an extension to possibilistic fuzzy cluster analysis we explore an approach to possibilistic fuzzy clustering that avoids a severe drawback of the conventional approach namely that the objective function is truly minimized only if all cluster centers are identical our approach is based on the idea that this undesired property can be avoided if we introduce a mutual repulsion of the clusters so that they are forced away from each other we develop this approach for the possibilistic fuzzy c means algorithm and the possibilistic gustafson kessel algorithm in our experiments we found that in this way we can combine the partitioning property of the probabilistic fuzzy c means algorithm with the advantages of a possibilistic approach w r t the interpretation of the membership degrees

block monotone iterative methods for numerical solutions of nonlinear elliptic equations two block monotone iterative schemes for a nonlinear algebraic system which is a finite difference approximation of a nonlinear elliptic boundary value problem are presented and are shown to converge monotonically either from above or from below to a solution of the system this monotone convergence result yields a computational algorithm for numerical solutions as well as an existence comparison theorem of the system including a sufficient condition for the uniqueness of the solution an advantage of the block iterative schemes is that the thomas algorithm can be used to compute numerical solutions of the sequence of iterations in the same fashion as for one dimensional problems the block iterative schemes are compared with the point monotone iterative schemes of picard jacobi and gauss seidel and various theoretical comparison results among these monotone iterative schemes are given these comparison results demonstrate that the sequence of iterations from the block iterative schemes converges faster than the corresponding sequence given by the point iterative schemes application of the iterative schemes is given to a logistic model problem in ecology and numerical ressults for a test problem with known analytical solution are given

formulae for the derivatives of heat semigroups abstract formulae for the derivatives of solutions of diffusion equations are derived which clearly exhibit and allow estimation of the equations smoothing properties these also give formulae for the logarithmic gradient of the corresponding heat kernels extending and giving a very elementary proof of bismut s well known formula corresponding formulae are derived for solutions of heat equations for differential forms and their exterior derivatives

connections and curvature in the riemannian geometry of configuration spaces torsion free connections and a notion of curvature are introduced on the infinite dimensional nonlinear configuration space of a riemannian manifold m under a poisson measure this allows us to state identities of weitzenbock type and energy identities for anticipating stochastic integral operators the one dimensional poisson case itself gives rise to a non trivial geometry a de rham hodge kodaira operator and a notion of ricci tensor under the poisson measure the methods used in this paper have been thus far applied to d dimensional brownian path groups and rely on the introduction of a particular tangent bundle and associated damped gradient

switching regression models and fuzzy clustering a family of objective functions called fuzzy c regression models which can be used too fit switching regression models to certain types of mixed data is presented minimization of particular objective functions in the family yields simultaneous estimates for the parameters of c regression models together with a fuzzy c partitioning of the data a general optimization approach for the family of objective functions is given and corresponding theoretical convergence results are discussed the approach is illustrated by two numerical examples that show how it can be used to fit mixed data to coupled linear and nonlinear models

gaussian clustering method based on maximum fuzzy entropy interpretation abstract a new method of fuzzy clustering is proposed this is a complete gaussian membership function derived by means of the maximum entropy interpretation compared to the traditional fuzzy c means fcm method our approach exhibits the following two advantages 1 having clearer physical meaning and well defined mathematical features 2 having an optimal choice for feature parameter in theory moreover we also review some existing measures of uncertainty of fuzzy sets and redefine fuzzy entropy as analogous to probabilistic entropy

the vanishing of l2 harmonic one forms on based path spaces abstract we prove the triviality of the first l 2 cohomology class of based path spaces of riemannian manifolds furnished with brownian motion measure and the consequent vanishing of l 2 harmonic one forms we give explicit formulae for closed and co closed one forms expressed as differentials of functions and co differentials of l 2 two forms respectively these are considered as extended clark ocone formulae a feature of the proof is the use of the temporal structure of path spaces to relate a rough exterior derivative operator on one forms to the exterior differentiation operator used to construct the de rham complex and the self adjoint laplacian on l 2 one forms this laplacian is shown to have a spectral gap

