of examples to show that f regularity does not deform we shall throughout be considering graded rings but local examples can be obtained in all cases by localizing at the homogeneous maximal ideals our main result is theorem 1 1 there exists an graded ring r of dimension three finitely generated over a field r 0 k of characteristic p 2 which is not f pure but has an f regular quotient r tr where t m is a homogeneous nonzerodivisor specifically for positive integers m and n satisfying m m n 2 consider the ring r k a b c d t i where i is generated by the size two minors of the

f signature of pairs and the asymptotic behavior of frobenius splittings abstract we generalize f signature to pairs r d where d is a cartier subalgebra on r as defined by the first two authors in particular we show the existence and positivity of the f signature for any strongly f regular pair in one application we answer an open question of aberbach and enescu by showing that the f splitting ratio of an arbitrary f pure local ring is strictly positive furthermore we derive effective methods for computing the f signature and the f splitting ratio in the spirit of the work of r fedder

test ideals and base change problems in tight closure theory test ideals are an important concept in tight closure theory and their behavior via flat base change can be very difficult to understand our paper presents results regarding this behavior under flat maps with reasonably nice but far from smooth fibers this involves analyzing in depth a special type of ideal of test elements called the cs test ideal besides providing new results the paper also contains extensions of a theorem by g lyubeznik and k e smith on the completely stable test ideal and of theorems by f enescu and independently m hashimoto on the behavior of f rationality under flat base change

rapid and brief communiction possibilistic support vector machines we propose new support vector machines svms that incorporate the geometric distribution of an input data set by associating each data point with a possibilistic membership which measures the relative strength of the self class membership by using a possibilistic distance measure based on the possibilistic membership we reformulate conventional svms in three ways the proposed methods are shown to have better classification performance than conventional svms in various tests

the rationality of the hilbert kunz multiplicity in graded dimension two we show that the hilbert kunz multiplicity is a rational number for an r primary homogeneous ideal i f1 fn in a two dimensional graded domain r of finite type over an algebraically closed field of positive characteristic more specific we give a formula for the hilbert kunz multiplicity in terms of certain rational numbers coming from the strong harder narasimhan filtration of the syzygy bundle syz f1 fn on the projective curve y projr

asymptotic hilbert kunz multiplicity abstract for a pair m i where m is finitely generated graded module over a standard graded ring r of dimension d 2 and i is a graded ideal with l r i and generated by elements of the same degree we prove that lim q e 1 m i q q d exists where e 1 m i q denotes the first coefficient of the hilbert samuel polynomial of m i q we use this to get an expression for lim k e h k m i k e 0 m i k d k d 1 where e h k denotes the hilbert kunz multiplicity in particular if dim m d then we deduce that the difference e h k m i k e m i k d grows at least as a fixed positive multiple of k d 1 as k this is proved using renormalized hk density functions

semistability and hilbert kunz multiplicities for curves we study hilbert kunz multiplicity of non singular curves in positive characteristic we analyse the relationship between the frobenius semistability of the kernel sheaf associated with the curve and its ample line bundle and the hk multiplicity this leads to a lower bound achieved iff the kernel sheaf is frobenius semistable and otherwise to formulas for the hk multiplicity in terms of parameters measuring the failure of frobenius semistability as a byproduct an explicit example of a vector bundle on a curve is given whose n th iterated frobenius pullback is not semistable while its n 1 th such pullback is semistable where n 0 is arbitrary

maxi min margin machine learning large margin classifiers locally and globally in this paper we propose a novel large margin classifier called the maxi min margin machine m4 this model learns the decision boundary both locally and globally in comparison other large margin classifiers construct separating hyperplanes only either locally or globally for example a state of the art large margin classifier the support vector machine svm considers data only locally while another significant model the minimax probability machine mpm focuses on building the decision hyperplane exclusively based on the global information as a major contribution we show that svm yields the same solution as m4 when data satisfy certain conditions and mpm can be regarded as a relaxation model of m4 moreover based on our proposed local and global view of data another popular model the linear discriminant analysis can easily be interpreted and extended as well we describe the m4 model definition provide a geometrical interpretation present theoretical justifications and propose a practical sequential conic programming method to solve the optimization problem we also show how to exploit mercer kernels to extend m4 for nonlinear classifications furthermore we perform a series of evaluations on both synthetic data sets and real world benchmark data sets comparison with svm and mpm demonstrates the advantages of our new model

