dissimilarity metric learning in the belief function framework the evidential k nearest neighbor ek nn method provided a global treatment of imperfect knowledge regarding the class membership of training patterns it has outperformed traditional k nn rules in many applications but still shares some of their basic limitations e g 1 classification accuracy depends heavily on how to quantify the dissimilarity between different patterns and 2 no guarantee for satisfactory performance when training patterns contain unreliable imprecise and or uncertain input features in this paper we propose to address these issues by learning a suitable metric using a low dimensional transformation of the input space so as to maximize both the accuracy and efficiency of the ek nn classification to this end a novel loss function to learn the dissimilarity metric is constructed it consists of two terms the first one quantifies the imprecision regarding the class membership of each training pattern while by means of feature selection the second one controls the influence of unreliable input features on the output linear transformation the proposed method has been compared with some other metric learning methods on several synthetic and real datasets it consistently led to comparable performance with regard to testing accuracy and class structure visualization

training free generic object detection using locally adaptive regression kernels we present a generic detection localization algorithm capable of searching for a visual object of interest without training the proposed method operates using a single example of an object of interest to find similar matches does not require prior knowledge learning about objects being sought and does not require any preprocessing step or segmentation of a target image our method is based on the computation of local regression kernels as descriptors from a query which measure the likeness of a pixel to its surroundings salient features are extracted from said descriptors and compared against analogous features from the target image this comparison is done using a matrix generalization of the cosine similarity measure we illustrate optimality properties of the algorithm using a naive bayes framework the algorithm yields a scalar resemblance map indicating the likelihood of similarity between the query and all patches in the target image by employing nonparametric significance tests and nonmaxima suppression we detect the presence and location of objects similar to the given query the approach is extended to account for large variations in scale and rotation high performance is demonstrated on several challenging data sets indicating successful detection of objects in diverse contexts and under different imaging conditions

learning a mahalanobis metric from equivalence constraints many learning algorithms use a metric defined over the input space as a principal tool and their performance critically depends on the quality of this metric we address the problem of learning metrics using side information in the form of equivalence constraints unlike labels we demonstrate that this type of side information can sometimes be automatically obtained without the need of human intervention we show how such side information can be used to modify the representation of the data leading to improved clustering and classification specifically we present the relevant component analysis rca algorithm which is a simple and efficient algorithm for learning a mahalanobis metric we show that rca is the solution of an interesting optimization problem founded on an information theoretic basis if dimensionality reduction is allowed within rca we show that it is optimally accomplished by a version of fisher s linear discriminant that uses constraints moreover under certain gaussian assumptions rca can be viewed as a maximum likelihood estimation of the within class covariance matrix we conclude with extensive empirical evaluations of rca showing its advantage over alternative methods

solvability of a nonlinear two point boundary value problem at resonance ii abstract in this article we apply the leray schauder continuation method to obtain existence theorems of solutions for i u u g x u h in 0 u 0 u 0 in which the nonlinearity g grow superlinearly in u in one of directions u and u and may grow sublinearly in the other and for ii u u g x u h in 0 u 0 u 0 in which the nonlinearity g has no growth restriction in u as u the l1 0 function h may satisfy 0 g x sin x d x 0 h x sin x d x 0 0 g x sin x d x where 0 g x lim inf u g x u u and g x lim sup u g x u u

feature combination and the knn framework in object classification in object classification feature combination can usually be used to combine the strength of multiple complementary features and produce better classification results than any single one while multiple kernel learning mkl is a popular approach to feature combination in object classification it does not always perform well in practical applications on one hand the optimization process in mkl usually involves a huge consumption of computation and memory space on the other hand in some cases mkl is found to perform no better than the baseline combination methods this observation motivates us to investigate the underlying mechanism of feature combination with average combination and weighted average combination as a result we empirically find that in average combination it is better to use a sample of the most powerful features instead of all whereas in one type of weighted average combination the best classification accuracy comes from a nearly sparse combination we integrate these observations into the k nearest neighbors knns framework based on which we further discuss some issues related to sparse solution and mkl finally by making use of the knn framework we present a new weighted average combination method which is shown to perform better than mkl in both accuracy and efficiency in experiments we believe that the work in this paper is helpful in exploring the mechanism underlying feature combination