de rham hodge kodaira operator on loop groups we consider a based loop group le g over a compact lie groupg endowed with its pinned wiener measure the law of the brownian bridge ong and we shall calculate the ricci curvature for differentialn forms over le g a type of bochner weitzenbock formula for general differentialn forms or shigekawa identity will be established

spectral gap on riemannian path space over static and evolving manifolds abstract in this article we continue the discussion of fang wu 2015 to estimate the spectral gap of the ornstein uhlenbeck operator on path space over a riemannian manifold of pinched ricci curvature along with explicit estimates we study the short time asymptotics of the spectral gap the results are then extended to the path space of riemannian manifolds evolving under a geometric flow our paper is strongly motivated by naber s recent work 2015 on characterizing bounded ricci curvature through stochastic analysis on path space

tangent processes on wiener space abstract this paper deals with the study of the malliavin calculus of euclidean motions on wiener space i e transformations induced by general measure preserving transformations called rotations and h valued shifts and the associated flows on abstract wiener spaces

a class of vector fields on path spaces abstract in this paper we show that the vector fieldx hon a based path spacewo m over a riemannian manifoldmdefined by parallel translating a curvehin the initial tangent spacetomvia an affine connection induces a solution flow which preserves the wiener measure on the based path spacewo m provided the affine connection is adjoint skew symmetric in the case when is a metric connection then is adjoint skew symmetric if and only if is torsion skew symmetric

absolutely continuous flows generated by sobolev class vector fields in finite and infinite dimensions abstract we prove the existence of the global flow ut generated by a vector field a from a sobolev class w1 1 on a finite or infinite dimensional space x with a measure provided is sufficiently smooth and that a a and a where a is the divergence with respect to are exponentially integrable in addition the measure is shown to be quasi invariant under ut in the case x r n and p dx where p w1 1loc r n is a locally uniformly positive probability density a sufficient condition is exp c a exp c a p p l1 for all c in the infinite dimensional case we get analogous results for measures differentiable along sufficiently many directions examples of measures which fit our framework important for applications are symmetric invariant measures of infinite dimensional diffusions and gibbs measures typically in both cases such measures are essentially non gaussian our result in infinite dimensions significantly extends previously studied cases where was a gaussian measure finally we study flows generated by vector fields whose values are not necessarily in the cameron martin space

flow equations on spaces of rough paths abstract given an ito vector fieldm there is a unique solution t h to the differential equation d t h dt m t h 0 h h for any continuous and piece wisely smooth pathh we show that for anyt r the maph t h is continuous in thep variation topology for anyp 1 so that it uniquely extends to a solution flow on the space of all geometric rough paths applying this result to the driver s geometric flow equation on the path space over a closed riemannian manifold d t dt x h t 0 id wherexhis the vector field defined by parallel translatinghvia a connection our result especially yields a deterministic construction of the driver s flow

flows associated to tangent processes on the wiener space we prove under certain regularity assumptions on the coefficients that tangent processes namely semimartingales d a dx b d where a is an antisymmetric matrix generate flows on the classical wiener space main applications of the result can be found in the study of the geometry of path spaces

interval type 2 relative entropy fuzzy c means clustering fuzzy set theory especially type 2 fuzzy set theory provides an efficient tool for handling uncertainties and vagueness in real world observations among various clustering techniques type 2 fuzzy clustering methods are the most effective methods in the case of having no prior knowledge about observations while uncertainties in type 2 fuzzy clustering parameters are investigated by researchers uncertainties associated with membership degrees are not very well discussed in the literature in this paper investigating the latter uncertainties is our concern and interval type 2 relative entropy fuzzy c means it2 refcm clustering method is proposed the computational complexity of the proposed method is discussed and its performance is examined using several experiments the obtained results show that the proposed method has a very good ability in detecting noises and assignment of suitable membership degrees to observations

integration by parts formulas and dilatation vector fields on elliptic probability spaces by coupling two arbitrary riemannian connections and on a riemannian manifold m we perform the stochastic calculus of variation on the path space p m of the manifold m the method uses direct calculations on ito s stochastic differential equations in this context we obtain intertwinning formulas with the ito map for first order operators on the path space p m of m by a judicious choice of the second connection in terms of the connection we can prolongate the intertwinning formulas to second order differential operators thus we obtain expressions of heat operators on the path space p m of a riemannian manifold m endowed with an arbitrary connection the integration by parts of the laplacians on p m leads us to the notion of dilatation vector field on the path space

