probabilistic visual learning for object representation we present an unsupervised technique for visual learning which is based on density estimation in high dimensional spaces using an eigenspace decomposition two types of density estimates are derived for modeling the training data a multivariate gaussian for unimodal distributions and a mixture of gaussians model for multimodal distributions those probability densities are then used to formulate a maximum likelihood estimation framework for visual search and target detection for automatic object recognition and coding our learning technique is applied to the probabilistic visual modeling detection recognition and coding of human faces and nonrigid objects such as hands

oscillations of first order neutral delay differential equations abstract consider the neutral delay differential equation d dt y t py t qy t 0 t t 0 where q and are positive constants while p 1 0 for the case p 1 0 see ladas and sficas oscillations of neutral delay differential equations to appear the following results are then proved theorem 1 assume p and q 1 p 1 e then every solution of eq oscillates theorems 3 assume p 0 then every nonoscillatory solution y t of eq tends to zero as t theorem 4 assume p 0 then a necessary condition for all solutions of eq to oscillate is that theorem 5 assume p 0 and q 1 p 1 e then every solution of eq oscillates extensions of these results to equations with variable coefficients are also obtained

surface from gradients without discrete integrability enforcement a gaussian kernel approach representative surface reconstruction algorithms taking a gradient field as input enforce the integrability constraint in a discrete manner while enforcing integrability allows the subsequent integration to produce surface heights existing algorithms have one or more of the following disadvantages they can only handle dense per pixel gradient fields smooth out sharp features in a partially integrable field or produce severe surface distortion in the results in this paper we present a method which does not enforce discrete integrability and reconstructs a 3d continuous surface from a gradient or a height field or a combination of both which can be dense or sparse the key to our approach is the use of kernel basis functions which transfer the continuous surface reconstruction problem into high dimensional space where a closed form solution exists by using the gaussian kernel we can derive a straightforward implementation which is able to produce results better than traditional techniques in general an important advantage of our kernel based method is that the method does not suffer discretization and finite approximation both of which lead to surface distortion which is typical of fourier or wavelet bases widely adopted by previous representative approaches we perform comparisons with classical and recent methods on benchmark as well as challenging data sets to demonstrate that our method produces accurate surface reconstruction that preserves salient and sharp features the source code and executable of the system are available for downloading

what is the goal of sensory coding a number of recent attempts have been made to describe early sensory coding in terms of a general information processing strategy in this paper two strategies are contrasted both strategies take advantage of the redundancy in the environment to produce more effective representations the first is described as a compact coding scheme a compact code performs a transform that allows the input to be represented with a reduced number of vectors cells with minimal rms error this approach has recently become popular in the neural network literature and is related to a process called principal components analysis pca a number of recent papers have suggested that the optimal compact code for representing natural scenes will have units with receptive field profiles much like those found in the retina and primary visual cortex however in this paper it is proposed that compact coding schemes are insufficient to account for the receptive field properties of cells in the mammalian visual pathway in contrast it is proposed that the visual system is near to optimal in representing natural scenes only if optimality is defined in terms of sparse distributed coding in a sparse distributed code all cells in the code have an equal response probability across the class of images but have a low response probability for any single image in such a code the dimensionality is not reduced rather the redundancy of the input is transformed into the redundancy of the firing pattern of cells it is proposed that the signature for a sparse code is found in the fourth moment of the response distribution i e the kurtosis in measurements with 55 calibrated natural scenes the kurtosis was found to peak when the bandwidths of the visual code matched those of cells in the mammalian visual cortex codes resembling wavelet transforms are proposed to be effective because the response histograms of such codes are sparse i e show high kurtosis when presented with natural scenes it is proposed that the structure of the image that allows sparse coding is found in the phase spectrum of the image it is suggested that natural scenes to a first approximation can be considered as a sum of self similar local functions the inverse of a wavelet possible reasons for why sensory systems would evolve toward sparse coding are presented

new oscillation criteria for first order nonlinear neutral delay differential equations some new oscillation criteria of first order nonlinear neutral delay differential equations with variable coefficients are given our results extend and improve some of the well known previously results in the literature some examples are considered to illustrate our main results

