a large sample study of cox s regression model strong consistency and asymptotic normality are established for the maximum partial likelihood estimate of the regression parameter in cox s regression model estimates are also derived for the underlying cumulative hazard function and survival distribution we establish the asymptotic normality of these estimates and calculate the limiting variances

heterogeneous tensor decomposition for clustering via manifold optimization tensor clustering is an important tool that exploits intrinsically rich structures in real world multiarray or tensor datasets often in dealing with those datasets standard practice is to use subspace clustering that is based on vectorizing multiarray data however vectorization of tensorial data does not exploit complete structure information in this paper we propose a subspace clustering algorithm without adopting any vectorization process our approach is based on a novel heterogeneous tucker decomposition model taking into account cluster membership information we propose a new clustering algorithm that alternates between different modes of the proposed heterogeneous tensor model all but the last mode have closed form updates updating the last mode reduces to optimizing over the multinomial manifold for which we investigate second order riemannian geometry and propose a trust region algorithm numerical experiments show that our proposed algorithm compete effectively with state of the art clustering algorithms that are based on tensor factorization

words avoiding repetitions in arithmetic progressions carpi constructed an infinite word over a 4 letter alphabet that avoids squares in all subsequences indexed by arithmetic progressions of odd difference we show a connection between carpi s construction and the paperfolding words we extend carpi s result by constructing uncountably many words that avoid squares in arithmetic progressions of odd difference we also construct infinite words avoiding overlaps and infinite words avoiding all sufficiently large squares in arithmetic progressions of odd difference we use these words to construct labelings of the 2 dimensional integer lattice such that any line through the lattice encounters a squarefree resp overlapfree sequence of labels

transcendence of formal power series with rational coefficients we give algebraic proofs of transcendence over q x of formal power series with rational coefficients by using inter alia reduction modulo prime numbers and the christol theorem applications to generating series of languages and combinatorial objects are given

discriminative learning and recognition of image set classes using canonical correlations we address the problem of comparing sets of images for object recognition where the sets may represent variations in an object s appearance due to changing camera pose and lighting conditions canonical correlations also known as principal or canonical angles which can be thought of as the angles between two d dimensional subspaces have recently attracted attention for image set matching canonical correlations offer many benefits in accuracy efficiency and robustness compared to the two main classical methods parametric distribution based and nonparametric sample based matching of sets here this is first demonstrated experimentally for reasonably sized data sets using existing methods exploiting canonical correlations motivated by their proven effectiveness a novel discriminative learning method over sets is proposed for set classification specifically inspired by classical linear discriminant analysis lda we develop a linear discriminant function that maximizes the canonical correlations of within class sets and minimizes the canonical correlations of between class sets image sets transformed by the discriminant function are then compared by the canonical correlations classical orthogonal subspace method osm is also investigated for the similar purpose and compared with the proposed method the proposed method is evaluated on various object recognition problems using face image sets with arbitrary motion captured under different illuminations and image sets of 500 general objects taken at different views the method is also applied to object category recognition using eth 80 database the proposed method is shown to outperform the state of the art methods in terms of accuracy and efficiency

information and asymptotic efficiency in parametric nonparametric models asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems for regular estimates and asymptotic minimax bounds the methods used involve i the notion of a hellinger differentiable root density where part of the differentiation is with respect to the nonparametric part of the model to obtain appropriate scores and ii calculation of the effective score for the real or vector finite dimensional parameter of interest as that component of the score function orthogonal to all nuisance parameter scores perhaps infinite dimensional the resulting asymptotic information for estimation of the parametric component of the model is just 4 times the squared l 2 norm of the effective score a corollary of these results is a simple necessary condition for adaptive estimation adaptation is possible only if the scores for the parameter of interest are orthogonal to the scores for the nuisance function or nonparametric part of the model examples considered include the one sample location model with and without symmetry mixture models the two sample shift model and cox s proportional hazards model

lambertian reflectance and linear subspaces we prove that the set of all lambertian reflectance functions the mapping from surface normals to intensities obtained with arbitrary distant light sources lies close to a 9d linear subspace this implies that in general the set of images of a convex lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low dimensional linear subspace explaining prior empirical results we also provide a simple analytic characterization of this linear space we obtain these results by representing lighting using spherical harmonics and describing the effects of lambertian materials as the analog of a convolution these results allow us to construct algorithms for object recognition based on linear methods as well as algorithms that use convex optimization to enforce nonnegative lighting functions we also show a simple way to enforce nonnegative lighting when the images of an object lie near a 4d linear space we apply these algorithms to perform face recognition by finding the 3d model that best matches a 2d query image