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

on the second order periodic problem at resonance with impulses abstract in this paper we consider the periodic problem for the second order equation at resonance with impulses in the derivative the impulses are considered at fixed times and depend on the actual value of the solution in a nonlinear way we formulate rather general sufficient condition in terms of the asymptotic properties of both nonlinear restoring force and nonlinear impulses which generalizes classical landesman lazer condition moreover our condition implies existence results for some open problems with vanishing and oscillating nonlinearities

scalable large margin mahalanobis distance metric learning for many machine learning algorithms such as k nearest neighbor k nn classifiers and k means clustering often their success heavily depends on the metric used to calculate distances between different data points an effective solution for defining such a metric is to learn it from a set of labeled training samples in this work we propose a fast and scalable algorithm to learn a mahalanobis distance metric the mahalanobis metric can be viewed as the euclidean distance metric on the input data that have been linearly transformed by employing the principle of margin maximization to achieve better generalization performances this algorithm formulates the metric learning as a convex optimization problem and a positive semidefinite p s d matrix is the unknown variable based on an important theorem that a p s d trace one matrix can always be represented as a convex combination of multiple rank one matrices our algorithm accommodates any differentiable loss function and solves the resulting optimization problem using a specialized gradient descent procedure during the course of optimization the proposed algorithm maintains the positive semidefiniteness of the matrix variable that is essential for a mahalanobis metric compared with conventional methods like standard interior point algorithms or the special solver used in large margin nearest neighbor our algorithm is much more efficient and has a better performance in scalability experiments on benchmark data sets suggest that compared with state of the art metric learning algorithms our algorithm can achieve a comparable classification accuracy with reduced computational complexity

existence of one signed periodic solutions of some second order differential equations via a krasnoselskii fixed point theorem this paper is devoted to study the existence of periodic solutions of the second order equation x 00 f t x where f is a caratheodory function by combining some new properties of green s function together with krasnoselskii fixed point theorem on compression and expansion of cones as applications we get new existence results for equations with jumping nonlinearities as well as equations with a repulsive or attractive singularity in this latter case our results cover equations with weak singularities and are compared with some recent results by i rachunkova m tvrdyand i vrkoc r 2002 elsevier science usa all rights reserved

texture characterization using shape co occurrence patterns texture characterization is a key problem in image understanding and pattern recognition in this paper we present a flexible shape based texture representation using shape co occurrence patterns more precisely texture images are first represented by a tree of shapes each of which is associated with several geometrical and radiometric attributes then four typical kinds of shape co occurrence patterns based on the hierarchical relationships among the shapes in the tree are learned as codewords three different coding methods are investigated for learning the codewords which can be used to encode any given texture image into a descriptive vector in contrast with existing works the proposed approach not only inherits the shape based method s strong ability to capture geometrical aspects of textures and high robustness to variations in imaging conditions but also provides a flexible way to consider shape relationships and to compute high order statistics on the tree to the best of our knowledge this is the first time that co occurrence patterns of explicit shapes have been used as a tool for texture analysis experiments on various texture and scene data sets demonstrate the efficiency of the proposed approach

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

the lack of a priori distinctions between learning algorithms this is the first of two papers that use off training set ots error to investigate the assumption free relationship between learning algorithms this first paper discusses the senses in which there are no a priori distinctions between learning algorithms the second paper discusses the senses in which there are such distinctions in this first paper it is shown loosely speaking that for any two algorithms a and b there are as many targets or priors over targets for which a has lower expected ots error than b as vice versa for loss functions like zero one loss in particular this is true if a is cross validation and b is anti cross validation choose the learning algorithm with largest cross validation error this paper ends with a discussion of the implications of these results for computational learning theory it is shown that one cannot say if empirical misclassification rate is low the vapnik chervonenkis dimension of your generalizer is small and the training set is large then with high probability your ots error is small other implications for membership queries algorithms and punting algorithms are also discussed

