rational curves and rational singularities we study rational curves on algebraic varieties especially on normal affine varieties endowed with a action for varieties with an isolated singularity covered by a family of rational curves with a general member not passing through the singular point we show that this singularity is rational in particular this provides an explanation of classical results due to h a schwartz and g h halphen on polynomial solutions of the generalized fermat equation

kernel pca for novelty detection kernel principal component analysis kernel pca is a non linear extension of pca this study introduces and investigates the use of kernel pca for novelty detection training data are mapped into an infinite dimensional feature space in this space kernel pca extracts the principal components of the data distribution the squared distance to the corresponding principal subspace is the measure for novelty this new method demonstrated a competitive performance on two dimensional synthetic distributions and on two real world data sets handwritten digits and breast cancer cytology

one class classifiers based on entropic spanning graphs one class classifiers offer valuable tools to assess the presence of outliers in data in this paper we propose a design methodology for one class classifiers based on entropic spanning graphs our approach also takes into account the possibility to process nonnumeric data by means of an embedding procedure the spanning graph is learned on the embedded input data and the outcoming partition of vertices defines the classifier the final partition is derived by exploiting a criterion based on mutual information minimization here we compute the mutual information by using a convenient formulation provided in terms of the alpha jensen difference once training is completed in order to associate a confidence level with the classifier decision a graph based fuzzy model is constructed the fuzzification process is based only on topological information of the vertices of the entropic spanning graph as such the proposed one class classifier is suitable also for data characterized by complex geometric structures we provide experiments on well known benchmarks containing both feature vectors and labeled graphs in addition we apply the method to the protein solubility recognition problem by considering several representations for the input samples experimental results demonstrate the effectiveness and versatility of the proposed method with respect to other state of the art approaches

multibody grouping from motion images we want to deduce from a sequence of noisy two dimensional images of a scene of several rigid bodies moving independently in three dimensions the number of bodies and the grouping of given feature points in the images to the bodies prior processing is assumed to have identified features or points common to all frames and the images are assumed to be created by orthographic projection i e perspective effects are minimal we describe a computationally inexpensive algorithm that can determine which points or features belong to which rigid body using the fact that with exact observations in orthographic projection points on a single body lie in a three or less dimensional linear manifold of frame space if there are enough observations and independent motions these manifolds can be viewed as a set linearly independent four or less dimensional subspaces we show that the row echelon canonical form provides direct information on the grouping of points to these subspaces treatment of the noise is the most difficult part of the problem this paper uses a statistical approach to estimate the grouping of points to subspaces in the presence of noise by computing which partition has the maximum likelihood the input data is assumed to be contaminated with independent gaussian noise the algorithm can base its estimates on a user supplied standard deviation of the noise or it can estimate the noise from the data the algorithm can also be used to estimate the probability of a user specified partition so that the hypothesis can be combined with others using bayesian statistics

learning the kernel with hyperkernels this paper addresses the problem of choosing a kernel suitable for estimation with a support vector machine hence further automating machine learning this goal is achieved by defining a reproducing kernel hilbert space on the space of kernels itself such a formulation leads to a statistical estimation problem similar to the problem of minimizing a regularized risk functional we state the equivalent representer theorem for the choice of kernels and present a semidefinite programming formulation of the resulting optimization problem several recipes for constructing hyperkernels are provided as well as the details of common machine learning problems experimental results for classification regression and novelty detection on uci data show the feasibility of our approach

a multibody factorization method for independently moving objects the structure from motion problem has been extensively studied in the field of computer vision yet the bulk of the existing work assumes that the scene contains only a single moving object the more realistic case where an unknown number of objects move in the scene has received little attention especially for its theoretical treatment in this paper we present a new method for separating and recovering the motion and shape of multiple independently moving objects in a sequence of images the method does not require prior knowledge of the number of objects nor is dependent on any grouping of features into an object at the image level for this purpose we introduce a mathematical construct of object shapes called the shape interaction matrix which is invariant to both the object motions and the selection of coordinate systems this invariant structure is computable solely from the observed trajectories of image features without grouping them into individual objects once the matrix is computed it allows for segmenting features into objects by the process of transforming it into a canonical form as well as recovering the shape and motion of each object the theory works under a broad set of projection models scaled orthography paraperspective and affine but they must be linear so it excludes projective cameras