conditional entropy of some automatic sequences burrows and sulston 1991 have introduced conditional block entropies hn from information theory in order to give a quantitative measure of disorder for sequences and if possible a characterization of quasicrystalline sequences we give here some properties concerning these block entropies and give an explicit formula for the sequences hn n in n corresponding to the thue morse sequence the rudin shapiro sequence and the paperfolding sequence we deduce from these computations that this measure of disorder does not enable us to distinguish between deterministic sequences even if they have different spectral properties

about the p paperfolding words abstract let p be an integer greater than or equal to 2 the aim of this paper is to study the language associated to a p paperfolding sequence it is known that the number of factors of length n of a 2 paperfolding sequence i e its complexity function is p n 4n for n 7 it is also known that the language of all the factors of all 2 paperfolding sequences is not context free and that its generating function is transcendental we show that the complexity function of a p paperfolding sequence is either strictly subaffine or ultimately linear the first case never happens if p 2 or 3 in the second case the complexity function is either p n 2n or p n 4n for n large enough we give a simple necessary and sufficient condition for the number of special factors to be p automatic we finally show that for any given p the language of all factors of all p paperfolding sequences is not context free and that the associated generating series is not algebraic

sparse coding on symmetric positive definite manifolds using bregman divergences this paper introduces sparse coding and dictionary learning for symmetric positive definite spd matrices which are often used in machine learning computer vision and related areas unlike traditional sparse coding schemes that work in vector spaces in this paper we discuss how spd matrices can be described by sparse combination of dictionary atoms where the atoms are also spd matrices we propose to seek sparse coding by embedding the space of spd matrices into the hilbert spaces through two types of the bregman matrix divergences this not only leads to an efficient way of performing sparse coding but also an online and iterative scheme for dictionary learning we apply the proposed methods to several computer vision tasks where images are represented by region covariance matrices our proposed algorithms outperform state of the art methods on a wide range of classification tasks including face recognition action recognition material classification and texture categorization

nonlinear mean shift over riemannian manifolds the original mean shift algorithm is widely applied for nonparametric clustering in vector spaces in this paper we generalize it to data points lying on riemannian manifolds this allows us to extend mean shift based clustering and filtering techniques to a large class of frequently occurring non vector spaces in vision we present an exact algorithm and prove its convergence properties as opposed to previous work which approximates the mean shift vector the computational details of our algorithm are presented for frequently occurring classes of manifolds such as matrix lie groups grassmann manifolds essential matrices and symmetric positive definite matrices applications of the mean shift over these manifolds are shown

subspace angles between arma models abstract we define a notion of subspace angles between two linear autoregressive moving average single input single output models by considering the principal angles between subspaces that are derived from these models we show how a recently defined metric for these models which is based on their cepstra relates to the subspace angles between the models

action recognition from video using feature covariance matrices we propose a general framework for fast and accurate recognition of actions in video using empirical covariance matrices of features a dense set of spatio temporal feature vectors are computed from video to provide a localized description of the action and subsequently aggregated in an empirical covariance matrix to compactly represent the action two supervised learning methods for action recognition are developed using feature covariance matrices common to both methods is the transformation of the classification problem in the closed convex cone of covariance matrices into an equivalent problem in the vector space of symmetric matrices via the matrix logarithm the first method applies nearest neighbor classification using a suitable riemannian metric for covariance matrices the second method approximates the logarithm of a query covariance matrix by a sparse linear combination of the logarithms of training covariance matrices the action label is then determined from the sparse coefficients both methods achieve state of the art classification performance on several datasets and are robust to action variability viewpoint changes and low object resolution the proposed framework is conceptually simple and has low storage and computational requirements making it attractive for real time implementation

statistical computations on grassmann and stiefel manifolds for image and video based recognition in this paper we examine image and video based recognition applications where the underlying models have a special structure the linear subspace structure we discuss how commonly used parametric models for videos and image sets can be described using the unified framework of grassmann and stiefel manifolds we first show that the parameters of linear dynamic models are finite dimensional linear subspaces of appropriate dimensions unordered image sets as samples from a finite dimensional linear subspace naturally fall under this framework we show that an inference over subspaces can be naturally cast as an inference problem on the grassmann manifold to perform recognition using subspace based models we need tools from the riemannian geometry of the grassmann manifold this involves a study of the geometric properties of the space appropriate definitions of riemannian metrics and definition of geodesics further we derive statistical modeling of inter and intraclass variations that respect the geometry of the space we apply techniques such as intrinsic and extrinsic statistics to enable maximum likelihood classification we also provide algorithms for unsupervised clustering derived from the geometry of the manifold finally we demonstrate the improved performance of these methods in a wide variety of vision applications such as activity recognition video based face recognition object recognition from image sets and activity based video clustering