global hashing system for fast image search hashing methods have been widely investigated for fast approximate nearest neighbor searching in large data sets most existing methods use binary vectors in lower dimensional spaces to represent data points that are usually real vectors of higher dimensionality we divide the hashing process into two steps data points are first embedded in a low dimensional space and the global positioning system method is subsequently introduced but modified for binary embedding we devise dataindependent and data dependent methods to distribute the satellites at appropriate locations our methods are based on finding the tradeoff between the information losses in these two steps experiments show that our data dependent method outperforms other methods in different sized data sets from 100k to 10m by incorporating the orthogonality of the code matrix both our data independent and data dependent methods are particularly impressive in experiments on longer bits

an asphericity conjecture and kaplansky problem on zero divisors suppose a group representationh a r is aspherical x a w a x is a word in alphabet a x 1with nonzero sum of exponents onx and the grouphnaturally embeds ing a x r w a x it is conjectured that the presentationg a x r w a x is aspherical if and only ifgis torsion free it is proven that if this conecture is false andg a x r w a x is a counterexample then the integral group ring z g of torsion free groupgwill contain zero divisors some special cases when this conjecture holds are also indicated

trivial unit conjecture and homotopy theory abstract a homotopy theoretic description is given for trivial unit conjecture in the group ring z g

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

on the resonance problem with nonlinearity which has arbitrary linear growth abstract this paper deals with the nonlinear two point boundary value problem at resonance even nonlinearities g with an arbitrary linear growth in resp may be considered but only on the cost of the corresponding bound on their linear growth at resp it generalizes the previous results in this direction obtained by m schechter j shapiro and m snow trans amer math soc 241 1978 69 78 l cesari and r kannan proc amer math soc 88 1983 605 613 and s ahmad proc amer math soc 93 1984 381 384

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

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

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

incorporating privileged information through metric learning in some pattern analysis problems there exists expert knowledge in addition to the original data involved in the classification process the vast majority of existing approaches simply ignore such auxiliary privileged knowledge recently a new paradigm learning using privileged information was introduced in the framework of svm this approach is formulated for binary classification and as typical for many kernel based methods can scale unfavorably with the number of training examples while speeding up training methods and extensions of svm to multiclass problems are possible in this paper we present a more direct novel methodology for incorporating valuable privileged knowledge in the model construction phase primarily formulated in the framework of generalized matrix learning vector quantization this is done by changing the global metric in the input space based on distance relations revealed by the privileged information hence unlike in svm any convenient classifier can be used after such metric modification bringing more flexibility to the problem of incorporating privileged information during the training experiments demonstrate that the manipulation of an input space metric based on privileged data improves classification accuracy moreover our methods can achieve competitive performance against the svm formulations

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

efficient circular thresholding otsu s algorithm for thresholding images is widely used and the computational complexity of determining the threshold from the histogram is o n where n is the number of histogram bins when the algorithm is adapted to circular rather than linear histograms then two thresholds are required for binary thresholding we show that surprisingly it is still possible to determine the optimal threshold in o n time the efficient optimal algorithm is over 300 times faster than traditional approaches for typical histograms and is thus particularly suitable for real time applications we further demonstrate the usefulness of circular thresholding using the adapted otsu criterion for various applications including analysis of optical flow data indoor outdoor image classification and non photorealistic rendering in particular by combining circular otsu feature with other colour texture features a 96 9 correct rate is obtained for indoor outdoor classification on the well known iitm scid2 data set outperforming the state of the art result by 4 3

learning with kernel smoothing models and low discrepancy sampling this brief presents an analysis of the performance of kernel smoothing models used to estimate an unknown target function addressing the case where the choice of the training set is part of the learning process in particular we consider a choice of the points at which the function is observed based on low discrepancy sequences which is a family of sampling methods commonly employed for efficient numerical integration we prove that under suitable regularity assumptions consistency of the empirical risk minimization is guaranteed with a good rate of convergence of the estimation error as well as the convergence of the approximation error simulation results confirm in practice the good theoretical properties given by the combination of kernel smoothing models with low discrepancy sampling