handbook of brownian motion facts and formulae i theory i stochastic processes in general ii linear diffusions iii stochastic calculus iv brownian motion v local time as a markov process vi differential systems associated to brownian motion appendix 1 briefly on some diffusions ii tables of distributions of functionals of brownian motion and related processes 1 brownian motion 2 brownian motion with drift 3 reflecting brownian motion 4 bessel process of order 5 bessel process of order 1 2 6 bessel process of order zero 7 ornstein uhlenbeck process 8 radial ornstein uhlenbeck process 9 geometric brownian motion appendix 2 special functions appendix 3 inverse laplace transforms appendix 4 differential equations and their solutions appendix 5 formulae for n fold differentiation

new oscillation criteria for delay difference equations abstract this paper is concerned with the oscillation of all solutions of the delay difference equations and where pn and pi n are sequences of nonnegative real numbers an k and ki are positive integers new oscillation criteria of the forms for equation and for equation are obtained where lim infn 1 k n 1i n k pi and c is the the best possible function of in some sense

depth estimation from image structure in the absence of cues for absolute depth measurements as binocular disparity motion or defocus the absolute distance between the observer and a scene cannot be measured the interpretation of shading edges and junctions may provide a 3d model of the scene but it will not provide information about the actual scale of the space one possible source of information for absolute depth estimation is the image size of known objects however object recognition under unconstrained conditions remains difficult and unreliable for current computational approaches we propose a source of information for absolute depth estimation based on the whole scene structure that does not rely on specific objects we demonstrate that by recognizing the properties of the structures present in the image we can infer the scale of the scene and therefore its absolute mean depth we illustrate the interest in computing the mean depth of the scene with application to scene recognition and object detection

filter based mean field inference for random fields with higher order terms and product label spaces recently a number of cross bilateral filtering methods have been proposed for solving multi label problems in computer vision such as stereo optical flow and object class segmentation that show an order of magnitude improvement in speed over previous methods these methods have achieved good results despite using models with only unary and or pairwise terms however previous work has shown the value of using models with higher order terms e g to represent label consistency over large regions or global co occurrence relations we show how these higher order terms can be formulated such that filter based inference remains possible we demonstrate our techniques on joint stereo and object labelling problems as well as object class segmentation showing in addition for joint object stereo labelling how our method provides an efficient approach to inference in product label spaces we show that we are able to speed up inference in these models around 10 30 times with respect to competing graph cut move making methods as well as maintaining or improving accuracy in all cases we show results on pascalvoc 10 for object class segmentation and leuven for joint object stereo labelling

the ordinal relation preserving binary codes hashing algorithm has been widely used for efficient approximate nearest neighbor ann search learning optimal hashing functions has been given focus and it is still a challenge this paper aims to effectively and efficiently generate relative similarity preserving binary codes most existing hashing methods try to preserve the locality similarity by preserving direct distance similarity while ignoring the relative similarity which advantages in ann search in this paper this issue is solved by proposing the relative error which emphasizes that the ordinal relations in hamming space and euclidean space should be consistent with each other we learn hashing projection functions via two steps the first step adopts the lookup based mechanism to find the optimal binary codes of training data which can preserve the relative similarity and simultaneously adapt to data distribution the binary codes in the first step are considered as supervision information in the second step the objective of the second step is to learn hashing projection functions which can efficiently regenerate the binary codes in the first step aim to be in accordance with the property of data distribution the hyper internal tangent planes of two specified spheres are chosen as hashing projection functions assisted by these projection functions the time complexity of encoding process is greatly reduced experimental results on four public data sets demonstrate that our method outperforms many other state of the art methods author highlightsan effective and efficient binary coding framework which enjoys the merits of lookup based and hamming based methods is proposed relative error is proposed to preserve the relative sensitivity the effective tangent planes are adopted as hashing functions to avoid computing the complex classification problem the encoding error guarantees that the selected hashing functions have good performance