markovian connection curvature and weitzenbock formula on riemannian path spaces abstract we shall consider on a riemannian path space p m o m the cruzeiro malliavin s markovian connection the laplace operator will be defined as the divergence of the gradient we shall compute explicitly the associated curvature tensor a weitzenbock formula will be established to this end we shall introduce an inner product between the tangent processes and simple vector fields

weak levi civita connection for the damped metric on the riemannian path space and vanishing of ricci tensor in adapted differential geometry abstract we shall establish in the context of adapted differential geometry on the path space p m o m a weitzenbock formula which generalizes that in a b cruzeiro and p malliavin j funct anal 177 2000 219 253 without hypothesis on the ricci tensor the renormalized ricci tensor will be vanished the connection introduced in a b cruzeiro and s fang 1997 j funct anal 143 400 414 will play a central role

deterministic annealing gustafson kessel fuzzy clustering algorithm abstract the gustafson and kessel gk fuzzy clustering algorithm proposed by gustafson and kessel in 1979 was the first important extension to the fuzzy c means fcm algorithm up to now the gk algorithm had become one of the most commonly used fuzzy clustering algorithms where the mahalanobis distance is used as a dissimilarity measure to provide more effectiveness and robustness than the fcm algorithm recently chaomurilige et al 2015 proposed a theoretical analysis on the parameter selection for the gk algorithm in which they indicated that the parameter of the fuzziness index heavily influences the performance of the gk algorithm in this paper we propose a novel gk fuzzy clustering algorithm based on the deterministic annealing approach for decreasing the effect of parameters we first consider maximizing the shannon s entropy of membership functions to the gk objective function and then use deterministic annealing to adjust the annealing parameter we also mathematically provide a theoretical initialization lower bound for the annealing parameter of the proposed deterministic annealing gk da gk algorithm comparisons between the da gk algorithm and other methods are made the computational complexity of the proposed method is also provided experimental results and comparisons actually verify theoretical results and also indicate the superiority and effectiveness of the proposed da gk algorithm

finite dimensional approximations to wiener measure and path integral formulas on manifolds abstract certain natural geometric approximation schemes are developed for wiener measure on a compact riemannian manifold these approximations closely mimic the informal path integral formulas used in the physics literature for representing the heat semi group on riemannian manifolds the path space is approximated by finite dimensional manifolds h p m consisting of piecewise geodesic paths adapted to partitions p of 0 1 the finite dimensional manifolds h p m carry both an h 1 and a l 2 type riemannian structures g 1 p and g 0 p respectively it is proved that 1 z i p e 1 2 e d vol g i p i d as mesh p 0 where e is the energy of the piecewise geodesic path h p m and for i 0 and 1 z i p is a normalization constant vol g i p is the riemannian volume form relative to g i p and is wiener measure on paths on m here 1 1 and 0 exp 1 6 1 0 scal s ds where scal is the scalar curvature of m these results are also shown to imply the well known integration by parts formula for the wiener measure

relative entropy collaborative fuzzy clustering method the main task of clustering methods especially fuzzy methods is to find whether natural grouping exists in data and to impose identity on them in some situations data are stored in several data sites and to discover the global structures clustering methods have to be aware of dependencies in all data sites collaborative fuzzy clustering methods have been proposed and widely studied to answer such need in this paper a novel collaborative fuzzy clustering method is proposed in this method relative entropy concept is used as the communication method a new approach is applied to calculate the interaction coefficient between data sites and horizontal and vertical modes of the proposed method are discussed performance of the proposed method is evaluated using several experiments and the results show that it has the highest quality of collaboration and could classify data more efficiently in many clustering methods it is assumed that the data are stored in one data site ways of communication between data sites effects the clustering results a new communication method based on relative entropy is proposed it minimizes the divergence of membership degrees of kth data in ith cluster in all data sites recfc and its two modes could efficiently classify data stored in several data sites