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

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

nenmf an optimal gradient method for nonnegative matrix factorization nonnegative matrix factorization nmf is a powerful matrix decomposition technique that approximates a nonnegative matrix by the product of two low rank nonnegative matrix factors it has been widely applied to signal processing computer vision and data mining traditional nmf solvers include the multiplicative update rule mur the projected gradient method pg the projected nonnegative least squares pnls and the active set method as however they suffer from one or some of the following three problems slow convergence rate numerical instability and nonconvergence in this paper we present a new efficient nenmf solver to simultaneously overcome the aforementioned problems it applies nesterov s optimal gradient method to alternatively optimize one factor with another fixed in particular at each iteration round the matrix factor is updated by using the pg method performed on a smartly chosen search point where the step size is determined by the lipschitz constant since nenmf does not use the time consuming line search and converges optimally at rate in optimizing each matrix factor it is superior to mur and pg in terms of efficiency as well as approximation accuracy compared to pnls and as that suffer from numerical instability problem in the worst case nenmf overcomes this deficiency in addition nenmf can be used to solve norm norm and manifold regularized nmf with the optimal convergence rate numerical experiments on both synthetic and real world datasets show the efficiency of nenmf for nmf and its variants comparing to representative nmf solvers extensive experiments on document clustering suggest the effectiveness of nenmf

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

double resonance with landesman lazer conditions for planar systems of ordinary differential equations abstract we prove the existence of periodic solutions for first order planar systems at resonance the nonlinearity is indeed allowed to interact with two positively homogeneous hamiltonians both at resonance and some kind of landesman lazer conditions are assumed at both sides we are thus able to obtain as particular cases the existence results proposed in the pioneering papers by lazer and leach 1969 27 and by frederickson and lazer 1969 18 our theorem also applies in the case of asymptotically piecewise linear systems and in particular generalizes fabry s results in fabry 1995 10 for scalar equations with double resonance with respect to the dancer fucik spectrum

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

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

hyperellipsoidal statistical classifications in a reproducing kernel hilbert space standard support vector machines svms have kernels based on the euclidean distance this brief extends standard svms to svms with kernels based on the mahalanobis distance the extended svms become a special case of the euclidean distance when the covariance matrix in a reproducing kernel hilbert space is degenerated to an identity the mahalanobis distance leads to hyperellipsoidal kernels and the euclidean distance results in hyperspherical ones in this brief the mahalanobis distance based kernel in a reproducing kernel hilbert space is developed systematically extensive experiments demonstrate that the hyperellipsoidal kernels slightly outperform the hyperspherical ones with fewer svs

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

wavelet domain multifractal analysis for static and dynamic texture classification in this paper we propose a new texture descriptor for both static and dynamic textures the new descriptor is built on the wavelet based spatial frequency analysis of two complementary wavelet pyramids standard multiscale and wavelet leader these wavelet pyramids essentially capture the local texture responses in multiple high pass channels in a multiscale and multiorientation fashion in which there exists a strong power law relationship for natural images such a power law relationship is characterized by the so called multifractal analysis in addition two more techniques scale normalization and multiorientation image averaging are introduced to further improve the robustness of the proposed descriptor combining these techniques the proposed descriptor enjoys both high discriminative power and robustness against many environmental changes we apply the descriptor for classifying both static and dynamic textures our method has demonstrated excellent performance in comparison with the state of the art approaches in several public benchmark datasets

max min distance analysis by using sequential sdp relaxation for dimension reduction we propose a new criterion for discriminative dimension reduction max min distance analysis mmda given a data set with c classes represented by homoscedastic gaussians mmda maximizes the minimum pairwise distance of these c classes in the selected low dimensional subspace thus unlike fisher s linear discriminant analysis flda and other popular discriminative dimension reduction criteria mmda duly considers the separation of all class pairs to deal with general case of data distribution we also extend mmda to kernel mmda kmmda dimension reduction via mmda kmmda leads to a nonsmooth max min optimization problem with orthonormal constraints we develop a sequential convex relaxation algorithm to solve it approximately to evaluate the effectiveness of the proposed criterion and the corresponding algorithm we conduct classification and data visualization experiments on both synthetic data and real data sets experimental results demonstrate the effectiveness of mmda kmmda associated with the proposed optimization algorithm