hashing with angular reconstructive embeddings large scale search methods are increasingly critical for many content based visual analysis applications among which hashing based approximate nearest neighbor search techniques have attracted broad interests due to their high efficiency in storage and retrieval however existing hashing works are commonly designed for measuring data similarity by the euclidean distances in this paper we focus on the problem of learning compact binary codes using the cosine similarity specifically we proposed novel angular reconstructive embeddings are method which aims at learning binary codes by minimizing the reconstruction error between the cosine similarities computed by original features and the resulting binary embeddings furthermore we devise two efficient algorithms for optimizing our are in continuous and discrete manners respectively we extensively evaluate the proposed are on several large scale image benchmarks the results demonstrate that are outperforms several state of the art methods

first exit time probability for multidimensional diffusions a pde based approach first exit time distributions for multidimensional processes are key quantities in many areas of risk management and option pricing the aim of this paper is to provide a flexible fast and accurate algorithm for computing the probability of the first exit time from a bounded domain for multidimensional diffusions first we show that the probability distribution of this stopping time is the unique weak solution of a parabolic initial and boundary value problem then we describe the algorithm which is based on a combination of the sparse tensor product finite element spaces and an hp discontinuous galerkin method we illustrate our approach with several examples we also compare the numerical results to classical monte carlo methods

stability of non monotone critical traveling waves for reaction diffusion equations with time delay abstract this paper is concerned with the stability of critical traveling waves for a kind of non monotone time delayed reaction diffusion equations including nicholson s blowflies equation which models the population dynamics of a single species with maturation delay such delayed reaction diffusion equations possess monotone or oscillatory traveling waves the latter occurs when the birth rate function is non monotone and the time delay is big it has been shown that such traveling waves x c t exist for all c c and are exponentially stable for all wave speed c c 13 where c is called the critical wave speed in this paper we prove that the critical traveling waves x c t monotone or oscillatory are also time asymptotically stable when the initial perturbations are small in a certain weighted sobolev norm the adopted method is the technical weighted energy method with some new flavors to handle the critical oscillatory waves finally numerical simulations for various cases are carried out to support our theoretical results

one shot detection with laplacian object and fast matrix cosine similarity one shot generic object detection involves searching for a single query object in a larger target image relevant approaches have benefited from features that typically model the local similarity patterns in this paper we combine local similarity encoded by local descriptors with a global context i e a graph structure of pairwise affinities among the local descriptors embedding the query descriptors into a low dimensional but discriminatory subspace unlike principal components that preserve global structure of feature space we actually seek a linear approximation to the laplacian eigenmap that permits us a locality preserving embedding of high dimensional region descriptors our second contribution is an accelerated but exact computation of matrix cosine similarity as the decision rule for detection obviating the computationally expensive sliding window search we leverage the power of fourier transform combined with integral image to achieve superior runtime efficiency that allows us to test multiple hypotheses for pose estimation within a reasonably short time our approach to one shot detection is training free and experiments on the standard data sets confirm the efficacy of our model besides low computation cost of the proposed codebook free object detector facilitates rather straightforward query detection in large data sets including movie videos

spatial multi scale gradient orientation consistency for place instance and scene category recognition gradient orientation consistency goc was proposed to encode local structure of images the goc feature is more robust to illumination variances the spatial multi scale goc histogram could achieve competitive performance for both place instance and scene category recognition this paper presents a novel image feature called gradient orientation consistency goc and an image representation based on the spatial multi scale goc histogram for place instance and scene category recognition gradient orientations have proven to be a more robust descriptor of the image information than intensities in the presence of illumination variances the goc feature is obtained by imposing a local binary pattern lbp type of non parametric operator to the gradient orientation codes hence captures the local structures in an image the histogram of goc further encodes the global structure of the entire image the multi scale analysis and spatial pyramid techniques are also used to enrich the longer range structure information resulting in a comprehensive image representation we apply this representation method for place instance and scene category recognition on five different datasets and show that it outperforms the state of the art

