rough support vector regression abstract this paper describes the relationship between support vector regression svr and rough or interval patterns svr is the prediction component of the support vector techniques rough patterns are based on the notion of rough values which consist of upper and lower bounds and are used to effectively represent a range of variable values predictions of rough values in a variety of different forms within the context of interval algebra and fuzzy theory are attracting research interest an extension of svr called rough support vector regression rsvr is proposed to improve the modeling of rough patterns in particular it is argued that the upper and lower bounds should be modeled separately the proposal is shown to be a more flexible version of lower possibilistic regression model using insensitivity experimental results on the dow jones industrial average demonstrate the suggested rsvr modeling technique

exact dimensional reduction of linear dynamics application to confined diffusion in their stochastic versions dynamical systems take the form of the linear dynamics of a probability distribution we show that exact dimensional reduction of such systems can be carried out and is physically relevant when the dimensions to be eliminated can be identified with those that represent transient behavior disappearing under typical coarse graining application is made to non uniform quasi low dimensional diffusion resulting in a systematic extension of the classical fick jacobs approximate reduction to an exact subdynamics

mapping of forced diffusion in quasi one dimensional systems diffusion in an external potential in a two dimensional channel of varying cross section is considered we show that a rigorous mapping procedure applied on the corresponding smoluchowski equation yields a one dimensional evolution equation of the fick jacobs type corrected by an effective coefficient d x the procedure enables us to derive this function within a recurrence scheme we test this result on a model of stationary diffusion in a linear cone in a homogeneous potential which is exactly solvable extension of the approximate formulas for d x derived for the diffusion alone is discussed

classical diffusion in channels with a spatially varying cross section we study the diffusion of classical particles in channels with varying boundaries the problem is characterized by the neumann boundary condition zero normal current in contrast to the dirichlet boundary condition zero function for quantum confinement problems eliminating transverse modes we derive an effective diffusion equation that describes particle propagation in the space of reduced dimension in the presence of a frozen drift field the latter stems from boundary variations of the original boundary problem boundary variations may thus result in an appreciable change of the particle transport and in particular in a nonlinear response to an external field we show also that there is a difference between the nonlinear responses of open and closed channels

clustering based on gaussian processes in this letter we develop a gaussian process model for clustering the variances of predictive values in gaussian processes learned from a training data are shown to comprise an estimate of the support of a probability density function the constructed variance function is then applied to construct a set of contours that enclose the data points which correspond to cluster boundaries to perform clustering tasks of the data points an associated dynamical system is built and its topological invariant property is investigated the experimental results show that the proposed method works successfully for clustering problems with arbitrary shapes

frsvc towards making support vector clustering consume less abstract in spite of with great advantage of discovering arbitrary shapes of clusters support vector clustering svc is frustrated by large scale data especially on resource limited platform it is due to pricey storage and computation consumptions from solving dual problem and labeling clusters upon the pre computed kernel matrix and sampling point pairs respectively towards on it we first present a dual coordinate descent method to reformulate the solver that leads to a flexible training phase carried out on any runtime platform with without sufficient memory then a novel labeling phase who does connectivity analysis between two nearest neighboring decomposed convex hulls referring to clusters is proposed in which a new designed strategy namely sample once connected checking first tries to reduces the scope of sampling analysis by integrating them together a faster and reformulated svc frsvc is created with less consumption achieved according to comparative analysis of time and space complexities furthermore experimental results confirm a significant improvement on flexibility of selective efficiency without losing accuracy with which a balance can be easily reached on the basis of resources a platform equipped

mapping of diffusion in a channel with soft walls we study diffusion of pointlike particles biased toward the x axis by a quadratic potential u x y ensuremath kappa x y 2 this system mimics a channel with soft walls of some varying effective cross section a x depending on the stiffness ensuremath kappa x we show that diffusion in this geometry can also be mapped rigorously onto the longitudinal coordinate x by a procedure known for channels with hard walls p kalinay and j k percus phys rev e 74 041203 2006 i e we arrive at a one dimensional evolution equation of the fick jacobs type on the other hand the calculation presented serves as a prototype for mapping of the smoluchowski equation with a wide class of potentials u x y varying in both the longitudinal as well as the transverse directions which is necessary for understanding e g stochastic resonance