contour detection and hierarchical image segmentation this paper investigates two fundamental problems in computer vision contour detection and image segmentation we present state of the art algorithms for both of these tasks our contour detector combines multiple local cues into a globalization framework based on spectral clustering our segmentation algorithm consists of generic machinery for transforming the output of any contour detector into a hierarchical region tree in this manner we reduce the problem of image segmentation to that of contour detection extensive experimental evaluation demonstrates that both our contour detection and segmentation methods significantly outperform competing algorithms the automatically generated hierarchical segmentations can be interactively refined by user specified annotations computation at multiple image resolutions provides a means of coupling our system to recognition applications

highly articulated kinematic structure estimation combining motion and skeleton information in this paper we present a novel framework for unsupervised kinematic structure learning of complex articulated objects from a single view 2d image sequence in contrast to prior motion based methods which estimate relatively simple articulations our method can generate arbitrarily complex kinematic structures with skeletal topology via a successive iterative merging strategy the iterative merge process is guided by a density weighted skeleton map which is generated from a novel object boundary generation method from sparse 2d feature points our main contributions can be summarised as follows i an unsupervised complex articulated kinematic structure estimation method that combines motion segments with skeleton information ii an iterative fine to coarse merging strategy for adaptive motion segmentation and structural topology embedding iii a skeleton estimation method based on a novel silhouette boundary generation from sparse feature points using an adaptive model selection method iv a new highly articulated object dataset with ground truth annotation we have verified the effectiveness of our proposed method in terms of computational time and estimation accuracy through rigorous experiments with multiple datasets our experiments show that the proposed method outperforms state of the art methods both quantitatively and qualitatively

solve partial differential equations by two or more radial basis functions abstract there are many partial differential equations their solution might be oscillatory or vary rapidly we will get an inaccurate result or encounter an ill conditioned problem whenever we solve it using kansa s collocation method mfs or other methods in this paper we will present a new method in which such pdes will be solved by two or more radial basis functions rbfs so these pdes can be solved efficiently and accurately

robust novelty detection via worst case cvar minimization novelty detection models aim to find the minimum volume set covering a given probability mass this paper proposes a robust single class support vector machine ssvm for novelty detection which is mainly based on the worst case conditional value at risk minimization by assuming that every input is subject to an uncertainty with a specified symmetric support this robust formulation results in a maximization term that is similar to the regularization term in the classical ssvm when the uncertainty set is ell 1 norm ell infty norm or box its training can be reformulated to a linear program while the uncertainty set is ell 2 norm or ellipsoidal its training is a tractable second order cone program the proposed method has a nice consistent statistical property as the training size goes to infinity the estimated normal region converges to the true provided that the magnitude of the uncertainty set decreases in a systematic way the experimental results on three data sets clearly demonstrate its superiority over three benchmark models

structural minimax probability machine minimax probability machine mpm is an interesting discriminative classifier based on generative prior knowledge it can directly estimate the probabilistic accuracy bound by minimizing the maximum probability of misclassification the structural information of data is an effective way to represent prior knowledge and has been found to be vital for designing classifiers in real world problems however mpm only considers the prior probability distribution of each class with a given mean and covariance matrix which does not efficiently exploit the structural information of data in this paper we use two finite mixture models to capture the structural information of the data from binary classification for each subdistribution in a finite mixture model only its mean and covariance matrix are assumed to be known based on the finite mixture models we propose a structural mpm smpm smpm can be solved effectively by a sequence of the second order cone programming problems moreover we extend a linear model of smpm to a nonlinear model by exploiting kernelization techniques we also show that the smpm can be interpreted as a large margin classifier and can be transformed to support vector machine and maxi min margin machine under certain special conditions experimental results on both synthetic and real world data sets demonstrate the effectiveness of smpm

entropic one class classifiers the one class classification problem is a well known research endeavor in pattern recognition the problem is also known under different names such as outlier and novelty anomaly detection the core of the problem consists in modeling and recognizing patterns belonging only to a so called target class all other patterns are termed nontarget and therefore they should be recognized as such in this paper we propose a novel one class classification system that is based on an interplay of different techniques primarily we follow a dissimilarity representation based approach we embed the input data into the dissimilarity space ds by means of an appropriate parametric dissimilarity measure this step allows us to process virtually any type of data the dissimilarity vectors are then represented by weighted euclidean graphs which we use to determine the entropy of the data distribution in the ds and at the same time to derive effective decision regions that are modeled as clusters of vertices since the dissimilarity measure for the input data is parametric we optimize its parameters by means of a global optimization scheme which considers both mesoscopic and structural characteristics of the data represented through the graphs the proposed one class classifier is designed to provide both hard boolean and soft decisions about the recognition of test patterns allowing an accurate description of the classification process we evaluate the performance of the system on different benchmarking data sets containing either feature based or structured patterns experimental results demonstrate the effectiveness of the proposed technique