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

landesman lazer condition for nonlinear problems with jumping nonlinearities abstract this paper was motivated by the result of iannacci and nkashama j differential equations 69 1987 289 309 concerning the existence of at least one solution for the differential equation x t m 2 x t g t x t e t with periodic boundary data x 0 x 2 x 0 x 2 0 where m 0 is an integer e is integrable and g satisfies caratheodory s conditions we intend to prove that the landesman lazer type condition is sufficient for solvability of this periodic problem under rather more general assumptions on the growth of the nonlinear term g particularly our hypotheses cover the nonlinearities which may jump over the eigenvalues different from m 2 while the assumptions of iannacci and nkashama allow g only to asymptotically touch the neighbour eigenvalues our approach may be used also for two point boundary value problems the proofs are based on the leray schauder degree theory and on the shooting method for ordinary differential equations

stability and generalization we define notions of stability for learning algorithms and show how to use these notions to derive generalization error bounds based on the empirical error and the leave one out error the methods we use can be applied in the regression framework as well as in the classification one when the classifier is obtained by thresholding a real valued function we study the stability properties of large classes of learning algorithms such as regularization based algorithms in particular we focus on hilbert space regularization and kullback leibler regularization we demonstrate how to apply the results to svm for regression and classification

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

a kernel classification framework for metric learning learning a distance metric from the given training samples plays a crucial role in many machine learning tasks and various models and optimization algorithms have been proposed in the past decade in this paper we generalize several state of the art metric learning methods such as large margin nearest neighbor lmnn and information theoretic metric learning itml into a kernel classification framework first doublets and triplets are constructed from the training samples and a family of degree 2 polynomial kernel functions is proposed for pairs of doublets or triplets then a kernel classification framework is established to generalize many popular metric learning methods such as lmnn and itml the proposed framework can also suggest new metric learning methods which can be efficiently implemented interestingly using the standard support vector machine svm solvers two novel metric learning methods namely doublet svm and triplet svm are then developed under the proposed framework experimental results show that doublet svm and triplet svm achieve competitive classification accuracies with state of the art metric learning methods but with significantly less training time

geometric mean for subspace selection subspace selection approaches are powerful tools in pattern classification and data visualization one of the most important subspace approaches is the linear dimensionality reduction step in the fisher s linear discriminant analysis flda which has been successfully employed in many fields such as biometrics bioinformatics and multimedia information management however the linear dimensionality reduction step in flda has a critical drawback for a classification task with c classes if the dimension of the projected subspace is strictly lower than c 1 the projection to a subspace tends to merge those classes which are close together in the original feature space if separate classes are sampled from gaussian distributions all with identical covariance matrices then the linear dimensionality reduction step in flda maximizes the mean value of the kullback leibler kl divergences between different classes based on this viewpoint the geometric mean for subspace selection is studied in this paper three criteria are analyzed 1 maximization of the geometric mean of the kl divergences 2 maximization of the geometric mean of the normalized kl divergences and 3 the combination of 1 and 2 preliminary experimental results based on synthetic data uci machine learning repository and handwriting digits show that the third criterion is a potential discriminative subspace selection method which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in flda and its several representative extensions

bayes optimality in linear discriminant analysis we present an algorithm that provides the one dimensional subspace where the bayes error is minimized for the c class problem with homoscedastic gaussian distributions our main result shows that the set of possible one dimensional spaces v for which the order of the projected class means is identical defines a convex region with associated convex bayes error function g v this allows for the minimization of the error function using standard convex optimization algorithms our algorithm is then extended to the minimization of the bayes error in the more general case of heteroscedastic distributions this is done by means of an appropriate kernel mapping function this result is further extended to obtain the d dimensional solution for any given d by iteratively applying our algorithm to the null space of the d l dimensional solution we also show how this result can be used to improve upon the outcomes provided by existing algorithms and derive a low computational cost linear approximation extensive experimental validations are provided to demonstrate the use of these algorithms in classification data analysis and visualization