kernel fuzzy c means with automatic variable weighting this paper presents variable wise kernel fuzzy c means clustering methods in which dissimilarity measures are obtained as sums of euclidean distances between patterns and centroids computed individually for each variable by means of kernel functions the advantage of the proposed approach over the conventional kernel clustering methods is that it allows us to use adaptive distances which change at each algorithm iteration and can either be the same for all clusters or different from one cluster to another this kind of dissimilarity measure is suitable to learn the weights of the variables during the clustering process improving the performance of the algorithms another advantage of this approach is that it allows the introduction of various fuzzy partition and cluster interpretation tools experiments with synthetic and benchmark datasets show the usefulness of the proposed algorithms and the merit of the fuzzy partition and cluster interpretation tools

spectral embedded clustering a framework for in sample and out of sample spectral clustering spectral clustering sc methods have been successfully applied to many real world applications the success of these sc methods is largely based on the manifold assumption namely that two nearby data points in the high density region of a low dimensional data manifold have the same cluster label however such an assumption might not always hold on high dimensional data when the data do not exhibit a clear low dimensional manifold structure e g high dimensional and sparse data the clustering performance of sc will be degraded and become even worse than k means clustering in this paper motivated by the observation that the true cluster assignment matrix for high dimensional data can be always embedded in a linear space spanned by the data we propose the spectral embedded clustering sec framework in which a linearity regularization is explicitly added into the objective function of sc methods more importantly the proposed sec framework can naturally deal with out of sample data we also present a new laplacian matrix constructed from a local regression of each pattern and incorporate it into our sec framework to capture both local and global discriminative information for clustering comprehensive experiments on eight real world high dimensional datasets demonstrate the effectiveness and advantages of our sec framework over existing sc methods and k means based clustering methods our sec framework significantly outperforms sc using the nystrom algorithm on unseen data

learning representative exemplars using one class gaussian process regression abstract an exemplar is an observation that represents a group of similar observations exemplars from data are examined to divide entire heterogeneous data into several homogeneous subgroups wherein each subgroup is represented by an exemplar with its inherent sparsity an exemplar based learning model provides a parsimonious model to represent or cluster large scale data a novel exemplar learning method using one class gaussian process gp regression is proposed in this study the proposed method constructs data distribution support from one class gp regression using automatic relevance determination prior and heterogeneous gp noise exemplars that correspond to the basis vectors of the constructed support function are then automatically located during the training process the proposed method is applied to various data sets to examine its operability characteristics of data representation and cluster analysis the exemplars of some real data generated by the proposed method are also reported

dynamics of a closed rod with twist and bend in fluid we investigate the instability and subsequent dynamics of a closed rod with twist and bend in a viscous incompressible fluid a new version of the immersed boundary ib method is used in which the immersed boundary applies torque as well as force to the surrounding fluid and in which the equations of motion of the immersed boundary involve the local angular velocity as well as the local linear velocity of the fluid an important feature of the ib method in this context is that self crossing of the rod is automatically avoided because the rod moves in a continuous interpolated velocity field a rod with a uniformly distributed twist that has been slightly perturbed away from its circular equilibrium configuration is used as an initial condition with the fluid initially at rest if the twist in the rod is sufficiently small the rod simply returns to its circular equilibrium configuration but for larger twists that equilibrium configuration becomes unstable and the rod undergoes large excursions before relaxing to a stable coiled configuration

semi supervised clustering via multi level random walk a key issue of semi supervised clustering is how to utilize the limited but informative pairwise constraints in this paper we propose a new graph based constrained clustering algorithm named scrawl it is composed of two random walks with different granularities in the lower level random walk scrawl partitions the vertices i e data points into constrained and unconstrained ones according to whether they are in the pairwise constraints for every constrained vertex its influence range or the degrees of influence it exerts on the unconstrained vertices is encapsulated in an intermediate structure called component the edge set between each pair of components determines the affecting scope of the pairwise constraints in the higher level random walk scrawl enforces the pairwise constraints on the components so that the constraint influence can be propagated to the unconstrained edges at last we combine the cluster membership of all the components to obtain the cluster assignment for each vertex the promising experimental results on both synthetic and real world data sets demonstrate the effectiveness of our method highlightswe propose a new semi supervised clustering algorithm given pairwise constraints it can expand the influence of the pairwise constraints locally and proportionally it utilizes the pairwise constraints in an edge vertex edge manner it introduces an intermediate structure to uncover the underlying sub structures given a k nn sparse similarity matrix its time complexity is approximately linear

