learning discriminative subspaces on random contrasts for image saliency analysis in visual saliency estimation one of the most challenging tasks is to distinguish targets and distractors that share certain visual attributes with the observation that such targets and distractors can sometimes be easily separated when projected to specific subspaces we propose to estimate image saliency by learning a set of discriminative subspaces that perform the best in popping out targets and suppressing distractors toward this end we first conduct principal component analysis on massive randomly selected image patches the principal components which correspond to the largest eigenvalues are selected to construct candidate subspaces since they often demonstrate impressive abilities to separate targets and distractors by projecting images onto various subspaces we further characterize each image patch by its contrasts against randomly selected neighboring and peripheral regions in this manner the probable targets often have the highest responses while the responses at background regions become very low based on such random contrasts an optimization framework with pairwise binary terms is adopted to learn the saliency model that best separates salient targets and distractors by optimally integrating the cues from various subspaces experimental results on two public benchmarks show that the proposed approach outperforms 16 state of the art methods in human fixation prediction

root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

aci matrices all of whose completions have the same rank we characterize the aci matrices all of whose completions have the same rank determine the largest number of indeterminates in such partial matrices of a given size and determine the partial matrices that attain this largest number

semiparametric instrumental variable estimation of simultaneous equation sample selection models the identification and estimation of a semiparametric simultaneous equation model with selectivity have been considered the identification of structural parameters from reduced form parameters in the semiparametric model requires stronger conditions than the usual rank condition in the classical simultaneous equation model or the parametric simultaneous equation sample selection model with normal disturbances the necessary order condition for identification in the semiparametric model corresponds to the overidentification condition in the classical model semiparametric two stage estimation methods which generalize the two stage least squares method and the generalized two stage least squares method for the parametric model are introduced the semiparametric generalized two stage least squares estimator is shown to be asymptotically efficient in a class of semiparametric instrumental variable estimators

salient region detection via integrating diffusion based compactness and local contrast salient region detection is a challenging problem and an important topic in computer vision it has a wide range of applications such as object recognition and segmentation many approaches have been proposed to detect salient regions using different visual cues such as compactness uniqueness and objectness however each visual cue based method has its own limitations after analyzing the advantages and limitations of different visual cues we found that compactness and local contrast are complementary to each other in addition local contrast can very effectively recover incorrectly suppressed salient regions using compactness cues motivated by this we propose a bottom up salient region detection method that integrates compactness and local contrast cues furthermore to produce a pixel accurate saliency map that more uniformly covers the salient objects we propagate the saliency information using a diffusion process our experimental results on four benchmark data sets demonstrate the effectiveness of the proposed method our method produces more accurate saliency maps with better precision recall curve and higher f measure than other 19 state of the arts approaches on asd cssd and ecssd data sets

characterization of full rank aci matrices over fields abstract an aci matrix over a field f is a matrix whose entries are polynomials with coefficients on f the degree of these polynomials is at most one in a number of indeterminates and where no indeterminate appears in two different columns in 2011 huang and zhan characterized the m n aci matrices such that all its completions have rank equal to min m n whenever f max m n 1 we will give a characterization for arbitrary fields by introducing two classes of aci matrices the maximal and the minimal full rank aci matrices

asymptotic efficiency in semi parametric models with censoring abstract we consider a regression model subject to bivariate censoring in which the errors are independent of the explanatory variables our objective is to drop the assumption of bivaraite normality and obtain an information bound on asymptotic efficiency when the error distribution is unrestricted except for smoothness and regularity conditions this bound has simple form if there are no exclusion restrictions on the selection equation then positive information requires a restriction on the regression slope parameters and a continuous distribution for a component of the explanatory variables we also consider a binary choice model under the weak assumption that the error distribution has zero median conditional on the explanatory variables here the semi parametric information bound is zero hence although a consistent estimator exists it is not possible to attain covergence at rate 1 n

structure sensitive saliency detection via multilevel rank analysis in intrinsic feature space this paper advocates a novel multiscale structure sensitive saliency detection method which can distinguish multilevel reliable saliency from various natural pictures in a robust and versatile way one key challenge for saliency detection is to guarantee the entire salient object being characterized differently from nonsalient background to tackle this our strategy is to design a structure aware descriptor based on the intrinsic biharmonic distance metric one benefit of introducing this descriptor is its ability to simultaneously integrate local and global structure information which is extremely valuable for separating the salient object from nonsalient background in a multiscale sense upon devising such powerful shape descriptor the remaining challenge is to capture the saliency to make sure that salient subparts actually stand out among all possible candidates toward this goal we conduct multilevel low rank and sparse analysis in the intrinsic feature space spanned by the shape descriptors defined on over segmented super pixels since the low rank property emphasizes much more on stronger similarities among super pixels we naturally obtain a scale space along the rank dimension in this way multiscale saliency can be obtained by simply computing differences among the low rank components across the rank scale we conduct extensive experiments on some public benchmarks and make comprehensive quantitative evaluation between our method and existing state of the art techniques all the results demonstrate the superiority of our method in accuracy reliability robustness and versatility