a scalable and implicit meshless rbf method for the 3d unsteady nonlinear richards equation with single and multi zone domains the local hermitian interpolation lhi method is a strong form meshless numerical technique which uses radial basis function rbf interpolants to satisfy linear and nonlinear governing equations and boundary operators recent developments have shown that for linear transport problems applying the pde governing equation directly to the basis functions can greatly improve the accuracy and stability of the resulting solutions in this work the lhi formulation with local pde interpolation is extended to the nonlinear gravity driven richards equation in order to solve unsteady problems involving flow in unsaturated porous media the application of the linearised pde operator to the basis functions incorporates information such as the effective velocity field directly into the solution construction this results in a form of analytical upwinding which helps to stabilise the solution in addition the local interpolation itself satisfies the linearised governing equation allowing for more accurate reconstruction of partial derivatives and hence a more accurate solution the procedure is tested using a 3d infiltration problem with a known analytical solution the performance of the lhi method both with and without local pde interpolation is compared to the finite element method via the femwater software the lhi formulation with pde data centres shows consistent improvement over the femwater solutions reducing errors by several orders of magnitude in addition a procedure is introduced to model strongly heterogeneous and layered soils the physically correct matching conditions are applied over layer interfaces i e continuity of pressure and mass flux the double collocation property of the hermitian rbf method is exploited to enforce both matching conditions at the same set of locations on the layer interface this procedure allows the accurate capture of solutions across such interfaces replicating the required discontinuities in the first derivatives of the pressure profile the multi layer formulation is validated using a transient two layer infiltration problem with the analytical solution replicated to a high precision in a variety of configurations copyright 2010 john wiley sons ltd

on unsymmetric collocation by radial basis functions solving partial differential equations by collocation with radial basis functions can be efficiently done by a technique first proposed by kansa in 1990 it rewrites the problem as a generalized interpolation problem and the solution is obtained by solving a possibly large linear system the method has been used successfully in a variety of applications but a proof of nonsingularity of the linear system was still missing this paper shows that a general proof of this fact is impossible however numerical evidence shows that cases of singularity are rare and have to be constructed with quite some effort

kernel density estimation via diffusion we present a new adaptive kernel density estimator based on linear diffusion processes the proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate in addition we propose a new plug in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods we present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability

reconstruct multiscale functions using different rbfs in different subdomains in practice we usually encounter many multiscale functions for example in the fields of condensed phase physics computational chemistry and nano structure it would be very difficult to reconstruct these functions in this paper we will provide an efficient meshless method we would reconstruct these functions by two or more rbfs the efficiency would be demonstrated by numerical experiments

boundary layer resolving pseudospectral methods for singular perturbation problems pseudospectral methods are investigated for singularly perturbed boundary value problems for ordinary differential equations odes which possess boundary layers it is well known that if the boundary layer is very small then a very large number of spectral collocation points is required to obtain accurate solutions we introduce here a new effective procedure based on coordinate stretching and the chebyshev pseudospectral method to resolve the boundary layers stable and accurate results are obtained for very thin boundary layers with a fairly small number of spectral collocation points

color invariance this paper presents the measurement of colored object reflectance under different general assumptions regarding the imaging conditions we exploit the gaussian scale space paradigm for color images to define a framework for the robust measurement of object reflectance from color images object reflectance is derived from a physical reflectance model based on the kubelka munk theory for colorant layers illumination and geometrical invariant properties are derived from the reflectance model invariance and discriminative power of the color invariants is experimentally investigated showing the invariants to be successful in discounting shadow illumination highlights and noise extensive experiments show the different invariants to be highly discriminative while maintaining invariance properties the presented framework for color measurement is well founded in the physics of color as well as in measurement science hence the proposed invariants are considered more adequate for the measurement of invariant color features than existing methods