data clustering using a model granular magnet we present a new approach to clustering based on the physical properties of an inhomogeneous ferromagnet no assumption is made regarding the underlying distribution of the data we assign a potts spin to each data point and introduce an interaction between neighboring points whose strength is a decreasing function of the distance between the neighbors this magnetic system exhibits three phases at very low temperatures it is completely ordered all spins are aligned at very high temperatures the system does not exhibit any ordering and in an intermediate regime clusters of relatively strongly coupled spins become ordered whereas different clusters remain uncorrelated this intermediate phase is identified by a jump in the order parameters the spin spin correlation function is used to partition the spins and the corresponding data points into clusters we demonstrate on three synthetic and three real data sets how the method works detailed comparison to the performance of other techniques clearly indicates the relative success of our method

soft clustering using weighted one class support vector machines this paper describes a new soft clustering algorithm in which each cluster is modelled by a one class support vector machine oc svm the proposed algorithm extends a previously proposed hard clustering algorithm also based on oc svm representation of clusters the key building block of our method is the weighted oc svm woc svm a novel tool introduced in this paper based on which an expectation maximization type soft clustering algorithm is defined a deterministic annealing version of the algorithm is also introduced and shown to improve the robustness with respect to initialization experimental results show that the proposed soft clustering algorithm outperforms its hard clustering counterpart namely in terms of robustness with respect to initialization as well as several other state of the art methods

unsupervised learning by minimal entropy encoding following basic principles of information theoretic learning in this paper we propose a novel approach to data clustering referred to as minimal entropy encoding mee which is based on a set of functions features projecting each input onto a minimum entropy configuration code inspired by traditional parsimony principles we seek solutions in reproducing kernel hilbert spaces and then we prove that the encoding functions are expressed in terms of kernel expansion in order to avoid trivial solutions the developed features must be as different as possible by means of a soft constraint on the empirical estimation of the entropy associated with the encoding functions this leads to an unconstrained optimization problem that can be efficiently solved by conjugate gradient we also investigate an optimization strategy based on concave convex algorithms the relationships with maximum margin clustering are studied showing that mee overcomes some of its critical issues such as the lack of a multiclass extension and the need to face problems with a large number of constraints a massive evaluation on several benchmarks of the proposed approach shows improvements over state of the art techniques both in terms of accuracy and computational complexity

a novel clustering method based on hybrid k nearest neighbor graph abstract most of the existing clustering methods have difficulty in processing complex nonlinear data sets to remedy this deficiency in this paper a novel data model termed hybrid k nearest neighbor hknn graph which combines the advantages of mutual k nearest neighbor graph and k nearest neighbor graph is proposed to represent the nonlinear data sets moreover a clustering method based on the hknn graph chknn is proposed the chknn first generates several tight and small subclusters then merges these subclusters by exploiting the connectivity among them in order to select the optimal parameters for chknn we further propose an internal validity index termed k nearest neighbor index knni which can also be used to evaluate the validity of nonlinear clustering results by varying a control parameter experimental results on synthetic and real world data sets as well as that on the video clustering have demonstrated the significant improvement on performance over existing nonlinear clustering methods and internal validity indices

diffusion in a two dimensional channel with curved midline and varying width reduction to an effective one dimensional description diffusion in a narrow two dimensional channel with a midline that need not be straight and a width that may vary is reduced to an effective one dimensional equation of motion this equation takes the form of the fick jacobs equation with a spatially varying effective diffusivity the effective diffusivity includes a contribution that comes from the slope of the midline as well as the usual term stemming from variations in the channel width along the length of the channel our derivation of our equation of motion is completely rigorous and is based on an asymptotic expansion in a small dimensionless parameter that characterizes the channel width for a channel that has a straight midline or wall our equation of motion reduces to zwanzig s equation r zwanzig j phys chem 96 3926 1992 our derivation therefore provides a rigorous proof of the validity of the latter equation finally the equation of motion is solved analytically for channels with curved midline and constant width