multiresolution gray scale and rotation invariant texture classification with local binary patterns presents a theoretically very simple yet efficient multiresolution approach to gray scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions the method is based on recognizing that certain local binary patterns termed uniform are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature we derive a generalized gray scale and rotation invariant operator presentation that allows for detecting the uniform patterns for any quantization of the angular space and for any spatial resolution and presents a method for combining multiple operators for multiresolution analysis the proposed approach is very robust in terms of gray scale variations since the operator is by definition invariant against any monotonic transformation of the gray scale another advantage is computational simplicity as the operator can be realized with a few operations in a small neighborhood and a lookup table experimental results demonstrate that good discrimination can be achieved with the occurrence statistics of simple rotation invariant local binary patterns

sparse representation for color image restoration sparse representations of signals have drawn considerable interest in recent years the assumption that natural signals such as images admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data in particular the design of well adapted dictionaries for images has been a major challenge the k svd has been recently proposed for this task and shown to perform very well for various grayscale image processing tasks in this paper we address the problem of learning dictionaries for color images and extend the k svd based grayscale image denoising algorithm that appears in this work puts forward ways for handling nonhomogeneous noise and missing information paving the way to state of the art results in applications such as color image denoising demosaicing and inpainting as demonstrated in this paper

on the asymptotic information bound on discute plusieurs resultats de borne inferieure pour la performance asymptotique d estimateurs de fonctionnelles regulieres dans des modeles independants et identiquement distribues l idee principale est de regarder un ensemble de lois limites locales d une suite d estimateurs plutot que d imposer des conditions de regularite ou de considerer des limites de risque maximum on accorde une attention particuliere a des situations ou le cone tangent n est pas un espace lineaire on calcule le risque minimax asymptotique local dans des modeles melanges

a random linear functional approach to efficiency bounds abstract this paper suggests a method for obtaining efficiency bounds in models containing either only infinite dimensional parameters or both finite and infinite dimensional parameters semiparametric models the method is based on a theory of random linear functionals applied to the gradient of the log likelihood functional and is illustrated by computing the lower bound for cox s regression model

the ring of k regular sequences ii in this paper we continue our study of k regular sequences begun in 1992 we prove some new results give many new examples from the literature and state some open problems

fisher s information in terms of the hazard rate if g t is a regular family of probability densities on the real line with corresponding hazard rates h t then the fisher information for can be expressed in terms of the hazard rate as follows f g 2 g h h 2 g r where the dot denotes this identity shows that the hazard rate transform of a probability density has an unexpected length preserving property we explore this property is continuous and discrete settings some geometric consequences and curvature formulas its connection with martingale theory and its relation to statistical issues in the theory of life time distributions and censored data

some combinatorial properties of the thue morse sequence and a problem in semigroups abstract some combinatorial properties of the special factors of the thue morse sequence in a two letter alphabet are considered an application of this analysis to a problem in semigroups is given

human gesture recognition on product manifolds action videos are multidimensional data and can be naturally represented as data tensors while tensor computing is widely used in computer vision the geometry of tensor space is often ignored the aim of this paper is to demonstrate the importance of the intrinsic geometry of tensor space which yields a very discriminating structure for action recognition we characterize data tensors as points on a product manifold and model it statistically using least squares regression to this aim we factorize a data tensor relating to each order of the tensor using higher order singular value decomposition hosvd and then impose each factorized element on a grassmann manifold furthermore we account for underlying geometry on manifolds and formulate least squares regression as a composite function this gives a natural extension from euclidean space to manifolds consequently classification is performed using geodesic distance on a product manifold where each factor manifold is grassmannian our method exploits appearance and motion without explicitly modeling the shapes and dynamics we assess the proposed method using three gesture databases namely the cambridge hand gesture the umd keck body gesture and the chalearn gesture challenge data sets experimental results reveal that not only does the proposed method perform well on the standard benchmark data sets but also it generalizes well on the one shot learning gesture challenge furthermore it is based on a simple statistical model and the intrinsic geometry of tensor space

unsupervised adaptation across domain shifts by generating intermediate data representations with unconstrained data acquisition scenarios widely prevalent the ability to handle changes in data distribution across training and testing data sets becomes important one way to approach this problem is through domain adaptation and in this paper we primarily focus on the unsupervised scenario where the labeled source domain training data is accompanied by unlabeled target domain test data we present a two stage data driven approach by generating intermediate data representations that could provide relevant information on the domain shift starting with a linear representation of domains in the form of generative subspaces of same dimensions for the source and target domains we first utilize the underlying geometry of the space of these subspaces the grassmann manifold to obtain a shortest geodesic path between the two domains we then sample points along the geodesic to obtain intermediate cross domain data representations using which a discriminative classifier is learnt to estimate the labels of the target data we subsequently incorporate non linear representation of domains by considering a reproducing kernel hilbert space representation and a low dimensional manifold representation using laplacian eigenmaps and also examine other domain adaptation settings such as i semi supervised adaptation where the target domain is partially labeled and ii multi domain adaptation where there could be more than one domain in source and or target data sets finally we supplement our adaptation technique with i fine grained reference domains that are created by blending samples from source and target data sets to provide some evidence on the actual domain shift and ii a multi class boosting analysis to obtain robustness to the choice of algorithm parameters we evaluate our approach for object recognition problems and report competitive results on two widely used office and bing adaptation data sets