finite dimensional approximation of riemannian path space geometry abstract in this paper we construct a finite dimensional approximation for the geometry on the path space over a compact riemannian manifold this approximation allows to construct the horizontal lift of the ornstein uhlenbeck process on the path space through the markovian connection we also prove a representation formula for the heat semigroup on adapted vector fields as well as a commutation formula for its derivative

numerical evaluation of the lambert w function and application to generation of generalized gaussian noise with exponent 1 2 we address the problem of synthesizing a generalized gaussian noise with exponent 1 2 by means of a nonlinear memoryless transformation applied to a uniform noise we show that this transformation is expressable in terms of a special function known under the name of the lambert w function we review the main methods for numerical evaluation of the relevant branch of the multivalued lambert w function with controlled accuracy and complement them with an original rational function approximation based on these methods synthesis of the generalized gaussian noise can be performed with arbitrary accuracy we construct a simple and fast evaluation algorithm with prescribed accuracy which is especially suited for monte carlo simulation requiring large numbers of realizations of the generalized gaussian noise

functional inequality on path space over a non compact riemannian manifold abstract we prove the existence of the o u dirichlet form and the damped o u dirichlet form on path space over a general non compact riemannian manifold which is complete and stochastically complete we show a weighted log sobolev inequality for the o u dirichlet form and the standard log sobolev inequality for the damped o u dirichlet form in particular the poincare inequality and the super poincare inequality can be established for the o u dirichlet form on path space over a class of riemannian manifolds with unbounded ricci curvatures moreover we construct a large class of quasi regular local dirichlet forms with unbounded random diffusion coefficients on path space over a general non compact manifold

relative entropy fuzzy c means clustering pattern recognition is a collection of computer techniques to classify various observations into different clusters of similar attributes in either supervised or unsupervised manner application of fuzzy logic to unsupervised classification or clustering methods has resulted in many wildly used techniques such as fuzzy c means fcm method however when the observations are too noisy the performance of such methods might be reduced thus in this paper a new fuzzy clustering method based on fcm is presented and the relative entropy is added to its objective function as a regularization function to maximize the dissimilarity between clusters several examples are provided to examine the performance of the proposed clustering method the obtained results show that the proposed method has a very good ability in detecting noises and assignment of suitable membership degrees to the observations

monotone iterations for numerical solutions of nonlinear elliptic partial differential equations11this work was supported by the natural sciences and engineering research council of canada employing a weighted difference scheme and the method of upper lower solutions we develop a monotone iterative scheme for the computation of solutions of nonlinear elliptic partial differential equations in each iteration we need only solve a linear system of which the coefficient matrix is an m matrix generally this matrix is nonsymmetric in contrast to the midly nonlinear problems however the squared conjugate gradient cgs method together with the diagonal preconditioning technique are proven to be very effective numerical results that are given for the nonlinear burger s equation clearly demonstrate the advantages of our method

integration by parts formula and logarithmic sobolev inequality on the path space over loop groups the geometric stochastic analysis on the riemannian path space developed recently gives rise to the concept of tangent processes roughly speaking it is the infinitesimal version of the girsanov theorem using this concept we shall establish a formula of integration by parts on the path space over a loop group following the martingale method developed in capitaine hsu and ledoux we shall prove that the logarithmic sobolev inequality holds on the full paths as a particular case of our result we obtain the driver lohrenz s heat kernel logarithmic sobolev inequalities over loop groups the stochastic parallel transport introduced by driver will play a crucial role

reducing the time complexity of the fuzzy c means algorithm in this paper we present an efficient implementation of the fuzzy c means clustering algorithm the original algorithm alternates between estimating centers of the clusters and the fuzzy membership of the data points the size of the membership matrix is on the order of the original data set a prohibitive size if this technique is to be applied to very large data sets with many clusters our implementation eliminates the storage of this data structure by combining the two updates into a single update of the cluster centers this change significantly affects the asymptotic runtime as the new algorithm is linear with respect to the number of clusters while the original is quadratic elimination of the membership matrix also reduces the overhead associated with repeatedly accessing a large data structure empirical evidence is presented to quantify the savings achieved by this new method