applying the possibilistic c means algorithm in kernel induced spaces in this paper we study a kernel extension of the classic possibilistic c means in the proposed extension we implicitly map input patterns into a possibly high dimensional space by means of positive semidefinite kernels in this new space we model the mapped data by means of the possibilistic clustering algorithm we study in more detail the special case where we model the mapped data using a single cluster only since it turns out to have many interesting properties the modeled memberships in kernel induced spaces yield a modeling of generic shapes in the input space we analyze in detail the connections to one class support vector machines and kernel density estimation thus suggesting that the proposed algorithm can be used in many scenarios of unsupervised learning in the experimental part we analyze the stability and the accuracy of the proposed algorithm on some synthetic and real datasets the results show high stability and good performances in terms of accuracy

a survey of kernel and spectral methods for clustering clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines the focus of this paper is the partitioning clustering problem with a special interest in two recent approaches kernel and spectral methods the aim of this paper is to present a survey of kernel and spectral clustering methods two approaches able to produce nonlinear separating hypersurfaces between clusters the presented kernel clustering methods are the kernel version of many classical clustering algorithms e g k means som and neural gas spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized an explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation besides fuzzy kernel clustering methods are presented as extensions of kernel k means clustering algorithm

support vector clustering we present a novel clustering method using the approach of support vector machines data points are mapped by means of a gaussian kernel to a high dimensional feature space where we search for the minimal enclosing sphere this sphere when mapped back to data space can separate into several components each enclosing a separate cluster of points we present a simple algorithm for identifying these clusters the width of the gaussian kernel controls the scale at which the data is probed while the soft margin constant helps coping with outliers and overlapping clusters the structure of a dataset is explored by varying the two parameters maintaining a minimal number of support vectors to assure smooth cluster boundaries we demonstrate the performance of our algorithm on several datasets

control of logic gates by dichotomous noise in energetic and entropic systems we consider the stochastic response of a nonlinear dynamical system towards a combination of input signals the response can assume binary values if the state of the system is considered to be the output and the system can make transitions between two states separated by an energetic or entropic barrier we show how the input output correspondence can be controlled by an external exponentially correlated dichotomous noise optimizing the logical response which exhibits a maximum at an intermediate value of correlation time this resonance manifests itself as a logical resonance correlation effect and sets the condition for performance of the stochastic system as a logic gate the role of asymmetry of the dichotomous noise is examined and the results on numerical simulations are correlated with a two state model using a master equation approach

a dynamical trajectory based methodology for systematically computing multiple optimal solutions of general nonlinear programming problems in this paper a novel dynamical trajectory based methodology is developed for systematically computing multiple local optimal solutions of general nonlinear programming problems with disconnected feasible components satisfying nonlinear equality inequality constraints the proposed methodology deterministic in nature exploits trajectories of two different nonlinear dynamical systems to find multiple local optimal solutions the methodology consists of two phases phase i starts from an arbitrary infeasible initial point and finds systematically multiple or all the disconnected feasible components phase ii finds an adjacent local optimal solution from a local optimum via a decomposition point thereby systematically locating multiple local optimal solutions which lie within each feasible component found in phase i by alternating between these two phases the methodology locates multiple or all the local optimal solutions which lie in all the disconnected feasible components a theoretical foundation for the proposed methodology is also developed the methodology is illustrated with a numerical example with promising results

finknn a fuzzy interval number k nearest neighbor classifier for prediction of sugar production from populations of samples this work introduces finknn a k nearest neighbor classifier operating over the metric lattice of conventional interval supported convex fuzzy sets we show that for problems involving populations of measurements data can be represented by fuzzy interval numbers fins and we present an algorithm for constructing fins from such populations we then present a lattice theoretic metric distance between fins with arbitrary shaped membership functions which forms the basis for finknn s similarity measurements we apply finknn to the task of predicting annual sugar production based on populations of measurements supplied by hellenic sugar industry we show that finknn improves prediction accuracy on this task and discuss the broader scope and potential utility of these techniques