some aspects of measurement error in a censored regression model abstract when a linear model with a censored dependent variable is written as a regression model the model is nonlinear in the explanatory variables this means that when the explanatory variables are measured with error estimation by instrumental variables will not lead to consistent estimates of the parameters my approach to the problem involves assuming that the variables measured with error can be represented by a reduced form equation and estimating the parameters of the censored regression model by the least absolute deviations estimator this estimator is based on the median of the distribution of the dependent variable rather than the mean and the median is not affected by censoring in the lower tail hence the estimator is consistent under general conditions i also consider the problem of testing for the presence of measurement error

matrix completion problems over integral domains the case with a diagonal of prescribed blocks abstract let r be an arbitrary integral domain let 1 n be a multiset of elements of r let be a permutation of 1 k let n 1 n k be positive integers such that n 1 n k n and for r 1 k let a r r n r n r we are interested in the problem of finding a block matrix q q rs r s 1 k r n n with spectrum and such that q r r a r for r 1 k cravo and silva completely characterized the existence of such a matrix when r is a field in this work we construct a solution matrix q that solves the problem when r is an integral domain with two exceptions i k 2 ii k 3 r r and n r n 2 for some r what makes this work quite unique in this area is that we consider the problem over the more general algebraic structure of integral domains which includes the important case of integers furthermore we provide an explicit and easy to implement finite step algorithm that constructs an specific solution matrix we point out that cravo and silva s proof is not constructive

random walks on graphs for salient object detection in images we formulate the problem of salient object detection in images as an automatic labeling problem on the vertices of a weighted graph the seed labeled nodes are first detected using markov random walks performed on two different graphs that represent the image while the global properties of the image are computed from the random walk on a complete graph the local properties are computed from a sparse k regular graph the most salient node is selected as the one which is globally most isolated but falls on a locally compact object a few background nodes and salient nodes are further identified based upon the random walk based hitting time to the most salient node the salient nodes and the background nodes will constitute the labeled nodes a new graph representation of the image that represents the saliency between nodes more accurately the pop out graph model is computed further based upon the knowledge of the labeled salient and background nodes a semisupervised learning technique is used to determine the labels of the unlabeled nodes by optimizing a smoothness objective label function on the newly created pop out graph model along with some weighted soft constraints on the labeled nodes

a matrix completion problem over integral domains the case with 2n 3 prescribed entries abstract let 1 n n 2 be a given multiset of elements in an integral domain r and let p be a matrix of order n with at most 2 n 3 prescribed entries that belong to r under the assumption that each row each column and the diagonal of p have at least one unprescribed entry we prove that p can be completed over r to obtain a matrix a with spectrum we describe an algorithm to construct a this result is an extension to integral domains of a classical completion result by herskowitz for fields

discriminative saliency propagation with sink points salient object detection is still very challenging especially in images with complex or cluttered background in this paper we present an efficient and discriminative framework to address it in specially a discriminative similarity metric is first proposed by measuring the chi square distance in a new constructed feature space then we apply it to calculate a background based coarse saliency map by introducing distribution prior to remove foreground noises in the image boundaries based on manifold ranking a robust saliency propagation mechanism is further developed to highlight salient object and simultaneously suppress background region by setting appropriate sink points finally several simple refinement techniques are utilized to generate pixel wise and smooth saliency maps extensive experimental results show the superior performance of the proposed method in terms of different evaluation metrics in addition the proposed framework can be also applied to the existing saliency propagation methods for significant performance boosting we also believe that it is a good choice for subsequent applications based on the achieved high performance and acceptable computational overhead a discriminative similarity metric is proposed to distinguish similar regions we propose an efficient distribution guided background based weak saliency method a discriminative propagation mechanism is developed to optimize coarse saliency maps several new refinements are utilized to enhance the visual quality of the output we make a good balance between saliency detection accuracy and computational cost