anisotropic diffusion of multivalued images with applications to color filtering a general framework for anisotropic diffusion of multivalued images is presented we propose an evolution equation where at each point in time the directions and magnitudes of the maximal and minimal rate of change in the vector image are first evaluated these are given by eigenvectors and eigenvalues of the first fundamental form in the given image metric then the image diffuses via a system of coupled differential equations in the direction of minimal change the diffusion strength is controlled by a function that measures the degree of dissimilarity between the eigenvalues we apply the proposed framework to the filtering of color images represented in cie l a b space

a class of single class minimax probability machines for novelty detection single class minimax probability machines mpms offer robust novelty detection with distribution free worst case bounds on the probability that a pattern will fall inside the normal region however in practice they are too cautious in labeling patterns as outlying and so have a high false negative rate fnr in this paper we propose a more aggressive version of the single class mpm that bounds the best case probability that a pattern will fall inside the normal region these two mpms can then be used together to delimit the solution space by using the hyperplane lying in the middle of this pair of mpms a better compromise between false positives fps and false negatives fns and between recall and precision can be obtained experiments on the real world data sets show encouraging results

color based object recognition abstract the purpose is to arrive at recognition of multicolored objects invariant to a substantial change in viewpoint object geometry and illumination assuming dichromatic reflectance and white illumination it is shown that normalized color rgb saturation s and hue h and the newly proposed color models c 1 c 2 c 3 and l 1 l 2 l 3 are all invariant to a change in viewing direction object geometry and illumination further it is shown that hue h and l1l2l3 are also invariant to highlights finally a change in spectral power distribution of the illumination is considered to propose a new color constant color model m1m2m3 to evaluate the recognition accuracy differentiated for the various color models experiments have been carried out on a database consisting of 500 images taken from 3 d multicolored man made objects the experimental results show that highest object recognition accuracy is achieved by l1l2l3 and hue h followed by c1c2c3 normalized color rgb and m1m2m3 under the constraint of white illumination also it is demonstrated that recognition accuracy degrades substantially for all color features other than m1m2m3 with a change in illumination color the recognition scheme and images are available within the pictoseek and pic2seek systems on line at http www wins uva nl research isis zomax

new support vector algorithms we propose a new class of support vector algorithms for regression and classification in these algorithms a parameter lets one effectively control the number of support vectors while this can be useful in its own right the parameterization has the additional benefit of enabling us to eliminate one of the other free parameters of the algorithm the accuracy parameter epsilon in the regression case and the regularization constant c in the classification case we describe the algorithms give some theoretical results concerning the meaning and the choice of and report experimental results

generalized principal component analysis gpca this paper presents an algebro geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points we represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a data point give normal vectors to the subspace passing through the point when the number of subspaces is known we show that these polynomials can be estimated linearly from data hence subspace segmentation is reduced to classifying one point per subspace we select these points optimally from the data set by minimizing certain distance function thus dealing automatically with moderate noise in the data a basis for the complement of each subspace is then recovered by applying standard pca to the collection of derivatives normal vectors extensions of gpca that deal with data in a high dimensional space and with an unknown number of subspaces are also presented our experiments on low dimensional data show that gpca outperforms existing algebraic algorithms based on polynomial factorization and provides a good initialization to iterative techniques such as k subspaces and expectation maximization we also present applications of gpca to computer vision problems such as face clustering temporal video segmentation and 3d motion segmentation from point correspondences in multiple affine views

in defense of the eight point algorithm the fundamental matrix is a basic tool in the analysis of scenes taken with two uncalibrated cameras and the eight point algorithm is a frequently cited method for computing the fundamental matrix from a set of eight or more point matches it has the advantage of simplicity of implementation the prevailing view is however that it is extremely susceptible to noise and hence virtually useless for most purposes this paper challenges that view by showing that by preceding the algorithm with a very simple normalization translation and scaling of the coordinates of the matched points results are obtained comparable with the best iterative algorithms this improved performance is justified by theory and verified by extensive experiments on real images