semantic preserving distance metric learning and applications how do we accurately browse a large set of images or efficiently annotate the images from an image library image clustering methods are invaluable tools for applications such as content based image retrieval and image annotation to perform these tasks it is critical to have proper features to describe the visual and semantic content of images and to define an accurate distance metric to measure the dissimilarity between any two images however existing methods which adopt the features of color histograms edge direction histograms and shape context lack the ability to describe semantic content to solve this problem we propose a new approach that utilizes user provided pairwise constraints to describe the semantic relationship between two images a semantic preserving distance metric learning sp dml algorithm is developed to explore the complementary characteristics of the visual features and pairwise constraints in a unified feature space in this space the learned distance metric can be used to measure the dissimilarity between two images specifically the manifold structure adopted in sp dml is revealed by the image s visual features to integrate semantic contents in distance metric learning sp dml utilizes pairwise constraints to build semantic patches and align these patches to obtain the optimal distance metric for the new feature space experimental results in image clustering demonstrate that the performance of sp dml is appealing

an approach to the parameterization of structure for fast categorization a decomposition is described which parameterizes the geometry and appearance of contours and regions of gray scale images with the goal of fast categorization to express the contour geometry a contour is transformed into a local global space from which parameters are derived classifying its global geometry arc inflexion or alternating and describing its local aspects degree of curvature edginess symmetry regions are parameterized based on their symmetric axes which are evolved with a wave propagation process enabling to generate the distance map for fragmented contour images the methodology is evaluated on three image sets the caltech 101 set and two sets drawn from the corel collection the performance nearly reaches the one of other categorization systems for unsupervised learning

towards robust discriminative projections learning via non greedy l2 1 norm minmax linear discriminant analysis lda is one of the most successful supervised dimensionality reduction methods and has been widely used in many real world applications however the l 2 norm is employed as the distance measure in objective of lda which is sensitive to outliers many previous works improve the robustness of lda by using l1 norm distance however the robustness against outliers is limited and the solver of l1 norm are mostly based on greedy search strategy which is time consuming and easy to get stuck in a local optimum in this paper we propose a novel robust lda measured by l 2 1 norm to learn robust discriminative projections since the proposed model needs to minimize and maximize minmax l 2 1 norm terms simultaneously it is challenging to solve as a result we first systematically derive an efficient iterative optimization algorithm to solve a general ratio minimization problem and rigorously prove its convergence more importantly an efficient non greedy iterative re weighted optimization algorithm is developed based on preceding approach for solving proposed l 2 1 norm minmax problem besides an optimal weighted mean mechanism is driven according to designed objective and solver which can be applied to other approach for robustness improvement extensive experimental results on several real world datasets show the effectiveness of proposed method

oscillation of first order delay differential equations abstract some new oscillation criteria for the first order delay differential equation x t p t x t 0 t t 0 t t are established in the case where t t p s ds 1 e and lim t t t p s ds 1 e an open problem by a elbert and i p stavroulakis 1995 proc amer math soc 123 1503 1510 is solved

scalable similarity search with topology preserving hashing hashing based similarity search techniques is becoming increasingly popular in large data sets to capture meaningful neighbors the topology of a data set which represents the neighborhood relationships between its subregions and the relative proximities between the neighbors of each subregion e g the relative neighborhood ranking of each subregion should be exploited however most existing hashing methods are developed to preserve neighborhood relationships while ignoring the relative neighborhood proximities moreover most hashing methods lack in providing a good result ranking since there are often lots of results sharing the same hamming distance to a query in this paper we propose a novel hashing method to solve these two issues jointly the proposed method is referred to as topology preserving hashing tph tph is distinct from prior works by also preserving the neighborhood ranking based on this framework we present three different tph methods including linear unsupervised tph semisupervised tph and kernelized tph particularly our unsupervised tph is capable of mining semantic relationship between unlabeled data without supervised information extensive experiments on four large data sets demonstrate the superior performances of the proposed methods over several state of the art unsupervised and semisupervised hashing techniques