weighted mahalanobis distance kernels for support vector machines the support vector machine svm has been demonstrated to be a very effective classifier in many applications but its performance is still limited as the data distribution information is underutilized in determining the decision hyperplane most of the existing kernels employed in nonlinear svms measure the similarity between a pair of pattern images based on the euclidean inner product or the euclidean distance of corresponding input patterns which ignores data distribution tendency and makes the svm essentially a ldquolocalrdquo classifier in this paper we provide a step toward a paradigm of kernels by incorporating data specific knowledge into existing kernels we first find the data structure for each class adaptively in the input space via agglomerative hierarchical clustering ahc and then construct the weighted mahalanobis distance wmd kernels using the detected data distribution information in wmd kernels the similarity between two pattern images is determined not only by the mahalanobis distance md between their corresponding input patterns but also by the sizes of the clusters they reside in although wmd kernels are not guaranteed to be positive definite pd or conditionally positive definite cpd satisfactory classification results can still be achieved because regularizers in svms with wmd kernels are empirically positive in pseudo euclidean pe spaces experimental results on both synthetic and real world data sets show the effectiveness of ldquopluggingrdquo data structure into existing kernels

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

unbounded perturbations of forced second order ordinary differential equations at resonance we prove the existence of at least one solution for the differential equation x t m2x t g t x t e t with periodicity conditions x 0 x 2 x 0 x 2 0 where m 0 is an integer e is integrable and g satisfies caratheodory conditions our results are obtained for the case when there is resonance at the eigenvalue m2 of the linear second order differential equation t x t 0 r with x 0 x 2 x 0 x 2 0 the function g may be unbounded and touching of the eigenvalue m 1 2 resp m 1 2 if m 0 on a subset of positive measure is allowed our approach also works when periodicity conditions are replaced by dirichlet or neumann boundary conditions the proofs are based on topological degree mawhin s continuation theorem and leray schauder techniques

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

multiclass linear dimension reduction by weighted pairwise fisher criteria we derive a class of computationally inexpensive linear dimension reduction criteria by introducing a weighted variant of the well known k class fisher criterion associated with linear discriminant analysis lda it can be seen that lda weights contributions of individual class pairs according to the euclidean distance of the respective class means we generalize upon lda by introducing a different weighting function

bayesian neighborhood component analysis learning a distance metric in feature space potentially improves the performance of the k nearest neighbor classifier and is useful in many real world applications many metric learning ml algorithms are however based on the point estimation of a quadratic optimization problem which is time consuming susceptible to overfitting and lacks a natural mechanism to reason with parameter uncertainty a property useful especially when the training set is small and or noisy to deal with these issues we present a novel bayesian ml bml method called bayesian neighborhood component analysis nca based on the well known nca method in which the metric posterior is characterized by the local label consistency constraints of observations encoded with a similarity graph instead of independent pairwise constraints for efficient bayesian inference we explore the variational lower bound over the log likelihood of the original nca objective experiments on several publicly available data sets demonstrate that the proposed method is able to learn robust metric measures from small size data set and or from challenging training set with labels contaminated by errors the proposed method is also shown to outperform a previous pairwise constrained bml method

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

constrained empirical risk minimization framework for distance metric learning distance metric learning dml has received increasing attention in recent years in this paper we propose a constrained empirical risk minimization framework for dml this framework enriches the state of the art studies on both theoretic and algorithmic aspects theoretically we comprehensively analyze the generalization by bounding the sample and the approximation errors with respect to the best model algorithmically we carefully derive an optimal gradient descent by using nesterov s method and provide two example algorithms that utilize the logarithmic loss and the smoothed hinge loss respectively we evaluate the new framework on data classification and image retrieval experiments results show that the new framework has competitive performance compared with the representative dml algorithms including xing s method large margin nearest neighbor classifier neighborhood component analysis and regularized metric learning

ambrosetti prodi type result in semi linear damped beam equations abstract the paper is concerned with the ambrosetti prodi type results for periodic solutions of damped beam equations using the topological degree theory the author obtains a multiplicity result which is similar the result for damped wave equations in the literature