a robust minimax approach to classification when constructing a classifier the probability of correct classification of future data points should be maximized we consider a binary classification problem where the mean and covariance matrix of each class are assumed to be known no further assumptions are made with respect to the class conditional distributions misclassification probabilities are then controlled in a worst case setting that is under all possible choices of class conditional densities with given mean and covariance matrix we minimize the worst case maximum probability of misclassification of future data points for a linear decision boundary this desideratum is translated in a very direct way into a convex second order cone optimization problem with complexity similar to a support vector machine problem the minimax problem can be interpreted geometrically as minimizing the maximum of the mahalanobis distances to the two classes we address the issue of robustness with respect to estimation errors in the means and covariances of the classes via a simple modification of the input data we also show how to exploit mercer kernels in this setting to obtain nonlinear decision boundaries yielding a classifier which proves to be competitive with current methods including support vector machines an important feature of this method is that a worst case bound on the probability of misclassification of future data is always obtained explicitly

a one class kernel fisher criterion for outlier detection recently dufrenois and noyer proposed a one class fisher s linear discriminant to isolate normal data from outliers in this paper a kernelized version of their criterion is presented originally on the basis of an iterative optimization process alternating between subspace selection and clustering i show here that their criterion has an upper bound making these two problems independent in particular the estimation of the label vector is formulated as an unconstrained binary linear problem ublp which can be solved using an iterative perturbation method once the label vector is estimated an optimal projection subspace is obtained by solving a generalized eigenvalue problem like many other kernel methods the performance of the proposed approach depends on the choice of the kernel constructed with a gaussian kernel i show that the proposed contrast measure is an efficient indicator for selecting an optimal kernel width this property simplifies the model selection problem which is typically solved by costly generalized cross validation procedures initialization convergence analysis and computational complexity are also discussed lastly the proposed algorithm is compared with recent novelty detectors on synthetic and real data sets

on the stopping criteria for k nearest neighbor in positive unlabeled time series classification problems positive unlabeled time series classification has become an important area during the last decade as often vast amounts of unlabeled time series data are available but obtaining the corresponding labels is difficult in this situation positive unlabeled learning is a suitable option to mitigate the lack of labeled examples in particular self training is a widely used technique due to its simplicity and adaptability within this technique the stopping criterion i e the decision of when to stop labeling is a critical part especially in the positive unlabeled context we propose a self training method that follows the positive unlabeled approach for time series classification and a family of parameter free stopping criteria for this method our proposal uses a graphical analysis applied to the minimum distances obtained by the k nearest neighbor as the base learner to estimate the class boundary the proposed method is evaluated in an experimental study involving various time series classification datasets the results show that our method outperforms the transductive results obtained by previous models

one class random forests one class classification is a binary classification task for which only one class of samples is available for learning in some preliminary works we have proposed one class random forests ocrf a method based on a random forest algorithm and an original outlier generation procedure that makes use of classifier ensemble randomization principles in this paper we propose an extensive study of the behavior of ocrf that includes experiments on various uci public datasets and comparison to reference one class namely gaussian density models parzen estimators gaussian mixture models and one class svms with statistical significance our aim is to show that the randomization principles embedded in a random forest algorithm make the outlier generation process more efficient and allow in particular to break the curse of dimensionality one class random forests are shown to perform well in comparison to other methods and in particular to maintain stable performance in higher dimension while the other algorithms may fail

optimal inequalities in probability theory a convex optimization approach we propose a semidefinite optimization approach to the problem of deriving tight moment inequalities for p x in s for a set s defined by polynomial inequalities and a random vector x defined on omega subseteq cal r n that has a given collection of up to kth order moments in the univariate case we provide optimal bounds on p x in s when the first k moments of x are given as the solution of a semidefinite optimization problem in k 1 dimensions in the multivariate case if the sets s and omega are given by polynomial inequalities we obtain an improving sequence of bounds by solving semidefinite optimization problems of polynomial size in n for fixed k we characterize the complexity of the problem of deriving tight moment inequalities we show that it is np hard to find tight bounds for k geq 4 and omega cal r n and for k geq 2 and omega cal r n when the data in the problem is rational for k 1 and omega cal r n we show that we can find tight upper bounds by solving n convex optimization problems when the set s is convex and we provide a polynomial time algorithm when s and omega are unions of convex sets over which linear functions can be optimized efficiently for the case k 2 and omega cal r n we present an efficient algorithm for finding tight bounds when s is a union of convex sets over which convex quadratic functions can be optimized efficiently