robust clustering using outlier sparsity regularization notwithstanding the popularity of conventional clustering algorithms such as k means and probabilistic clustering their clustering results are sensitive to the presence of outliers in the data even a few outliers can compromise the ability of these algorithms to identify meaningful hidden structures rendering their outcome unreliable this paper develops robust clustering algorithms that not only aim to cluster the data but also to identify the outliers the novel approaches rely on the infrequent presence of outliers in the data which translates to sparsity in a judiciously chosen domain leveraging sparsity in the outlier domain outlier aware robust k means and probabilistic clustering approaches are proposed their novelty lies on identifying outliers while effecting sparsity in the outlier domain through carefully chosen regularization a block coordinate descent approach is developed to obtain iterative algorithms with convergence guarantees and small excess computational complexity with respect to their non robust counterparts kernelized versions of the robust clustering algorithms are also developed to efficiently handle high dimensional data identify nonlinearly separable clusters or even cluster objects that are not represented by vectors numerical tests on both synthetic and real datasets validate the performance and applicability of the novel algorithms

on the dynamics of rods in the theory of kirchhoff and clebsch we discuss here the dynamical equations of a theory of elastic rods that is due to kmcm ioff 1 2 and cl bsc 3 4 this properly invariant theory is applicable to motions in which the strains relative to an undistorted configuration remain small although rotations may be large it is constructed to be a first order theory i e a theory that is complete to within an error of order two in an appropriate dimensionless measure of thickness curvature twist and extension in a first order theory of thin rods one can treat the rod as inextensible and we do so here at the outset thus at each time t the arc length parameter s for the axial curve t is employed as a material coordinate i e a parameter whose value at a material point is constant in time and not only the resultant of the shearing forces on a cross section but also the tension in the rod are reactive quantities not given by constitutive equations consider for a moment a rod that is naturally prismatic and dynamically symmetric i e a rod that in an undistorted stress free configuration is a cylinder whose directrix although not necessarily a circle bounds a figure with equal principal moments of inertia a motion of the rod is said to be planar and twist flee i e a motion of pure flexure if it is such that t lies at all times in a fixed plane which contains a principal axis of inertia of each cross section for such a motion we employ a fixed cartesian coordinate system on and for consistency with a discussion of more general motions to be given later in this paper we call the abscissa z and the ordinate x we may write fz s t fx s t for the z and x components of the resultant force f at time t on the cross section with arc length coordinate s the motion of the rod may be described by giving the z x coordinates of the points on t as functions of s and t with o s t the counterclockwise angle from the z axis to the tangent of t at s we have

cluster validity measure and merging system for hierarchical clustering considering outliers clustering algorithms have evolved to handle more and more complex structures however the measures that allow to qualify the quality of such clustering partitions are rare and have been developed only for specific algorithms in this work we propose a new cluster validity measure cvm to quantify the clustering performance of hierarchical algorithms that handle overlapping clusters of any shape and in the presence of outliers this work also introduces a cluster merging system cms to group clusters that share outliers when located in regions of cluster overlap these outliers may be issued by a mixture of nearby cores the proposed cvm and cms are applied to hierarchical extensions of the support vector and gaussian process clustering algorithms both in synthetic and real experiments these results show that the proposed metrics help to select the appropriate level of hierarchy and the appropriate hyperparameters highlightscluster validity measure for arbitrary shaped clusters with outliers cluster merging system grouping cluster cores based on the outliers structure truly hierarchical variants of support vector and gaussian process clustering benefits for unsupervised change detection applications are presented

clustering irregular shapes using high order neurons this article introduces a method for clustering irregularly shaped data arrangements using high order neurons complex analytical shapes are modeled by replacing the classic synaptic weight of the neuron by high order tensors in homogeneous coordinates in the first and second order cases this neuron corresponds to a classic neuron and to an ellipsoidalmetric neuron we show how high order shapes can be formulated to follow the maximum correlation activation principle and permit simple local hebbian learning we also demonstrate decomposition of spatial arrangements of data clusters including very close and partially overlapping clusters which are difficult to distinguish using classic neurons superior results are obtained for the iris data

dynamic pattern denoising method using multi basin system with kernels in this paper we propose a novel pattern denoising method that utilizes the topological property of a support that describes the distribution of normal patterns to denoise noisy patterns the method first trains a support function which captures the domain of normal patterns and then construct a so called multi basin system associated with the trained support function by moving noisy patterns along the trajectories of the multi basin system noise is removed while the pattern recovers its normality the denoised pattern is obtained when the noisy pattern arrives at the attracting manifold generated by a set of normal patterns and this is the most similar normal pattern with the noisy pattern in the topological sense through simulations on some toy dataset and real image datasets we show that the proposed framework effectively removes the noise while preserving the information contained in the noisy pattern