efficient estimation of limited dependent variable models with endogenous explanatory variables abstract this paper discusses asymptotically efficient estimation of the parameters of limited dependent variable models with endogenous explanatory variables general results on asymptotic efficiency of two stage and amemiya gls estimators are derived and used to obtain a simple asymptotically efficient estimator of the structural coefficients this estimator can be calculated by applying gls to estimates of the reduced form coefficients that are obtained by using reduced form residuals as additional explanatory variables it is also shown that it is possible to obtain asymptotically efficient estimators of the other coefficients by a modified minimum chi square method

a novel multiresolution spatiotemporal saliency detection model and its applications in image and video compression salient areas in natural scenes are generally regarded as areas which the human eye will typically focus on and finding these areas is the key step in object detection in computer vision many models have been proposed to simulate the behavior of eyes such as saliencytoolbox stb neuromorphic vision toolkit nvt and others but they demand high computational cost and computing useful results mostly relies on their choice of parameters although some region based approaches were proposed to reduce the computational complexity of feature maps these approaches still were not able to work in real time recently a simple and fast approach called spectral residual sr was proposed which uses the sr of the amplitude spectrum to calculate the image s saliency map however in our previous work we pointed out that it is the phase spectrum not the amplitude spectrum of an image s fourier transform that is key to calculating the location of salient areas and proposed the phase spectrum of fourier transform pft model in this paper we present a quaternion representation of an image which is composed of intensity color and motion features based on the principle of pft a novel multiresolution spatiotemporal saliency detection model called phase spectrum of quaternion fourier transform pqft is proposed in this paper to calculate the spatiotemporal saliency map of an image by its quaternion representation distinct from other models the added motion dimension allows the phase spectrum to represent spatiotemporal saliency in order to perform attention selection not only for images but also for videos in addition the pqft model can compute the saliency map of an image under various resolutions from coarse to fine therefore the hierarchical selectivity hs framework based on the pqft model is introduced here to construct the tree structure representation of an image with the help of hs a model called multiresolution wavelet domain foveation mwdf is proposed in this paper to improve coding efficiency in image and video compression extensive tests of videos natural images and psychological patterns show that the proposed pqft model is more effective in saliency detection and can predict eye fixations better than other state of the art models in previous literature moreover our model requires low computational cost and therefore can work in real time additional experiments on image and video compression show that the hs mwdf model can achieve higher compression rate than the traditional model

rank estimation of a location parameter in the binary choice model abstract this paper proposes a rank based estimator for a location parameter in the binary choice model under a monotonic index and symmetry condition given an initial n consistent estimator for the slope parameter the estimator converges at the usual parametric rate compared with existing estimators no nonparametric smoothing is needed here a small monte carlo study illustrates the usefulness of the estimator we also point out that the location and slope parameters can be jointly estimated

a multisize superpixel approach for salient object detection based on multivariate normal distribution estimation this paper presents a new method for salient object detection based on a sophisticated appearance comparison of multisize superpixels those superpixels are modeled by multivariate normal distributions in cie lab color space which are estimated from the pixels they comprise this fitting facilitates an efficient application of the wasserstein distance on the euclidean norm formula see text to measure perceptual similarity between elements saliency is computed in two ways on the one hand we compute global saliency by probabilistically grouping visually similar superpixels into clusters and rate their compactness on the other hand we use the same distance measure to determine local center surround contrasts between superpixels then an innovative locally constrained random walk technique that considers local similarity between elements balances the saliency ratings inside probable objects and background the results of our experiments show the robustness and efficiency of our approach against 11 recently published state of the art saliency detection methods on five widely used benchmark data sets

on two extremal matrix problems abstract let w be a linear subspace of symmetric n n matrices whose rank is at most t it is shown that if the underlying field has more than n elements then let l be an affine space of n n matrices all having rank at least k it is shown that if the underlying field is algebraically closed then dim l n 2 k 1 2 the last result is applied to a problem of valiant concerning permanents and determinants

limited information estimators and exogeneity tests for simultaneous probit models a two step maximum likelihood procedure is proposed for estimating simultaneous probit models and is compared to alternative limited information estimators conditions under which each estimator attains the cramer rao lower bound are obtained simple tests for exogeneity based on the new two step estimator are proposed and are shown to be asymptotically equivalent to one another and to have the same local asymptotic power as classical tests based on the limited information maximum likelihood estimator finite sample comparisons between the new and alternative estimators are presented based on some monte carlo evidence the performance of the proposed tests for exogeneity is also assessed