joint image clustering and labeling by matrix factorization we propose a novel algorithm to cluster and annotate a set of input images jointly where the images are clustered into several discriminative groups and each group is identified with representative labels automatically for these purposes each input image is first represented by a distribution of candidate labels based on its similarity to images in a labeled reference image database a set of these label based representations are then refined collectively through a non negative matrix factorization with sparsity and orthogonality constraints the refined representations are employed to cluster and annotate the input images jointly the proposed approach demonstrates performance improvements in image clustering over existing techniques and illustrates competitive image labeling accuracy in both quantitative and qualitative evaluation in addition we extend our joint clustering and labeling framework to solving the weakly supervised image classification problem and obtain promising results

oscillation of delay difference equation we introduce some new techniques to analyze generalized characteristic equations to obtain several infinite sum sharp conditions for oscillation of the following delay difference equation xn 1 xn i 1mpi n xn ki 0 n 0 1 2 where pi n 0 and ki are positive integers

depth analogy data driven approach for single image depth estimation using gradient samples inferring scene depth from a single monocular image is a highly ill posed problem in computer vision this paper presents a new gradient domain approach called depth analogy that makes use of analogy as a means for synthesizing a target depth field when a collection of rgb d image pairs is given as training data specifically the proposed method employs a non parametric learning process that creates an analogous depth field by sampling reliable depth gradients using visual correspondence established on training image pairs unlike existing data driven approaches that directly select depth values from training data our framework transfers depth gradients as reconstruction cues which are then integrated by the poisson reconstruction the performance of most conventional approaches relies heavily on the training rgb d data used in the process and such a dependency severely degenerates the quality of reconstructed depth maps when the desired depth distribution of an input image is quite different from that of the training data e g outdoor versus indoor scenes our key observation is that using depth gradients in the reconstruction is less sensitive to scene characteristics providing better cues for depth recovery thus our gradient domain approach can support a great variety of training range datasets that involve substantial appearance and geometric variations the experimental results demonstrate that our depth gradient domain approach outperforms existing data driven approaches directly working on depth domain even when only uncorrelated training datasets are available

oscillatory criteria for third order difference equation with impulses in this paper we investigate the oscillation of third order difference equation with impulses some sufficient conditions for the oscillatory behavior of the solutions of third order impulsive difference equations are obtained

space time hole filling with random walks in view extrapolation for 3d video in this paper a space time hole filling approach is presented to deal with a disocclusion when a view is synthesized for the 3d video the problem becomes even more complicated when the view is extrapolated from a single view since the hole is large and has no stereo depth cues although many techniques have been developed to address this problem most of them focus only on view interpolation we propose a space time joint filling method for color and depth videos in view extrapolation for proper texture and depth to be sampled in the following hole filling process the background of a scene is automatically segmented by the random walker segmentation in conjunction with the hole formation process then the patch candidate selection process is formulated as a labeling problem which can be solved with random walks the patch candidates that best describe the hole region are dynamically selected in the space time domain and the hole is filled with the optimal patch for ensuring both spatial and temporal coherence the experimental results show that the proposed method is superior to state of the art methods and provides both spatially and temporally consistent results with significantly reduced flicker artifacts

multiple feature kernel hashing for large scale visual search recently hashing has become attractive in large scale visual search owing to its theoretical guarantee and practical success however most of the state of the art hashing methods can only employ a single feature type to learn hashing functions related research on image search clustering and other domains has proved the advantages of fusing multiple features in this paper we propose a novel multiple feature kernel hashing framework where hashing functions are learned to preserve certain similarities with linearly combined multiple kernels corresponding to different features the framework is not only compatible with general types of data and diverse types of similarities indicated by different visual features but also general for both supervised and unsupervised scenarios we present efficient alternating optimization algorithms to learn both the hashing functions and the optimal kernel combination experimental results on three large scale benchmarks cifar 10 nus wide and a trecvid show that the proposed approach can achieve superior accuracy and efficiency over state of the art methods highlightswe propose a generic multiple feature hashing framework using multiple kernels visual features are implicitly mapped and concatenated to reduce complexity we formulate both supervised and unsupervised hashing problems in the framework alternating optimization ways efficiently learn hashing functions and the kernel space experiments validate the superior performances and efficiency of the proposed approach