an examination of procedures for determining the number of clusters in a data set a monte carlo evaluation of 30 procedures for determining the number of clusters was conducted on artificial data sets which contained either 2 3 4 or 5 distinct nonoverlapping clusters to provide a variety of clustering solutions the data sets were analyzed by four hierarchical clustering methods external criterion measures indicated excellent recovery of the true cluster structure by the methods at the correct hierarchy level thus the clustering present in the data was quite strong the simulation results for the stopping rules revealed a wide range in their ability to determine the correct number of clusters in the data several procedures worked fairly well whereas others performed rather poorly thus the latter group of rules would appear to have little validity particularly for data sets containing distinct clusters applied researchers are urged to select one or more of the better criteria however users are cautioned that the performance of some of the criteria may be data dependent

gaussian processes for classification mean field algorithms we derive a mean field algorithm for binary classification with gaussian processes that is based on the tap approach originally proposed in statistical physics of disordered systems the theory also yields an approximate leave one out estimator for the generalization error which is computed with no extra computational cost we show that from the tap approach it is possible to derive both a simpler naive mean field theory and support vector machines svms as limiting cases for both mean field algorithms and support vector machines simulation results for three small benchmark data sets are presented they show that one may get state of the art performance by using the leave one out estimator for model selection and the built in leave one out estimators are extremely precise when compared to the exact leave one out estimate the second result is taken as strong support for the internal consistency of the mean field approach

ellipsoidal support vector clustering for functional mri analysis as an exploratory approach the clustering of fmri time series has proved its effectiveness in analyzing the functional mri especially in the detection of activated regions due to the arbitrary distribution of fmri time series in the temporal domain imposing simple assumption on the data structure usually could be misleading and limit the detector s performance therefore a true data driven clustering algorithm that adapts to the data structure is preferred and only high level control over the clustering procedure is desired support vector clustering svc is a suitable one in some extent because of its advantages such as no cluster shape restriction no need to explicitly specify the number of clusters and the mechanism in outlier elimination in this work we propose an extension of the svc to step further toward a data sensitive detector this approach is named as ellipsoidal support vector clustering esvc to be robust to noise the clustering is performed on features extracted from the fmri time series via fourier transform experimental results on simulated and real data sets demonstrate the effectiveness of incorporating data structure in clustering fmri time series

dynamic cluster formation using level set methods density based clustering has the advantages for 1 allowing arbitrary shape of cluster and 2 not requiring the number of clusters as input however when clusters touch each other both the cluster centers and cluster boundaries as the peaks and valleys of the density distribution become fuzzy and difficult to determine we introduce the notion of cluster intensity function cif which captures the important characteristics of clusters when clusters are well separated cifs are similar to density functions but when clusters become closed to each other cifs still clearly reveal cluster centers cluster boundaries and degree of membership of each data point to the cluster that it belongs clustering through bump hunting and valley seeking based on these functions are more robust than that based on density functions obtained by kernel density estimation which are often oscillatory or oversmoothed these problems of kernel density estimation are resolved using level set methods and related techniques comparisons with two existing density based methods valley seeking and dbscan are presented which illustrate the advantages of our approach

constructing sparse kernel machines using attractors in this brief a novel method that constructs a sparse kernel machine is proposed the proposed method generates attractors as sparse solutions from a built in kernel machine via a dynamical system framework by readjusting the corresponding coefficients and bias terms a sparse kernel machine that approximates a conventional kernel machine is constructed the simulation results show that the constructed sparse kernel machine improves the efficiency of testing phase while maintaining comparable test error

smoothly approximated support vector domain description support vector domain description svdd is a well known tool for pattern analysis when only positive examples are reliable the svdd model is often fitted by solving a quadratic programming problem which is time consuming this paper attempts to fit svdd in the primal form directly however the primal objective function of svdd is not differentiable which prevents the well behaved gradient based optimization methods from being applicable as such we propose to approximate the primal objective function of svdd by a differentiable function and a conjugate gradient method is applied to minimize the smoothly approximated objective function extensive experiments on pattern classification were conducted and compared to the quadratic programming based svdd the proposed approach is much more computationally efficient and yields similar classification performance on these problems highlightssmoothly approximates the objective function of support vector domain description gradient based optimization method could be applied to the smoothed model the proposed algorithms have asymptotic training complexity n 2 the algorithm is easy to implement without requiring any optimization package