endogenous selection or treatment model estimation in a sample selection or treatment effects model common unobservables may affect both the outcome and the probability of selection in unknown ways this paper shows that the distribution function of potential outcomes conditional on covariates can be identified given an observed variable v that affects the treatment or selection probability in certain ways and is conditionally independent of the error terms in a model of potential outcomes selection model estimators based on this identification are provided which take the form of simple weighted averages gmm or two stage least squares these estimators permit endogenous and mismeasured regressors empirical applications are provided to estimation of a firm investment model and a schooling effects on wages model

partial matrices of constant rank abstract a partial matrix over a field f is a matrix whose entries are either elements of f or independent indeterminates a completion of a partial matrix is obtained by specifying values from f for the indeterminates a partial matrix of constant rank is one whose completions all have the same rank we show that every partial matrix of constant rank r over f possesses an r r partial submatrix of constant rank r if and only if f r if f r we show that there exist counterexamples of size m n to this assertion provided that max m n r f 1

treatment effects with censoring and endogeneity this article develops a nonparametric approach to identification and estimation of treatment effects on censored outcomes when treatment may be endogenous and have arbitrarily heterogenous effects identification is based on an instrumental variable that satisfies the exclusion and monotonicity conditions standard in the local average treatment effects framework the article proposes a censored quantile treatment effects estimator derives its asymptotic distribution and illustrates its performance using monte carlo simulations even in the exogenous case the estimator performs better in finite samples than existing censored quantile regression estimators and performs nearly as well as maximum likelihood estimators in cases where their distributional assumptions hold an empirical application to a subsidized job training program finds that participation significantly and dramatically reduced the duration of jobless spells especially at the right tail of the distribution

quantile regression with censoring and endogeneity in this paper we develop a new censored quantile instrumental variable cqiv estimator and describe its properties and computation the cqiv estimator combines powell 1986 censored quantile regression cqr to deal with censoring with a control variable approach to incorporate endogenous regressors the cqiv estimator is obtained in two stages that are nonadditive in the unobservables the first stage estimates a nonadditive model with infinite dimensional parameters for the control variable such as a quantile or distribution regression model the second stage estimates a nonadditive censored quantile regression model for the response variable of interest including the estimated control variable to deal with endogeneity for computation we extend the algorithm for cqr developed by chernozhukov and hong 2002 to incorporate the estimation of the control variable we give generic regularity conditions for asymptotic normality of the cqiv estimator and for the validity of resampling methods to approximate its asymptotic distribution we verify these conditions for quantile and distribution regression estimation of the control variable our analysis covers two stage uncensored quantile regression with nonadditive first stage as an important special case we illustrate the computation and applicability of the cqiv estimator with a monte carlo numerical example and an empirical application on estimation of engel curves for alcohol

partial matrices whose completions all have the same rank abstract a partial matrix over a field f is a matrix whose entries are either elements of f or independent indeterminates a completion of such a partial matrix is obtained by specifying values from f for the indeterminates we determine the maximum possible number of indeterminates in an m n partial matrix m n whose completions all have a particular rank r and we fully describe those examples in which this maximum is attained without any restriction on the field f

spaces of matrices without non zero eigenvalues in their field of definition and a question of szechtman abstract let v be a vector space of dimension n over any field f extreme values for the possible dimension of a linear subspace of end f v with a particular property are considered in two specific cases it is shown that if e 1 is a subspace of end f v and there exists an endomorphism g of v not in e 1 such that for every hyperplane h of v some element of e 1 agrees with g on h then e 1 has dimension at least n n 1 2 1 this answers a question that was posed by szechtman in 2003 it is also shown that a linear subspace of m n f in which no element possesses a non zero eigenvalue in f may have dimension at most n n 1 2 the connection between these two properties which arises from duality considerations is discussed

efficient graph based image segmentation this paper addresses the problem of segmenting an image into regions we define a predicate for measuring the evidence for a boundary between two regions using a graph based representation of the image we then develop an efficient segmentation algorithm based on this predicate and show that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties we apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph and illustrate the results with both real and synthetic images the algorithm runs in time nearly linear in the number of graph edges and is also fast in practice an important characteristic of the method is its ability to preserve detail in low variability image regions while ignoring detail in high variability regions