uniform object generation for optimizing one class classifiers in one class classification one class of data called the target class has to be distinguished from the rest of the feature space it is assumed that only examples of the target class are available this classifier has to be constructed such that objects not originating from the target set by definition outlier objects are not classified as target objects in previous research the support vector data description svdd is proposed to solve the problem of one class classification it models a hypersphere around the target set and by the introduction of kernel functions more flexible descriptions are obtained in the original optimization of the svdd two parameters have to be given beforehand by the user to automatically optimize the values for these parameters the error on both the target and outlier data has to be estimated because no outlier examples are available we propose a method for generating artificial outliers uniformly distributed in a hypersphere an relative efficient estimate for the volume covered by the one class classifiers is obtained and so an estimate for the outlier error results are shown for artificial data and for real world data

robust histogram construction from color invariants for object recognition an effective object recognition scheme is to represent and match images on the basis of histograms derived from photometric color invariants a drawback however is that certain color invariant values become very unstable in the presence of sensor noise to suppress the effect of noise for unstable color invariant values in this paper histograms are computed by variable kernel density estimators to apply variable kernel density estimation in a principled way models are proposed for the propagation of sensor noise through color invariant variables as a result the associated uncertainty is obtained for each color invariant value the associated uncertainty is used to derive the parameterization of the variable kernel for the purpose of robust histogram construction it is empirically verified that the proposed density estimator compares favorably to traditional histogram schemes for the purpose of object recognition

multisurface proximal support vector machine classification via generalized eigenvalues a new approach to support vector machine svm classification is proposed wherein each of two data sets are proximal to one of two distinct planes that are not parallel to each other each plane is generated such that it is closest to one of the two data sets and as far as possible from the other data set each of the two nonparallel proximal planes is obtained by a single matlab command as the eigenvector corresponding to a smallest eigenvalue of a generalized eigenvalue problem classification by proximity to two distinct nonlinear surfaces generated by a nonlinear kernel also leads to two simple generalized eigenvalue problems the effectiveness of the proposed method is demonstrated by tests on simple examples as well as on a number of public data sets these examples show the advantages of the proposed approach in both computation time and test set correctness

shape and motion from image streams under orthography a factorization method inferring scene geometry and camera motion from a stream of images is possible in principle but is an ill conditioned problem when the objects are distant with respect to their size we have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step an image stream can be represented by the 2fxp measurement matrix of the image coordinates of p points tracked through f frames we show that under orthographic projection this matrix is of rank 3 based on this observation the factorization method uses the singular value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively two of the three translation components are computed in a preprocessing stage the method can also handle and obtain a full solution from a partially filled in measurement matrix that may result from occlusions or tracking failures the method gives accurate results and does not introduce smoothing in either shape or motion we demonstrate this with a series of experiments on laboratory and outdoor image streams with and without occlusions

selection and fusion of color models for image feature detection the choice of a color model is of great importance for many computer vision algorithms e g feature detection object recognition and tracking as the chosen color model induces the equivalence classes to the actual algorithms as there are many color models available the inherent difficulty is how to automatically select a single color model or alternatively a weighted subset of color models producing the best result for a particular task the subsequent hurdle is how to obtain a proper fusion scheme for the algorithms so that the results are combined in an optimal setting to achieve proper color model selection and fusion of feature detection algorithms in this paper we propose a method that exploits nonperfect correlation between color models or feature detection algorithms derived from the principles of diversification as a consequence a proper balance is obtained between repeatability and distinctiveness the result is a weighting scheme which yields maximal feature discrimination the method is verified experimentally for three different image feature detectors the experimental results show that the fusion method provides feature detection results having a higher discriminative power than the standard weighting scheme further it is experimentally shown that the color model selection scheme provides a proper balance between color invariance repeatability and discriminative power distinctiveness

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

nearest neighbor variance estimation nnve robust covariance estimation commonly proceeds by downweighting outliers in this article we measure the outlyingness of a data point by the standardized distance between the point and its kth nearest neighbor the appropriate weights for robust estimation are found by a model based mixture modeling approach that follows from considering the data cloud as a realization of a high dimensional point process to correct a potential bias when there are no outliers we introduce a boundary correction procedure that artificially adds in extra outlying points the resulting methodology is called nearest neighbor variance estimation nnve the strength of nnve is its robustness against a large proportion of noise points and against deviation from normality of the signal a consistency result for the method is established under some reasonable assumptions it is shown that the covariance estimate is bounded and that each point has only bounded influence on the final estimates nnve outperformed the popular mini