a cameron martin type quasi invariance theorem for brownian motion on a compact riemannian manifold abstract let m be a compact manifold without boundary o be a fixed base point in m g be a riemannian metric on m and be a g compatible covariant derivative on tm the tangent space to m assume the torsion t of satisfies the skew symmetry condition g t x y y 0 for all vector fields x and y on m for example take to be the levi civita covariant derivative on m g also let denote the wiener measure on w0 m c 0 1 m 0 o and let h s denote stochastic parallel translation relative to along the path w0 m up to time s 0 1 given a c1 function h 0 1 t0m it is shown that the differential equation t h t h with initial condition 0 id w m w m has a solution r maps w m w m the measurable maps from w m to w m this function is a flow on w m i e for all t r t t furthermore t has the quasi invariance property the law t of t with respect to the wiener measure is equivalent to for all t r this result is used to prove an integration by parts formula for the h derivative hf defined by h f d dt 0 f t where f is a c2 cylinder function on w m

integration by parts and quasi invariance for the horizontal wiener measure on foliated compact manifolds abstract we prove several sub riemannian versions of driver s integration by parts formula which first appeared in 17 namely our results are for the horizontal wiener measure on a totally geodesic riemannian foliation equipped with a sub riemannian structure it is also shown that the horizontal wiener measure is quasi invariant under the action of flows generated by suitable tangent processes

monotone iterative methods for differential systems with finite delay this paper presents iterative methods for nonlinear differential systems with finite delay the basic idea of the iterative method is the monotone approach which involves the notion of upper and lower solutions and the construction of monotone sequences this approach provides constructive proof of existence as well as numerical procedures for computation of solutions

flows associated to adapted vector fields on the wiener space the existence and uniqueness of a flow associated to an adapted vector field on the wiener space with d a d b d are proved by a modified picard s iteration method mainly under the conditions of exponential integrability concerning b as well as the first order malliavin gradients of a and b a newton leibnitz type inequality for a kind of malliavin differentiable functionals is also proved which is the key point to prove the above result and has an independent interest

a weighted difference scheme and monotone iterative methods for quasilinear boundary value problems abstract we consider the boundary value problem y xx f x y y x g x y 0 0 x y 0 b 0 y 1 b 1 we present a weighted two sided difference scheme to approximate the differential equation monotone iterative methods are proposed to solve the resulting nonlinear system the scheme applies equally well to multidimensional analogues numerical results are included

stochastic calculus of variations on complex line bundle and construction of unitarizing measures for the poincare disk abstract holomorphic representation of lie algebra can be realized through kahlerian symplectic formalism underlying holomorphic convexity requires then the introduction of elliptic operators with complex coefficients we construct the stochastic calculus of variations for those elliptic operators remote past vanishing of projections of the underlying process implies convergence in law then limit laws lead to the unitarizing measure of the given representation this general approach is developed in full details on poincare disk

numerical solutions for some coupled systems of nonlinear boundary value problems in the well known volterra lotka model concerning two competing species with diffusion the densities of the species are governed by a coupled system of reaction diffusion equations the aim of this paper is to present an iterative scheme for the steady state solutions of a finite difference system which corresponds to the coupled nonlinear boundary value problems this iterative scheme is based on the method of upper lower solutions which leads to two monotone sequences from some uncoupled linear systems it is shown that each of the two sequences converges to a nontrivial solution of the discrete equations the model under consideration may have one two or three nonzero solutions and each of these solutions can be computed by a suitable choice of initial iteration numerical results are given for these solutions under both the dirichlet boundary condition and the mixed type boundary condition

a new fuzzy c means method with total variation regularization for segmentation of images with noisy and incomplete data the objective function of the original fuzzy c mean method is modified by a regularizing functional in the form of total variation tv with regard to gradient sparsity and a regularization parameter is used to balance clustering and smoothing an alternating direction method of multipliers in conjunction with the fast discrete cosine transform is used to solve the tv regularized optimization problem the new algorithm is tested on both synthetic and real data and is demonstrated to be effective and robust in treating images with noise and missing data incomplete data