salient region detection using diffusion process on a two layer sparse graph diffusion based salient region detection has recently received intense research attention in this paper we present some effective improvements concerning two important aspects of diffusion based methods the construction of the diffusion matrix and the seed vector first we construct a two layer sparse graph which is generated by connecting each node to its neighboring nodes and the most similar node that shares common boundaries with its neighboring nodes compared with the most frequently used two layer neighborhood graph our graph not only effectively uses local spatial relationships but also removes dissimilar redundant nodes second we use the spatial variance of superpixel clusters to obtain the seed vector and compared with the previously most used boundary prior our approach can better distinguish saliency seeds from the background seeds especially when salient objects appear near the image boundaries finally we calculate two preliminary saliency maps using the saliency and background seed vectors and more accurate results are obtained using the manifold ranking diffusion method integrating these two diffusion based saliency maps we obtain the final saliency map extensive experiments in which we compare our method with 20 existing state of the art methods on five benchmark data sets asd dut omron ecssd msra5k and msra10k show that the proposed method performs better in terms of various evaluation metrics

efficient implementation of quaternion fourier transform convolution and correlation by 2 d complex fft the concepts of quaternion fourier transform qft quaternion convolution qcv and quaternion correlation which are based on quaternion algebra have been found to be useful for color image processing however the necessary computational algorithms and their complexity still need some attention we develop efficient algorithms for qft qcv and quaternion correlation the conventional complex two dimensional 2 d fourier transform ft is used to implement these quaternion operations very efficiently with these algorithms we only need two complex 2 d fts to implement a qft six complex 2 d fts to implement a one side qcv or a quaternion correlation and 12 complex 2 d fts to implement a two side qcv and the efficiency of these quaternion operations is much improved meanwhile we also discuss two additional topics the first one is about how to use qft and qcv for quaternion linear time invariant qlti system analysis this topic is important for quaternion filter design and color image processing besides we also develop the spectrum product qcv it is an improvement of the conventional form of qcv for any arbitrary input functions it always corresponds to the product operation in the frequency domain it is very useful for quaternion filter design

two step estimation of panel data models with censored endogenous variables and selection bias this paper presents some two step estimators for a wide range of parametric panel data models with censored endogenous variables and sample selection bias our approach is to derive estimates of the unobserved heterogeneity responsible for the endogeneity selection bias to include as additional explanatory variables in the primary equation these are obtained through a decomposition of the reduced form residuals the panel nature of the data allows adjustment and testing for two forms of endogeneity and or sample selection bias furthermore it incorporates roles for dynamics and state dependence in the reduced form finally we provide an empirical illustration which features our procedure and highlights the ability to test several of the underlying assumptions

the wst decomposition for partial matrices abstract a partial matrix over a field f is a matrix whose entries are either an element of f or an indeterminate and each indeterminate only appears once a completion is a matrix obtained by giving values to each of the indeterminates we can decompose any partial matrix through elementary row operations and column permutations into a block matrix of the form w 0 s 0 0 t where w is wide has more columns than rows s is square t is tall has more rows than columns and with these three blocks having at least one completion with full rank and importantly w s and t are unique up to elementary row operations and column permutations whenever s is required to be as large as possible when this is the case w 0 s 0 0 t will be called a wst decomposition as an application of this decomposition we will see that the maximal rank over all completions of the original partial matrix is rows w rows s cols t in fact we introduce the wst decomposition for a broader class of matrices the aci matrices

slic superpixels compared to state of the art superpixel methods computer vision applications have come to rely increasingly on superpixels in recent years but it is not always clear what constitutes a good superpixel algorithm in an effort to understand the benefits and drawbacks of existing methods we empirically compare five state of the art superpixel algorithms for their ability to adhere to image boundaries speed memory efficiency and their impact on segmentation performance we then introduce a new superpixel algorithm simple linear iterative clustering slic which adapts a k means clustering approach to efficiently generate superpixels despite its simplicity slic adheres to boundaries as well as or better than previous methods at the same time it is faster and more memory efficient improves segmentation performance and is straightforward to extend to supervoxel generation

a comparison of the amemiya gls and the lee maddala trost g2sls in a simultaneous equations tobit model abstract this paper proposes a class of gls estimators for the structural parameters of a simultaneous equations tobit model and shows that this class contains an estimator which is asymptotically more efficient than an alternative estimator proposed by lee maddala and trost in 1980

singular nonsingular and bounded rank completions of aci matrices an affine column independent matrix is a matrix whose entries are polynomials of degree at most 1 in a number of indeterminates where no indeterminate appears with a nonzero coefficient in two different columns a completion is a matrix obtained by giving values to each of the indeterminates affine column independent matrices are more general than partial matrices where each entry is either a constant or a distinct indeterminate we determine when the rank of all completions of an affine column independent matrix is bounded by a given number generalizing known results for partial matrices we also characterize the square partial matrices over a field all of whose completions are nonsingular the maximum number of free entries in such matrices of a given order is determined as well as the partial matrices with this maximum number of free entries