a classification framework for anomaly detection one way to describe anomalies is by saying that anomalies are not concentrated this leads to the problem of finding level sets for the data generating density we interpret this learning problem as a binary classification problem and compare the corresponding classification risk with the standard performance measure for the density level problem in particular it turns out that the empirical classification risk can serve as an empirical performance measure for the anomaly detection problem this allows us to compare different anomaly detection algorithms empirically i e with the help of a test set furthermore by the above interpretation we can give a strong justification for the well known heuristic of artificially sampling labeled samples provided that the sampling plan is well chosen in particular this enables us to propose a support vector machine svm for anomaly detection for which we can easily establish universal consistency finally we report some experiments which compare our svm to other commonly used methods including the standard one class svm

one class proximal support vector machines recently in dufrenois 1 a new fisher type contrast measure has been proposed to extract a target population in a dataset contaminated by outliers although mathematically sound this work presents some further shortcomings in both the formalism and the field of use first we propose to re express this problem from the formalism of proximal support vector machines as introduced in mangasarian and wild 2 this change is far from harmless since it introduces a suited writing for solving the problem another limiting factor of the method is that its performance relies on the assumption that the density between the target and outliers are different this consideration can easily prove to be over optimistic for real world datasets making the method unreliable at least directly the computation of the decision boundary is a time consuming part of the algorithm since it is based on solving a generalized eigenvalue problem gep this method is therefore limited to medium sized data sets in this paper we propose appropriate strategies to unlock all these shortcomings and fully benefit from the interest of the approach firstly we show under some conditions that generating appropriate artificial outliers allows to stay within the constraints of the method and thus enlarges the conditions of use secondly we show that the gep can be advantageously replaced by a conjugate gradient solution cg significantly decreasing the computational cost lastly the proposed algorithm is compared with recent novelty detectors on synthetic and real datasets highlightswe study the extraction of a target population from a dataset contaminated by outliers to this end we propose a new fisher type contrast measure we reconsider this problem from the formalism of proximal support vector machines an approximation of the contrast measure is done using a conjugate gradient method no matrix inversion is needed which lowers the computational complexity

a new class of radial basis functions with compact support radial basis functions are well known and successful tools for the interpolation of data in many dimensions several radial basis functions of compact support that give rise to nonsingular interpolation problems have been proposed and in this paper we study a new larger class of smooth radial functions of compact support which contains other compactly supported ones that were proposed earlier in the literature

sparse subspace clustering algorithm theory and applications many real world problems deal with collections of high dimensional data such as images videos text and web documents dna microarray data and more often such high dimensional data lie close to low dimensional structures corresponding to several classes or categories to which the data belong in this paper we propose and study an algorithm called sparse subspace clustering to cluster data points that lie in a union of low dimensional subspaces the key idea is that among the infinitely many possible representations of a data point in terms of other points a sparse representation corresponds to selecting a few points from the same subspace this motivates solving a sparse optimization program whose solution is used in a spectral clustering framework to infer the clustering of the data into subspaces since solving the sparse optimization program is in general np hard we consider a convex relaxation and show that under appropriate conditions on the arrangement of the subspaces and the distribution of the data the proposed minimization program succeeds in recovering the desired sparse representations the proposed algorithm is efficient and can handle data points near the intersections of subspaces another key advantage of the proposed algorithm with respect to the state of the art is that it can deal directly with data nuisances such as noise sparse outlying entries and missing entries by incorporating the model of the data into the sparse optimization program we demonstrate the effectiveness of the proposed algorithm through experiments on synthetic data as well as the two real world problems of motion segmentation and face clustering

multiquadric collocation method with integralformulation for boundary layer problems singularly perturbed boundary value problems often have solutions with very thinlayers in which the solution changes rapidly this paper concentrates on the case where theses layers occur near the boundary although our method can be applied to problems with interior layers one technique to deal with the increased resolution requirements in these layers is the use of domain transformations a coordinate stretching based transform allows to move collocation points into the layer a requirement to resolve the layer accurately previously such transformations have been studied in the context of finite difference and spectral collocation methods in this paper we use radial basis functions rbfs to solve the boundary value problem specifically we present a collocation method based on multiquadric mq functions with an integral formulation combined with a coordinate transformation we find that our scheme is ultimately more accurate than a recently proposed adaptive mq scheme the rbf scheme is also amenable to adaptivity