logarithmic sobolev inequalities for pinned loop groups abstract letgbe a connected compact type lie group equipped with anadg invariant inner product on the lie algebra g ofg given this data there is a well known left invariant h1 riemannian structure on l l g the infinite dimensional group of continuous based loops ing using this riemannian structure we define and construct a heat kernel t g0 associated to the laplace beltrami operator on l g heret 0 g0 l g and t g0 is a certain probability measure on l g for fixedg0 l g andt 0 we use the measure t g0 and the riemannian structure on l g to construct a classical pre dirichlet form the main theorem of this paper asserts that this pre dirichlet form admits a logarithmic sobolev inequality

stochastic analysis on the path space of a riemannian manifold i markovian stochastic calculus abstract on the brownian flow of a compact riemannian manifold an intrinsic stochastic calculus is defined this calculus is markovian the stochastic calculus of variation on the bundle of orthonormal frames appears only as an intermediate tool the bismut connection plays a paramount role in the final construction

diffusions on path and loop spaces existence finite dimensional approximation and holder continuity we construct ornstein uhlenbeck processes and more general diffusion processes on path and loop spaces of riemannian manifolds by finite dimensional approximation we also show holder continuity of the sample paths w r t the supremum norm the proofs are based on the lyons zheng decomposition

a novel kernel fuzzy clustering algorithm for geo demographic analysis we proposed a novel kernel based fuzzy clustering for geo demographic analysis it relied on gaussian kernel function updated elements and standardized weights the algorithm was both theoretical and experimental validated its clustering quality was better than those of other relevant algorithms some properties of solutions were examined geo demographic analysis gda is a major concentration of various interdisciplinary researches and has been used in many decision making processes regarding the provision and distribution of products and services in society machine learning methods namely principal component analysis self organizing map k means fuzzy clustering and fuzzy geographically weighted clustering were proposed to enhance the quality of gda among them the state of the art method modified intuitionistic possibilistic fuzzy geographically weighted clustering mipfgwc has some drawbacks such as i using the euclidean similarity measure often results in high error rate and sensitivity to noises and outliers ii updating the membership matrix by the spatial interaction modification model sim2 model leads to new centers not being geographically aware in this paper we present a novel fuzzy clustering algorithm named as kernel fuzzy geographically clustering kfgc that utilizes both the kernel similarity function and the new update mechanism of the sim2 model to remedy the disadvantages of mipfgwc some supported properties and theorems of kfgc are also examined in the paper specifically the differences between solutions of kfgc and those of mipfgwc and of some variants of kfgc are theoretically validated lastly experimental analysis is performed to compare the performance of kfgc with those of the relevant algorithms in terms of clustering quality

explicit stochastic analysis of brownian motion and point measures on riemannian manifolds abstract the gradient and divergence operators of stochastic analysis on riemannian manifolds are expressed using the gradient and divergence of the flat brownian motion by this method we obtain the almost sure version of several useful identities that are usually stated under expectations the manifold valued brownian motion and random point measures on manifolds are treated successively in the same framework and stochastic analysis of the brownian motion on a riemannian manifold turns out to be closely related to classical stochastic calculus for jump processes in the setting of point measures we introduce a damped gradient that was lacking in the multidimensional case

dilatation vector fields on the loop group abstract on the loop space l g over a compact connected lie group g we explicitly determine the first order differential operator c t dilatation vector field such that the heat equation holds with respect to the wiener measure l t defined on the loop space