aci matrices of constant rank over arbitrary fields abstract the columns of an m n aci matrix over a field f are independent affine subspaces of f m an aci matrix has constant rank if all its completions have rank huang and zhan 2011 4 characterized the m n aci matrices of constant rank when f min m n 1 we complete their result characterizing the m n aci matrices of constant rank over arbitrary fields quinlan and mctigue 2014 8 proved that every partial matrix of constant rank has a submatrix of constant rank if and only f we obtain an analogous result for aci matrices over arbitrary fields by introducing the concept of complete irreducibility

on completions of symmetric and antisymmetric block diagonal partial matrices abstract a partial matrix is a matrix where only some of the entries are given we determine the maximum rank of the symmetric completions of a symmetric partial matrix where only the diagonal blocks are given and the minimum rank and the maximum rank of the antisymmetric completions of an antisymmetric partial matrix where only the diagonal blocks are given

image signature highlighting sparse salient regions we introduce a simple image descriptor referred to as the image signature we show within the theoretical framework of sparse signal mixing that this quantity spatially approximates the foreground of an image we experimentally investigate whether this approximate foreground overlaps with visually conspicuous image locations by developing a saliency algorithm based on the image signature this saliency algorithm predicts human fixation points best among competitors on the bruce and tsotsos 1 benchmark data set and does so in much shorter running time in a related experiment we demonstrate with a change blindness data set that the distance between images induced by the image signature is closer to human perceptual distance than can be achieved using other saliency algorithms pixel wise or gist 2 descriptor methods

semiparametric estimation of binary response models with endogenous regressors abstract in this paper we propose a two step semiparametric maximum likelihood sml estimator for the coefficients of a single index binary choice model with endogenous regressors when identification is achieved via a control function approach the first step consists of estimating a reduced form equation for the endogenous regressors and extracting the corresponding residuals in the second step the latter are added as control variates to the outcome equation which is in turn estimated by sml we establish the estimator s n consistency and asymptotic normality in a simulation study we compare the properties of our estimator with those of existing alternatives highlighting the advantages of our approach

partial matrices all of whose completions have the same spectrum abstract we characterize the square partial matrices over a field all of whose completions have the same spectrum and determine the maximum number of indeterminates in such partial matrices of a given order as well as the matrices that attain this maximum number

partial matrices whose completions have ranks bounded below abstract a partial matrix over a field f is a matrix whose entries are either elements of f or independent indeterminates a completion of such a partial matrix is obtained by specifying values from f for the indeterminates we determine the maximum possible number of indeterminates in a partial m n matrix whose completions all have rank at least equal to a particular k and we fully describe those examples in which this maximum is attained our main theoretical tool which is developed in section 2 is a duality relationship between affine spaces of matrices in which ranks are bounded below and affine spaces of matrices in which the left or right nullspaces of elements possess a certain covering property

distribution free estimation of the random coefficient dummy endogenous variable model this paper considers the estimation of the random coefficient dummy endogenous variable model under a symmetry and index condition for the error distribution we follow a two step approach the selection equation is estimated first in the second step an instrumental variables estimator is proposed for the ourcome equation through a pairwise comparison method our approach can be readily extended to the general switching regression model in constrast to the existing literature on sample selection models the exclusion restriction is not needed here for model identification furthermore the intercept term for the outcome equation can be estimated at the usual parametric rate

a co saliency model of image pairs in this paper we introduce a method to detect co saliency from an image pair that may have some objects in common the co saliency is modeled as a linear combination of the single image saliency map sism and the multi image saliency map mism the first term is designed to describe the local attention which is computed by using three saliency detection techniques available in literature to compute the mism a co multilayer graph is constructed by dividing the image pair into a spatial pyramid representation each node in the graph is described by two types of visual descriptors which are extracted from a representation of some aspects of local appearance e g color and texture properties in order to evaluate the similarity between two nodes we employ a normalized single pair simrank algorithm to compute the similarity score experimental evaluation on a number of image pairs demonstrates the good performance of the proposed method on the co saliency detection task