fast semi supervised clustering with enhanced spectral embedding in recent years semi supervised clustering ssc has aroused considerable interests from the machine learning and data mining communities in this paper we propose a novel ssc approach with enhanced spectral embedding ese which not only considers the geometric structure information contained in data sets but also can make use of the given side information such as pairwise constraints specially we first construct a symmetry favored k nn graph which is highly robust to noise and outliers and can reflect the underlying manifold structures of data sets then we learn the enhanced spectral embedding towards an ideal data representation as consistent with the given pairwise constraints as possible finally by using the regularization of spectral embedding we formulate learning the new data representation as a semidefinite quadratic linear programming sqlp problem which can be efficiently solved experimental results on a variety of synthetic and real world data sets show that our ese approach outperforms the state of the art ssc algorithms in terms of speed and quality on both vector based and graph based clustering

multiview alignment hashing for efficient image search hashing is a popular and efficient method for nearest neighbor search in large scale data spaces by embedding high dimensional feature descriptors into a similarity preserving hamming space with a low dimension for most hashing methods the performance of retrieval heavily depends on the choice of the high dimensional feature descriptor furthermore a single type of feature cannot be descriptive enough for different images when it is used for hashing thus how to combine multiple representations for learning effective hashing functions is an imminent task in this paper we present a novel unsupervised multiview alignment hashing approach based on regularized kernel nonnegative matrix factorization which can find a compact representation uncovering the hidden semantics and simultaneously respecting the joint probability distribution of data in particular we aim to seek a matrix factorization to effectively fuse the multiple information sources meanwhile discarding the feature redundancy since the raised problem is regarded as nonconvex and discrete our objective function is then optimized via an alternate way with relaxation and converges to a locally optimal solution after finding the low dimensional representation the hashing functions are finally obtained through multivariable logistic regression the proposed method is systematically evaluated on three data sets 1 caltech 256 2 cifar 10 and 3 cifar 20 and the results show that our method significantly outperforms the state of the art multiview hashing techniques

learning dictionary of discriminative part detectors for image categorization and cosegmentation this paper proposes a novel approach to learning mid level image models for image categorization and cosegmentation we represent each image class by a dictionary of part detectors that best discriminate that class from the background we learn category specific part detectors in a weakly supervised setting in which the training images are only annotated with category labels without part object location information we use a latent svm model regularized using the ell 2 1 l2 1 group sparsity norm to learn the part detectors starting from a large set of initial parts the group sparsity regularizer forces the model to jointly select and optimize a set of discriminative part detectors in a max margin framework we propose a stochastic version of a proximal algorithm to solve the corresponding optimization problem we apply the learned part detectors to image classification and cosegmentation and present extensive comparative experiments with standard benchmarks

supervised discrete hashing with relaxation data dependent hashing has recently attracted attention due to being able to support efficient retrieval and storage of high dimensional data such as documents images and videos in this paper we propose a novel learning based hashing method called supervised discrete hashing with relaxation sdhr based on supervised discrete hashing sdh sdh uses ordinary least squares regression and traditional zero one matrix encoding of class label information as the regression target code words thus fixing the regression target in sdhr the regression target is instead optimized the optimized regression target matrix satisfies a large margin constraint for correct classification of each example compared with sdh which uses the traditional zero one matrix sdhr utilizes the learned regression target matrix and therefore more accurately measures the classification error of the regression model and is more flexible as expected sdhr generally outperforms sdh experimental results on two large scale image data sets cifar 10 and mnist and a large scale and challenging face data set frgc demonstrate the effectiveness and efficiency of sdhr

modeling the shape of the scene a holistic representation of the spatial envelope in this paper we propose a computational model of the recognition of real world scenes that bypasses the segmentation and the processing of individual objects or regions the procedure is based on a very low dimensional representation of the scene that we term the spatial envelope we propose a set of perceptual dimensions naturalness openness roughness expansion ruggedness that represent the dominant spatial structure of a scene then we show that these dimensions may be reliably estimated using spectral and coarsely localized information the model generates a multidimensional space in which scenes sharing membership in semantic categories e g streets highways coasts are projected closed together the performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category