fast support based clustering method for large scale problems in many support vector based clustering algorithms a key computational bottleneck is the cluster labeling time of each data point which restricts the scalability of the method in this paper we review a general framework of support vector based clustering using dynamical system and propose a novel method to speed up labeling time which is log linear to the size of data we also give theoretical background of the proposed method various large scale benchmark results are provided to show the effectiveness and efficiency of the proposed method

a novel kernel method for clustering kernel methods are algorithms that by replacing the inner product with an appropriate positive definite function implicitly perform a nonlinear mapping of the input data into a high dimensional feature space in this paper we present a kernel method for clustering inspired by the classical k means algorithm in which each cluster is iteratively refined using a one class support vector machine our method which can be easily implemented compares favorably with respect to popular clustering algorithms like k means neural gas and self organizing maps on a synthetic data set and three uci real data benchmarks iris data wisconsin breast cancer database spam database

dynamic characterization of cluster structures for robust and inductive support vector clustering a topological and dynamical characterization of the cluster structures described by the support vector clustering is developed it is shown that each cluster can be decomposed into its constituent basin level cells and can be naturally extended to an enlarged clustered domain which serves as a basis for inductive clustering a simplified weighted graph preserving the topological structure of the clusters is also constructed and is employed to develop a robust and inductive clustering algorithm simulation results are given to illustrate the robustness and effectiveness of the proposed method

continuous probability distributions from finite data recent approaches to the problem of inferring a continuous probability distribution from a finite set of data have used a scalar field theory for the form of the prior probability distribution this paper presents a more general form for the prior distribution that has a geometrical interpretation and can improve the specificity of likely solutions it is also demonstrated that a numerical sampling of the posterior probability distribution can be used as an alternative to a histogram for visualization and to make probabilistic inferences from the data

estimating the support of a high dimensional distribution suppose you are given some data set drawn from an underlying probability distribution p and you want to estimate a simple subset s of input space such that the probability that a test point drawn from p lies outside of s equals some a priori specified value between 0 and 1 we propose a method to approach this problem by trying to estimate a function f that is positive on s and negative on the complement the functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data it is regularized by controlling the length of the weight vector in an associated feature space the expansion coefficients are found by solving a quadratic programming problem which we do by carrying out sequential optimization over pairs of input patterns we also provide a theoretical analysis of the statistical performance of our algorithm the algorithm is a natural extension of the support vector algorithm to the case of unlabeled data

shear flow past slender elastic rods attached to a plane shear flow past an elastic rod or a doubly periodic array of elastic rods attached to a plane is investigated with reference to flow over a ciliated surface or a carbon nanomat in the absence of flow the rods are straight cylinders with circular cross sectional shape the mathematical framework combines slender body theory for computing the hydrodynamic load with classical beam theory for computing the rod deflection small deflections are computed using a finite element method and large deflections are computed using an iterative procedure where a rod shape is assumed the hydrodynamic load is found and a new shape is obtained by solving a boundary value problem involving ordinary differential equations at equilibrium deflected rod profiles are presented and the macroscopic slip velocity is computed in the case of flow past a doubly periodic square or triangular array of rods over a broad range of surface coverage

variational gaussian process classifiers gaussian processes are a promising nonlinear regression tool but it is not straightforward to solve classification problems with them in the paper the variational methods of jaakkola and jordan 2000 are applied to gaussian processes to produce an efficient bayesian binary classifier