formulating robust linear regression estimation as a one class lda criterion discriminative hat matrix linear discriminant analysis such as fisher s criterion is a statistical learning tool traditionally devoted to separating a training dataset into two or even several classes by the way of linear decision boundaries in this paper we show that this tool can formalize the robust linear regression problem as a robust estimator will do more precisely we develop a one class fischer s criterion in which the maximization provides both the regression parameters and the separation of the data in two classes typical data and atypical data or outliers this new criterion is built on the statistical properties of the subspace decomposition of the hat matrix from this angle we improve the discriminative properties of the hat matrix which is traditionally used as outlier diagnostic measure in linear regression naturally we call this new approach discriminative hat matrix the proposed algorithm is fully nonsupervised and needs only the initialization of one parameter synthetic and real datasets are used to study the performance both in terms of regression and classification of the proposed approach we also illustrate its potential application to image recognition and fundamental matrix estimation in computer vision

kernel fisher discriminants for outlier detection the problem of detecting atypical objects or outliers is one of the classical topics in robust statistics recently it has been proposed to address this problem by means of one class svm classifiers the method presented in this letter bridges the gap between kernelized one class classification and gaussian density estimation in the induced feature space having established the exact relation between the two concepts it is now possible to identify atypical objects by quantifying their deviations from the gaussian model this model based formalization of outliers overcomes the main conceptual shortcoming of most one class approaches which in a strict sense are unable to detect outliers since the expected fraction of outliers has to be specified in advance in order to overcome the inherent model selection problem of unsupervised kernel methods a cross validated likelihood criterion for selecting all free model parameters is applied experiments for detecting atypical objects in image databases effectively demonstrate the applicability of the proposed method in real world scenarios

bayes point machines kernel classifiers comprise a powerful class of non linear decision functions for binary classification the support vector machine is an example of a learning algorithm for kernel classifiers that singles out the consistent classifier with the largest margin i e minimal real valued output on the training sample within the set of consistent hypotheses the so called version space we suggest the bayes point machine as a well founded improvement which approximates the bayes optimal decision by the centre of mass of version space we present two algorithms to stochastically approximate the centre of mass of version space a billiard sampling algorithm and a sampling algorithm based on the well known perceptron algorithm it is shown how both algorithms can be extended to allow for soft boundaries in order to admit training errors experimentally we find that for the zero training error case bayes point machines consistently outperform support vector machines on both surrogate data and real world benchmark data sets in the soft boundary soft margin case the improvement over support vector machines is shown to be reduced finally we demonstrate that the real valued output of single bayes points on novel test points is a valid confidence measure and leads to a steady decrease in generalisation error when used as a rejection criterion

dense trajectories and motion boundary descriptors for action recognition this paper introduces a video representation based on dense trajectories and motion boundary descriptors trajectories capture the local motion information of the video a dense representation guarantees a good coverage of foreground motion as well as of the surrounding context a state of the art optical flow algorithm enables a robust and efficient extraction of dense trajectories as descriptors we extract features aligned with the trajectories to characterize shape point coordinates appearance histograms of oriented gradients and motion histograms of optical flow additionally we introduce a descriptor based on motion boundary histograms mbh which rely on differential optical flow the mbh descriptor shows to consistently outperform other state of the art descriptors in particular on real world videos that contain a significant amount of camera motion we evaluate our video representation in the context of action classification on nine datasets namely kth youtube hollywood2 ucf sports ixmas uiuc olympic sports ucf50 and hmdb51 on all datasets our approach outperforms current state of the art results

approximate polytope ensemble for one class classification in this work a new one class classification ensemble strategy called approximate polytope ensemble is presented the main contribution of the paper is threefold first the geometrical concept of convex hull is used to define the boundary of the target class defining the problem expansions and contractions of this geometrical structure are introduced in order to avoid over fitting second the decision whether a point belongs to the convex hull model in high dimensional spaces is approximated by means of random projections and an ensemble decision process finally a tiling strategy is proposed in order to model non convex structures experimental results show that the proposed strategy is significantly better than state of the art one class classification methods on over 200 datasets highlightsthe methodology uses a convex hull for modeling one class classification problems random projections are used to approximate the convex hull in high dimensional spaces expansions of the approximate hulls are considered to set the optimal operating point exhaustive validation is performed on three different typologies of problems