depth video enhancement based on weighted mode filtering this paper presents a novel approach for depth video enhancement given a high resolution color video and its corresponding low quality depth video we improve the quality of the depth video by increasing its resolution and suppressing noise for that a weighted mode filtering method is proposed based on a joint histogram when the histogram is generated the weight based on color similarity between reference and neighboring pixels on the color image is computed and then used for counting each bin on the joint histogram of the depth map a final solution is determined by seeking a global mode on the histogram we show that the proposed method provides the optimal solution with respect to l1 norm minimization for temporally consistent estimate on depth video we extend this method into temporally neighboring frames simple optical flow estimation and patch similarity measure are used for obtaining the high quality depth video in an efficient manner experimental results show that the proposed method has outstanding performance and is very efficient compared with existing methods we also show that the temporally consistent enhancement of depth video addresses a flickering problem and improves the accuracy of depth video

feature selection for clustering using instance based learning by exploring the nearest and farthest neighbors feature selection for clustering is an active research topic and is used to identify salient features that are helpful for data clustering while partitioning a dataset into clusters a data instance and its nearest neighbors will belong to the same cluster and this instance and its farthest neighbors will belong to different clusters we propose a new feature selection method to identify salient features that are useful for maintaining the instance s nearest neighbors and farthest neighbors referred to here as fsnf in particular fsnf uses the mutual information criterion to estimate feature salience by considering maintainability experiments on benchmark datasets demonstrate the effectiveness of fsnf within the context of cluster analysis

oscillation behavior of even order nonlinear neutral differential equations with variable coefficients in this paper some sufficient conditions are obtained for the oscillation of all solutions of even order nonlinear neutral differential equations with variable coefficients our results improve and generalize known results in particular the results are new even when n 2

oscillation of second order self conjugate differential equation with impulses in this paper we investigate the oscillation of second order self conjugate differential equation with impulses a t x t p t x t q t x t 0 t tk t t0 1 x tk 1 bk x tk k 1 2 2 x tk 1 bk x tk k 1 2 3 where a p q are continuous functions in t0 q t 0 a t 0 t0 1 a s ds 0 0 bk 1 0 t0 t1 t2 tk and limk tk we get some sufficient conditions for the oscillation of solutions of eqs 1 3

new fractional order legendre fourier moments for pattern recognition applications abstract orthogonal moments enable computer based systems to discriminate between similar objects mathematicians proved that the orthogonal polynomials of fractional orders outperformed their corresponding counterparts in representing the fine details of a given function in this work novel orthogonal fractional order legendre fourier moments are proposed for pattern recognition applications the basis functions of these moments are defined and the essential mathematical equations for the recurrence relations orthogonality and the similarity transformations rotation and scaling are derived the proposed new fractional order moments are tested where their performance is compared with the existing orthogonal quaternion multi channel and fractional moments new descriptors were found to be superior to the existing ones in terms of accuracy stability noise resistance invariance to similarity transformations recognition rates and computational times

oscillations of delay differential equations with variable coefficients consider the delay differential equation t p t x t 0 where p t c t0 r and is a positive constant we show that every solution of this equation oscillates if tt p t dt 1 e for sufficiently large t and t0 p t exp tt p s ds 1 e 1 dt

correlated logistic model with elastic net regularization for multilabel image classification in this paper we present correlated logistic corrlog model for multilabel image classification corrlog extends conventional logistic regression model into multilabel cases via explicitly modeling the pairwise correlation between labels in addition we propose to learn the model parameters of corrlog with elastic net regularization which helps exploit the sparsity in feature selection and label correlations and thus further boost the performance of multilabel classification corrlog can be efficiently learned though approximately by regularized maximum pseudo likelihood estimation and it enjoys a satisfying generalization bound that is independent of the number of labels corrlog performs competitively for multilabel image classification on benchmark data sets mulan scene mit outdoor scene pascal voc 2007 and pascal voc 2012 compared with the state of the art multilabel classification algorithms