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

linear dimensionality reduction via a heteroscedastic extension of lda the chernoff criterion we propose an eigenvector based heteroscedastic linear dimension reduction ldr technique for multiclass data the technique is based on a heteroscedastic two class technique which utilizes the so called chernoff criterion and successfully extends the well known linear discriminant analysis lda the latter which is based on the fisher criterion is incapable of dealing with heteroscedastic data in a proper way for the two class case the between class scatter is generalized so to capture differences in co variances it is shown that the classical notion of between class scatter can be associated with euclidean distances between class means from this viewpoint the between class scatter is generalized by employing the chernoff distance measure leading to our proposed heteroscedastic measure finally using the results from the two class case a multiclass extension of the chernoff criterion is proposed this criterion combines separation information present in the class mean as well as the class covariance matrices extensive experiments and a comparison with similar dimension reduction techniques are presented

a kernel approach for semisupervised metric learning while distance function learning for supervised learning tasks has a long history extending it to learning tasks with weaker supervisory information has only been studied recently in particular some methods have been proposed for semisupervised metric learning based on pairwise similarity or dissimilarity information in this paper we propose a kernel approach for semisupervised metric learning and present in detail two special cases of this kernel approach the metric learning problem is thus formulated as an optimization problem for kernel learning an attractive property of the optimization problem is that it is convex and hence has no local optima while a closed form solution exists for the first special case the second case is solved using an iterative majorization procedure to estimate the optimal solution asymptotically experimental results based on both synthetic and real world data show that this new kernel approach is promising for nonlinear metric learning

semisupervised kernel matrix learning by kernel propagation the goal of semisupervised kernel matrix learning ss kml is to learn a kernel matrix on all the given samples on which just a little supervised information such as class label or pairwise constraint is provided despite extensive research the performance of ss kml still leaves some space for improvement in terms of effectiveness and efficiency for example a recent pairwise constraints propagation pcp algorithm has formulated ss kml into a semidefinite programming sdp problem but its computation is very expensive which undoubtedly restricts pcps scalability in practice in this paper a novel algorithm called kernel propagation kp is proposed to improve the comprehensive performance in ss kml the main idea of kp is first to learn a small sized sub kernel matrix named seed kernel matrix and then propagate it into a larger sized full kernel matrix specifically the implementation of kp consists of three stages 1 separate the supervised sample sub set from the full sample set 2 learn a seed kernel matrix on through solving a small scale sdp problem and 3 propagate the learnt seed kernel matrix into a full kernel matrix on furthermore following the idea in kp we naturally develop two conveniently realizable out of sample extensions for kml one is batch style extension and the other is online style extension the experiments demonstrate that kp is encouraging in both effectiveness and efficiency compared with three state of the art algorithms and its related out of sample extensions are promising too

non negative patch alignment framework in this paper we present a non negative patch alignment framework npaf to unify popular non negative matrix factorization nmf related dimension reduction algorithms it offers a new viewpoint to better understand the common property of different nmf algorithms although multiplicative update rule mur can solve npaf and is easy to implement it converges slowly thus we propose a fast gradient descent fgd to overcome the aforementioned problem fgd uses the newton method to search the optimal step size and thus converges faster than mur experiments on synthetic and real world datasets confirm the efficiency of fgd compared with mur for optimizing npaf based on npaf we develop non negative discriminative locality alignment ndla experiments on face image and handwritten datasets suggest the effectiveness of ndla in classification tasks and its robustness to image occlusions compared with representative nmf related dimension reduction algorithms

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

asphericity and zero divisors in group algebras abstract s v ivanov recently discovered a surprising connection between asphericity of certain spaces and the existence of zero divisors in group algebras we give a different proof of a more general result

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