image segmentation using active contours driven by the bhattacharyya gradient flow this paper addresses the problem of image segmentation by means of active contours whose evolution is driven by the gradient flow derived from an energy functional that is based on the bhattacharyya distance in particular given the values of a photometric variable or of a set thereof which is to be used for classifying the image pixels the active contours are designed to converge to the shape that results in maximal discrepancy between the empirical distributions of the photometric variable inside and outside of the contours the above discrepancy is measured by means of the bhattacharyya distance that proves to be an extremely useful tool for solving the problem at hand the proposed methodology can be viewed as a generalization of the segmentation methods in which active contours maximize the difference between a finite number of empirical moments of the ldquoinsiderdquo and ldquooutsiderdquo distributions furthermore it is shown that the proposed methodology is very versatile and flexible in the sense that it allows one to easily accommodate a diversity of the image features based on which the segmentation should be performed as an additional contribution a method for automatically adjusting the smoothness properties of the empirical distributions is proposed such a procedure is crucial in situations when the number of data samples supporting a certain segmentation class varies considerably in the course of the evolution of the active contour in this case the smoothness properties of the empirical distributions have to be properly adjusted to avoid either over or underestimation artifacts finally a number of relevant segmentation results are demonstrated and some further research directions are discussed

the power of convex relaxation near optimal matrix completion this paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries this is known as the matrix completion problem and comes up in a great number of applications including the famous netflix prize and other similar questions in collaborative filtering in general accurate recovery of a matrix from a small number of entries is impossible but the knowledge that the unknown matrix has low rank radically changes this premise making the search for solutions meaningful this paper presents optimality results quantifying the minimum number of entries needed to recover a matrix of rank r exactly by any method whatsoever the information theoretic limit more importantly the paper shows that under certain incoherence assumptions on the singular vectors of the matrix recovery is possible by solving a convenient convex program as soon as the number of entries is on the order of the information theoretic limit up to logarithmic factors this convex program simply finds among all matrices consistent with the observed entries that with minimum nuclear norm as an example we show that on the order of nr log n samples are needed to recover a random n x n matrix of rank r by any method and to be sure nuclear norm minimization succeeds as soon as the number of entries is of the form nr polylog n

on the matrices of given rank in a large subspace abstract let v be a linear subspace of m n p k with codimension lesser than n where k is an arbitrary field and n p in a recent work of the author it was proven that v is always spanned by its rank p matrices unless n p 2 and k f 2 here we give a sufficient condition on codim v for v to be spanned by its rank r matrices for a given r 1 p 1 this involves a generalization of the gerstenhaber theorem on linear subspaces of nilpotent matrices

hypercomplex fourier transforms of color images fourier transforms are a fundamental tool in signal and image processing yet until recently there was no definition of a fourier transform applicable to color images in a holistic manner in this paper hypercomplex numbers specifically quaternions are used to define a fourier transform applicable to color images the properties of the transform are developed and it is shown that the transform may be computed using two standard complex fast fourier transforms the resulting spectrum is explained in terms of familiar phase and modulus concepts and a new concept of hypercomplex axis a method for visualizing the spectrum using color graphics is also presented finally a convolution operational formula in the spectral domain is discussed

nonsingular aci matrices over integral domains abstract an aci matrix is a matrix whose entries are polynomials of degree at most one in a number of indeterminates where no indeterminate appears in two different columns consider the next two problems a characterize the aci matrices of order n all of whose completions have the same nonzero constant determinant b characterize the aci matrices of order n all of whose completions are nonsingular in 2010 brualdi huang and zhan solved both problems for fields of at least n 1 elements we extend their result on problem a to integral domains and extend their result on problem b to arbitrary fields

nonlocal center surround reconstruction based bottom up saliency estimation many saliency models consider the feature extraction as the algorithmic core and the performance of their methods relies on the selection of the features to a great extent however there can hardly be a set of features effective to pop out the salient regions under various visual environments moreover because saliency is not tuned to certain visual features a location winning the spatial competition in any feature space can be defined as salient instead of seeking for or learning the features to highlight the difference between the salient areas and the background we focus more on the sparsity and uniqueness carried by the original image itself the source of all the features to propose a nonlocal reconstruction based saliency model in the proposed approach the saliency is measured by the sparse reconstruction residual of representing the central patch with a linear combination of its surrounding patches sampled in a nonlocal manner in addition this is generalized to model the global aspect saliency which provides a complement to the nonlocal saliency and improves the performance further as a generalization of itti et al s classical center surround comparison scheme the proposed approach performs well on images where itti et al s method fails as well as on general natural images numerical experiments show the proposed approach produces better results compared with the state of the art algorithms on three public databases highlightsa nonlocal reconstruction based bottom up saliency estimation method is proposed nonlocal image processing is employed to provide a better treatment of textures sparsity pursuit is very effective for removing duplicated similar image regions reconstruction residual is inherently coherent with the bottom up saliency our method is stable under three public datasets and consistent with human fixations