simulating the dynamics and interactions of flexible fibers in stokes flows the dynamics of slender filaments or fibers suspended in stokesian fluids are fundamental to understanding many flows arising in physics biology and engineering such filaments can have aspect ratios of length to radius ranging from a few tens to several thousands full discretizations of such 3d flows are very costly instead we employ a nonlocal slender body theory that yields an integral equation along the filament centerline relating the force exerted on the body to the filament velocity this hydrodynamical description takes into account the effect of the filament on the fluid and is extended to capture the interaction of multiple filaments as mediated by the intervening fluid we consider filaments that are inextensible and elastic replacing the force in the slender body integral equation by an explicit expression that uses euler bernoulli theory to model bending and tensile forces yields an integral expression for the velocity of the filament centerlines coupled to auxiliary integro differential equations for the filament tensions based on a regularized version of these slender body equations that is asymptotically equivalent to the original formulation we construct a numerical method which uses a combination of finite differences implicit time stepping to avoid severe stability constraints and special quadrature methods for nearly singular integrals we present simulations of single flexible filaments as well as multiple interacting filaments evolving in a background shear flow these simulations show shear induced buckling and relaxation of the filaments leading to the storage and release of elastic energy these dynamics are responsible for the development of positive first normal stress differences commonly associated with visco elastic fluids that are suspensions of microscopic elastic fibers

online primal dual learning for a data dependent multi kernel combination model with multiclass visual categorization applications the task of visual categorization becomes very challenging as the number of samples or classes increases this is mainly due to large memory requirements or a crowded semantic space which causes class separation difficulties in this paper a new approach called oprdum2 online primal dual multiple kernel multiple class is proposed this new algorithm can significantly reduce the complexity of visual categorization under this approach an elegant heterogeneous feature fusion machine is used to consolidate complementary class discriminative information and online learning is applied to deal with large sample sizes to be specific a data dependent multi kernel machine that fuses multiple heterogeneous features in a nonlinear manner is defined by extending the multi kernel learning model and multivariate hinge loss and conservative updating rules are used to increase the sample level sparsity in the model given the intrinsic hierarchical structure of samples features and classes an innovative triple mixed norm regularizer with strong convexity is utilized to facilitate optimization an iterative solution is derived using the language of duality leading to a low regret bound of o t where t is the number of online iterations this paper details a proof of the algorithm s convergence and describes extensive visual data classification experiments that demonstrate the effectiveness and robustness of this new approach

effective one dimensional description of confined diffusion biased by a transverse gravitational force diffusion of pointlike noninteracting particles in a two dimensional channel of varying cross section is considered the particles are biased by a constant force in the transverse direction a recurrence mapping procedure is applied which enables the derivation of an effective one dimensional 1d evolution equation that governs the 1d density of the particles in the channel in the limit of stationary flow an extended fick jacobs equation is reached which is corrected by an effective diffusion coefficient d x that depends on the longitudinal coordinate x the result is an approximate formula for d x that also involves the influence of the transverse force the calculations are verified by the stationary diffusion in a linear cone which is exactly solvable

approximations of the generalized fick jacobs equation we analyze the generalized fick jacobs equation obtained by a rigorous mapping of the diffusion equation in a quasi one dimensional quasi 1d narrow 2d or 3d channel with varying cross section a x onto the longitudinal coordinate x we show that for constructing approximations and understanding their applicability in practice it is crucial to study the 2d 3d density inside the channel in the regime of stationary flow we present algorithms enabling us to derive approximate formulas for the effective diffusion coefficient involving derivatives of a x higher than a ensuremath x and give examples for 2d channels effects of the boundary conditions at the ends of a finite channel and the case of nonsmooth a x are also discussed

bayesian classification with gaussian processes we consider the problem of assigning an input vector to one of m classes by predicting p c x for c 1 m for a two class problem the probability of class one given x is estimated by spl sigma y x where spl sigma y 1 1 e sup y a gaussian process prior is placed on y x and is combined with the training data to obtain predictions for new x points we provide a bayesian treatment integrating over uncertainty in y and in the parameters that control the gaussian process prior the necessary integration over y is carried out using laplace s approximation the method is generalized to multiclass problems m 2 using the softmax function we demonstrate the effectiveness of the method on a number of datasets

an efficient algorithm for the smallest enclosing ball problem in high dimensions abstract consider the problem of computing the smallest enclosing ball of a set of m balls in r n this problem arises in many applications such as location analysis military operations and pattern recognition etc in this paper we reformulate this problem as an unconstrained convex optimization problem involving the maximum function max 0 t and then develop a simple algorithm particularly suitable for problems in high dimensions this algorithm could efficiently handle problems of dimension n up to 10 000 under a moderately large m as well as problems of dimension m up to 10 000 under a moderately large n numerical results are given to show the efficiency of algorithm