renormalized differential geometry on path space structural equation curvature abstract the theory of integration in infinite dimensions is in some sense the backbone of probability theory on this backbone the stochastic calculus of variations has given rise to the flesh of differential calculus its first step is the construction at each point of the probability space of a cameron martin like tangent space in which the desired differential calculus can be developed this construction proceeds along the lines of first order differential geometry in this paper we address the following questions what could be the meaning of curvature of the probability space how and why how can curvatures be defined and computed why could a second order differential geometry be relevant to stochastic analysis we try to answer these questions for the probability space associated to the brownian motion of a compact riemannian manifold why a basicenergy identity for anticipative stochastic integralswill be obtained as a byproduct of our computation of curvature how there are essentially four bottlenecks in the development of differential geometry on wiener riemann manifolds i the difficulty of finding an atlas of local charts such that the changes of charts preserve the class of the wiener like measures together with their associated cameron martin like tangent spaces ii the difficulty of finding cylindrical approximations preserving the natural geometrical objects iii the difficulty of renormalizing the divergent series to which the summation operations of finite dimensional differential geometry give rise in the non intrinsic context of local charts iv the nonavailability of the computational procedures analogous to the local coordinates systems of the classical differential geometry in the context of path space the ito filtration provides a much richer structure than that available in the framework of an abstract wiener riemann manifold our work is a systematic attempt to replace the machinery of local charts with amethodology of moving frames in our context stochastic parallel transport provides a canonical moving frame on the path space the concept of a cylindrical approximation has to be reshaped in our new situation into some geometric limit theorems establishing that the riemannian geometric objects of the cylindrical approximations induce by a limiting procedure geometric objects on the path space those limit theorems are reminiscent of the classical theorems which say that a stratonovich sde is the limit of an appropriate sequence of ode the canonical coordinate system provided by the moving frame will make it possible to proceed to the needed renormalizations byintrinsicstochastic integrals in this context the anticipative stochastic integral theory of nualart and pardoux will play a decisive role finally the moving frame will provide aneffective algorithm of computation for this differential geometry in infinite dimensions in our study we encounter a new type of renormalization thehypoelliptic renormalization which corresponds to the fact that the bracket of smooth vector fields taking their values in the cameron martin space can get out of this cameron martin space this hypoelliptic problem induces the nonrenormalizability of some geometrical objects it leads also to a concept oftangent processesto probability spaces extending that based on the cameron martin theorem for tangent processes a formula of integration by parts still holds furthermore the tangent processes form a lie algebra under the bracket on the other hand tangent processes cannot be stochastically integrated this operation is well defined only for cameron martin type vector fields

asymptotic behavior of divergences and cameron martin theorem on loop spaces we first prove the lp convergence p 1 and a fernique type exponential integrability of divergence functionals for all cameron martin vector fields with respect to the pinned wiener measure on loop spaces over a compact riemannian manifold we then prove that the driver flow is a smooth transform on path spaces in the sense of the malliavin calculus and has an quasi continuous modification which can be quasi surely well defined on path spaces this leads us to construct the driver flow on loop spaces through the corresponding flow on path spaces combining these two results with the cruzeiro lemma j funct anal 54 1983 206 227 we give an alternative proof of the quasi invariance of the pinned wiener measure under driver s flow on loop spaces which was established earlier by driver trans amer math soc 342 1994 375 394 and enchev and stroock adv math 119 1996 127 154 by doob s h processes approach together with the short time estimates of the gradient and the hessian of the logarithmic heat kernel on compact riemannian manifolds we also establish the lp convergence p 1 and a fernique type exponential integrability theorem for the stochastic anti development of pinned brownian motions on compact riemannian manifold with an explicit exponential exponent our results generalize and sharpen some earlier results due to gross j funct anal 102 1991 268 313 and hsu math ann 309 1997 331 339 our method does not need any heat kernel estimate and is based on quasi sure analysis and sobolev estimates on path spaces

quasi invariance of brownian measures on the group of circle homeomorphisms and infinite dimensional riemannian geometry abstract a cameron martin type theorem is proved for the canonical brownian motion on the group of homeomorphisms of the circle

the divergence of banach space valued random variables on wiener space the domain of definition of the divergence operator on an abstract wiener space w h is extended to include w valued and open image in new window valued integrands the main properties and characterizations of this extension are derived and it is shown that in some sense the added elements in s extended domain have divergence zero these results are then applied to the analysis of quasiinvariant flows induced by w valued vector fields and among other results it turns out that these divergence free vector fields are responsible for generating measure preserving flows

fuzzy clustering of time series in the frequency domain traditional and fuzzy cluster analyses are applicable to variables whose values are uncorrelated hence in order to cluster time series data which are usually serially correlated one needs to extract features from the time series the values of which are uncorrelated the periodogram which is an estimator of the spectral density function of a time series is a feature that can be used in the cluster analysis of time series because its ordinates are uncorrelated additionally the normalized periodogram and the logarithm of the normalized periodogram are also features that can be used in this paper we consider a fuzzy clustering approach for time series based on the estimated cepstrum the cepstrum is the spectrum of the logarithm of the spectral density function we show in our simulation studies for the typical generating processes that have been considered fuzzy clustering based on the cepstral coefficients performs very well compared to when it is based on other features