saliency detection by multitask sparsity pursuit this paper addresses the problem of detecting salient areas within natural images we shall mainly study the problem under unsupervised setting i e saliency detection without learning from labeled images a solution of multitask sparsity pursuit is proposed to integrate multiple types of features for detecting saliency collaboratively given an image described by multiple features its saliency map is inferred by seeking the consistently sparse elements from the joint decompositions of multiple feature matrices into pairs of low rank and sparse matrices the inference process is formulated as a constrained nuclear norm and as an l2 1 norm minimization problem which is convex and can be solved efficiently with an augmented lagrange multiplier method compared with previous methods which usually make use of multiple features by combining the saliency maps obtained from individual features the proposed method seamlessly integrates multiple features to produce jointly the saliency map with a single inference step and thus produces more accurate and reliable results in addition to the unsupervised setting the proposed method can be also generalized to incorporate the top down priors obtained from supervised environment extensive experiments well validate its superiority over other state of the art methods

specification tests for distributional assumptions in the tobit model abstract the recent development of distribution robust estimators for the censored regression model allows for the construction of specification tests of the normality and homoskedasticity assumption of the tobit model this paper considers hausman 1978 specification tests for the tobit model that are based on powell s 1986 symmetrically censored least squares estimator testing for models with explanatory variables that are endogeneous is considered as well as the simpler case where the explanatory variables are exogenous testing of the maintained conditional symmetry assumption of the symmetrically censored least squares estimator is also considered the tests are implemented in an empirical example of a model of female labor supply

almost nonsingular entry pattern matrices abstract in an entry pattern matrix a all entries are indeterminates and the same indeterminate may appear in multiple positions for a field f an f completion of a results from assigning a value from f to each indeterminate entry we say that a square entry pattern matrix is almost nonsingular over a field f if all of its f completions are nonsingular except for those in which all indeterminates are assigned the same value this work investigates bounds for the maximum number of indeterminates of almost nonsingular entry pattern matrices over some fields including the real field the rational field and finite fields

efficient estimation of binary choice models under symmetry abstract this paper proposes a semiparametric maximum likelihood estimator for both the intercept and slope parameters in a binary choice model under symmetry and index restrictions the estimator attains the semiparametric efficiency bound in cosslett 1987 under the symmetry and independence restrictions compared with the estimator of klein and spady 1993 which attains the semiparametric efficiency bound in chamberlain 1986 and cosslett 1987 under the independence restriction we show that there are possible efficiency gains in estimating the slope parameters by imposing the additional symmetry restriction a small monte carlo study is carried out to illustrate the usefulness of our estimator

efficiency bounds for distribution free estimators of the binary choice and the censored regression models we derive lower bounds on the asymptotic variances for regular distribution free estimators of the parameters of the binary choice model and the censored regression tobit model a distribution free or semiparametric estimator is one that does not require any assumption about the distribution of the stochastic error term in the model apart from regularity conditions for the binary choice model we obtain an explicit lower bound for the asymptotic variance for the slope parameters or more generally the parameters of a nonlinear regression function in the underlying latent variable model but we find that there is no regular semiparametric estimator of the constant term identified by requiring the error distribution to have zero median lower bounds are also obtained under the further assumption that the error distribution is symmetric and in this case there is a finite lower bound for the constant term too comparison of the bounds with those for the classical parametric problem shows the loss of information due to lack of a priori knowledge of the functional form of the error distribution we give the conditions for equality of the parametric and semiparametric lower bounds in which case adaptive estimation may be possible both with and without the assumption of a symmetric error distribution in general adaptive estimation is not possible but one special case where these conditions hold is when the regression function is linear and the explanatory variables have a multivariate normal distribution the tobit model considered here is the censored nonlinear regression model with a fixed censoring point we again give an explicit lower bound for the asymptotic variance for the regression parameters this time including a constant term if the error term has zero median comparison with the corresponding lower bound for the parametric case shows that adaptive estimation is in general not possible for this model

on the maximum rank of completions of entry pattern matrices abstract in an entry pattern matrix a all entries are indeterminates but the same indeterminate can appear in numerous positions for a field f an f completion of a results from assigning a value from f to each indeterminate entry we define the generic f rank of an entry pattern matrix to be its rank when considered over the function field generated over f by its indeterminate entries we investigate the situation where the generic f rank of a is not attained by any f completion of a which can occur only if the generic f rank exceeds the field order