a locality correlation preserving support vector machine abstract this paper proposes a locality correlation preserving based support vector machine lcpsvm by combining the idea of margin maximization between classes and local correlation preservation of class data it is a support vector machine svm like algorithm which explicitly considers the locality correlation within each class in the margin and the penalty term of the optimization function canonical correlation analysis cca is used to reveal the hidden correlations between two datasets and a variant of correlation analysis model which implements locality preserving has been proposed by integrating local information into the objective function of cca inspired by the idea used in canonical correlation analysis we propose a locality correlation preserving within class scatter matrix to replace the within class scatter matrix in minimum class variance support machine mcvsvm this substitution has the property of keeping the locality correlation of data and inherits the properties of svm and other similar modified class of support vector machines lcpsvm is discussed under linearly separable small sample size and nonlinearly separable conditions and experimental results on benchmark datasets demonstrate its effectiveness

systems of fixed point sets let g be a compact lie group a canonical method is given for constructing a c space from homotopy theoretic information about its fixed point sets the construction is a special case of the categorical bar construction applications include easy constructions of certain classifying spaces as well as c eilenbergmac lane spaces and postnikov towers 0 introduction let g be a compact lie group and x a g space the equivariant homotopy theory of x is reflected to a remarkable extent in its system of fixed point sets defined as a functor from a certain category 0g to top the category of topological spaces our spaces will be compactly generated weak hausdorff they may or may not be equipped with a basepoint depending on the context these functors or systems have considerable technical advantages over g spaces it is easy to apply most homotopy theoretic constructions to them whereas in many cases it is unclear how to proceed for g spaces it is the purpose of this paper to present a canonical way of recovering from any system a g space which preserves all the homotopy theoretic structure of the system this allows us to give easy equivariant versions of some standard topological constructions such as eilenberg mac lane spaces and postnikov towers and to simplify other equivariant constructions 1 1 statements of the main theorems throughout g is a fixed compact lie group definitions the category of canonical orbits written 0g is a topological category with discrete object space 0g g 77 77 a closed subgroup of g and morphisms the g maps topologized by requiring the natural bijection hoxn0cig h g k g k h to be a homeomorphism by an oc space we shall mean a continuous contravariant functor from 0g to top these functors form the objects of a topological category in the usual manner we will also consider gg rings oc groups etc defined similarly definition let a1 be a g space the fixed point set system of x written x is an gg space defined as follows g 77 x received by the editors october 30 1981 and in revised form april 26 1982 1980 mathematics subject classification primary 57s10 55n25

face recognition using total margin based adaptive fuzzy support vector machines this paper presents a new classifier called total margin based adaptive fuzzy support vector machines taf svm that deals with several problems that may occur in support vector machines svms when applied to the face recognition the proposed taf svm not only solves the overfitting problem resulted from the outlier with the approach of fuzzification of the penalty but also corrects the skew of the optimal separating hyperplane due to the very imbalanced data sets by using different cost algorithm in addition by introducing the total margin algorithm to replace the conventional soft margin algorithm a lower generalization error bound can be obtained those three functions are embodied into the traditional svm so that the taf svm is proposed and reformulated in both linear and nonlinear cases by using two databases the chung yuan christian university cycu multiview and the facial recognition technology feret face databases and using the kernel fisher s discriminant analysis kfda algorithm to extract discriminating face features experimental results show that the proposed taf svm is superior to svm in terms of the face recognition accuracy the results also indicate that the proposed taf svm can achieve smaller error variances than svm over a number of tests such that better recognition stability can be obtained

big tight closure test elements for some non reduced excellent rings abstract this paper is concerned with existence of big tight closure test elements for a commutative noetherian ring r of prime characteristic p let r denote the complement in r of the union of the minimal prime ideals of r a big test element for r is an element of r which can be used in every tight closure membership test for every r module and not just the finitely generated ones the main results of the paper are that if r is excellent and satisfies condition r 0 and c r is such that r c is gorenstein and weakly f regular then some power of c is a big test element for r if i r is a homomorphic image of an excellent regular ring of characteristic p for which the frobenius homomorphism is intersection flat or ii r is f pure or iii r is local the gamma construction is not used