stochastic jacobi fields and vector fields induced by varying area on path spaces we study two classes of vector fields on the path space over a closed manifold with a wiener riemannian measure by adopting the viewpoint of yang mills field theory we study a vector field defined by varying a metric connection we prove that the vector field obtained in this way satisfies a jacobi field equation which is different from that of classical one by taking in account that a brownian motion is invariant under the orthogonal group action so that it is a geometric vector field on the space of continuous paths and induces a quasi invariant solution flow on the path space the second object of this paper is vector fields obtained by varying area here we follow the idea that a continuous semimartingale is indeed a rough path consisting of not only the path in the classical sense but also its levy area we prove that the vector field obtained by parallel translating a curve in the initial tangent space via a connection is just the vector field generated by translating the path along a direction in the cameron martin space in the malliavin calculus sense and at the same time changing its levy area in an appropriate way this leads to a new derivation of the integration by parts formula on the path space

frame bundle of riemannian path space and ricci tensor in adapted differential geometry abstract the vanishing of the renormalized ricci tensor of the path space above a ricci flat riemannian manifold is discussed

le processus d ornstein uhlenbeck sur l espace des chemins riemanniens et le probleme des martingales resume we discuss the ornstein uhlenbeck process over a compact riemannian manifold in the framework of a martingale problem we obtain a solution to this problem as the limit of approximate finite dimensional processes to this end we prove a kolmogorov type estimate by making use of an expression of the ornstein uhlenbeck operator

the geometry of loop groups l espace g des boucles basees sur un groupe de lie compact admet une metrique de kahler on exprime sa courbure en termes d operateurs de toeplitz et on definit des classes de chern par analogie avec la theorie de chern weil aux dimensions finies il y a une structure de fredhohn naturelle sur g induite a partir de la famille des operateurs de toeplitz on obtient des formules explicites pour su n

the fuzzy c spherical shells algorithm a new approach the fuzzy c spherical shells fcss algorithm is specially designed to search for clusters that can be described by circular arcs or generally by shells of hyperspheres a new approach to the fcss algorithm is presented this algorithm is computationally and implementationally simpler than other clustering algorithms that have been suggested for this purpose an unsupervised algorithm which automatically finds the optimum number of clusters is not known it uses a cluster validity measure to identify good clusters merges all compatible clusters and eliminates spurious clusters to achieve the final results experimental results on several data sets are presented

stochastic anticipative integrals on a riemannian manifold we shall use the nualart pardoux approach to the skorohod integral on rd to construct the divergence operator on the path space over a riemannian manifold the cruzeiro malliavin structure equation on the path space is crucial for us to obtain the energy inequality

a possibilistic fuzzy c means clustering algorithm in 1997 we proposed the fuzzy possibilistic c means fpcm model and algorithm that generated both membership and typicality values when clustering unlabeled data fpcm constrains the typicality values so that the sum over all data points of typicalities to a cluster is one the row sum constraint produces unrealistic typicality values for large data sets in this paper we propose a new model called possibilistic fuzzy c means pfcm model pfcm produces memberships and possibilities simultaneously along with the usual point prototypes or cluster centers for each cluster pfcm is a hybridization of possibilistic c means pcm and fuzzy c means fcm that often avoids various problems of pcm fcm and fpcm pfcm solves the noise sensitivity defect of fcm overcomes the coincident clusters problem of pcm and eliminates the row sum constraints of fpcm we derive the first order necessary conditions for extrema of the pfcm objective function and use them as the basis for a standard alternating optimization approach to finding local minima of the pfcm objective functional several numerical examples are given that compare fcm and pcm to pfcm our examples show that pfcm compares favorably to both of the previous models since pfcm prototypes are less sensitive to outliers and can avoid coincident clusters pfcm is a strong candidate for fuzzy rule based system identification

asymptotic ergodicity of the process of conditional law in some problem of non linear filtering abstract we consider a sample of a trajectory of an ergodic process m x through a stationary noisy observation process we study the asymptotic ergodicity of the phase process