what does the retina know about natural scenes by examining the experimental data on the statistical properties of natural scenes together with retinal contrast sensitivity data we arrive at a first principle theoretical hypothesis for the purpose of retinal processing and its relationship to an animal s environment we argue that the retinal goal is to transform the visual input as much as possible into a statistically independent basis as the first step in creating a redundancy reduced representation in the cortex as suggested by barlow the extent of this whitening of the input is limited however by the need to suppress input noise our explicit theoretical solutions for the retinal filters also show a simple dependence on mean stimulus luminance they predict an approximate weber law at low spatial frequencies and a de vries rose law at high frequencies assuming that the dominant source of noise is quantum we generate a family of contrast sensitivity curves as a function of mean luminance this family is compared to psychophysical data

oscillations of delay differential equations with variable coefficients abstract consider the delay differential equation x t p t x t 0 where p t c t 0 r and is a positive constant we obtain a sharp sufficient condition for the oscillation of this equation which improves previously known results

the expected lifetime of an extraction project when a mining company begins extraction from a finite resource it does so in the presence of numerous uncertainties one key uncertainty is the future price of the commodity being extracted since a large enough drop in price can make a resource no longer cost effective to extract resulting in the mine being closed down by specifying a stochastic price process and implementing a financial type model which leads to the use of partial differential equations this paper creates the framework for efficiently capturing the probability of a mine remaining open throughout its planned extraction period and derives the associated expected lifetime of extraction an approximation to the abandonment price is described which enables a closed form solution to be derived for the probability of operational success and expected lifetime this approximation compares well with the full solution obtained using a semi lagrangian numerical technique

faster independent component analysis by preconditioning with hessian approximations independent component analysis ica is a technique for unsupervised exploration of multichannel data that is widely used in observational sciences in its classic form ica relies on modeling the data as linear mixtures of nongaussian independent sources the maximization of the corresponding likelihood is a challenging problem if it has to be completed quickly and accurately on large sets of real data this problem has been addressed by resorting to quasi newton methods which rely on sparse approximations of the hessian of the log likelihood however those approximations are not accurate when the ica model does not hold exactly as is often the case for real datasets we propose a new algorithm dubbed picard which makes use of sparse approximate hessians only as a preconditioner to the l bfgs algorithm refining the hessian approximation from a memory of the past iterates extensive numerical comparisons to several algorithms of the same class demonstrate the superior performance of the proposed technique especially on real data

oscillation of first order delay differential equations with distributed delay abstract in this paper we obtain some oscillation criteria for the first order delay differential equation with distributed delay x t 0 b t r t s x t s d s 0 by applying these results we also establish some integral conditions for oscillation of the higher order delay differential equations

learning descriptive visual representation for image classification and annotation abstract this paper presents a novel semantic regularized matrix factorization method for learning descriptive visual bag of words bow representation although very influential in image classification the traditional visual bow representation has one distinct drawback that is for efficiency purposes this visual representation is often generated by directly clustering the low level visual feature vectors extracted from local keypoints or regions without considering the high level semantics of images in other words it still suffers from the semantic gap and may lead to significant performance degradation in more challenging tasks e g image classification over social collections with large intra class variations to learn descriptive visual bow representation for such image classification task we develop a semantic regularized matrix factorization method by adding laplacian regularization defined with the tags easy to access of social images into matrix factorization moreover given that image annotation only provides the tags of training images in advance while the tags of all social images are available we can readily apply the proposed method to image annotation by first running a round of image annotation to predict the tags maybe incorrect of test images and thus obtaining the tags of all images experimental results show the promising performance of the proposed method

geometric invariant features in the radon transform domain for near duplicate image detection radon transform has been widely used in content based image representation due to its excellent geometric properties in this paper we propose a family of geometric invariant features based on radon transform for near duplicate image detection according to the theoretical analysis between geometric operations translation scaling and rotation and radon transform we present a geometric invariant feature model based on the feature model we developed four kinds of geometric invariant features in addition a uniform sampling technique is introduced to combine different features the comprehensive performance of the combined feature is better than that of a single one extensive experiments show that the proposed features are robust not only to rotation and scaling but also to other operations such as compression noise contamination blurring illumination modification cropping etc and achieve strong competitive performance compared with the state of the art image features