an efficient nonparametric estimator for models with nonlinear dependence we provide a convenient econometric framework for the analysis of nonlinear dependence in financial applications we introduce models with constrained nonparametric dependence which specify the conditional distribution or the copula in terms of a one dimensional functional parameter our approach is intermediate between standard parametric specifications which are in general too restrictive and the fully unrestricted approach which suffers from the curse of dimensionality we introduce a nonparametric estimator defined by minimizing a chi square distance between the constrained densities in the family and an unconstrained kernel estimator of the density we derive the nonparametric efficiency bound for linear forms and show that the minimum chi square estimator is nonparametrically efficient for linear forms

canonical positions for the factors in paperfolding sequences it has been proved by the first author that the number of factors of length k in any paperfolding sequence is equal to 4k once k 7 we prove here that for every integer k there exists a set of integers pk of cardinality 4k for k 7 such that the factors of length k of any paperfolding sequence are exactly the factors beginning at the places indexed by the integers in pk this gives a bijective proof of the result mentioned above then we give an explicit uniform linear upper bound for the recurrence function of paperfolding sequences finally we study the set of all factors of all paperfolding sequences evaluating their number for a given length and studying the language of these words

on the factors of the sturmian sequences resume cet article a pour objet l etude d une construction associant a toute droite de pente p q p et q premiers entre eux et q n un mot de longueur n sur l alphabet 0 1 nous montrons que nous obtenons par cette construction le langage constitue de tous les facteurs des suites de sturm nous formulons apres avoir obtenu une equation fonctionelle dont la solution est la serie generatrice de ce langage une conjecture reliant cette serie generatrice a la fonction d euler

semi nonparametric maximum likelihood estimation on developpe une approche basee sur une innovation due a phillips 1983 sur les approximations des fonctions de densite

schrodinger operators with rudin shapiro potentials are not palindromic we prove a conjecture of a hof o knill and b simon commun math phys 174 149 159 1995 by showing that the rudin shapiro sequence is not palindromic i e does not contain arbitrarily long palindromes we prove actually this property for all paperfolding sequences and all rudin shapiro sequences deduced from paperfolding sequences as a consequence and as guessed by the above authors their method cannot be used for establishing that discrete schrodinger operators with rudin shapiro potentials have a purely singular continuous spectrum

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

canonical correlation analysis of video volume tensors for action categorization and detection this paper addresses a spatiotemporal pattern recognition problem the main purpose of this study is to find a right representation and matching of action video volumes for categorization a novel method is proposed to measure video to video volume similarity by extending canonical correlation analysis cca a principled tool to inspect linear relations between two sets of vectors to that of two multiway data arrays or tensors the proposed method analyzes video volumes as inputs avoiding the difficult problem of explicit motion estimation required in traditional methods and provides a way of spatiotemporal pattern matching that is robust to intraclass variations of actions the proposed matching is demonstrated for action classification by a simple nearest neighbor classifier we moreover propose an automatic action detection method which performs 3d window search over an input video with action exemplars the search is speeded up by dynamic learning of subspaces in the proposed cca experiments on a public action data set kth and a self recorded hand gesture data showed that the proposed method is significantly better than various state of the art methods with respect to accuracy our method has low time complexity and does not require any major tuning parameters

extrinsic methods for coding and dictionary learning on grassmann manifolds sparsity based representations have recently led to notable results in various visual recognition tasks in a separate line of research riemannian manifolds have been shown useful for dealing with features and models that do not lie in euclidean spaces with the aim of building a bridge between the two realms we address the problem of sparse coding and dictionary learning in grassmann manifolds i e the space of linear subspaces to this end we propose to embed grassmann manifolds into the space of symmetric matrices by an isometric mapping this in turn enables us to extend two sparse coding schemes to grassmann manifolds furthermore we propose an algorithm for learning a grassmann dictionary atom by atom lastly to handle non linearity in data we extend the proposed grassmann sparse coding and dictionary learning algorithms through embedding into higher dimensional hilbert spaces experiments on several classification tasks gender recognition gesture classification scene analysis face recognition action recognition and dynamic texture classification show that the proposed approaches achieve considerable improvements in discrimination accuracy in comparison to state of the art methods such as kernelized affine hull method and graph embedding grassmann discriminant analysis

efficiency bounds for semiparametric regression efficiency bounds for conditional moment restrictions with a nonparametric component are derived there is a given function of the data a random sample from a distribution f and a parameter the restriction is that a conditional expectation of this function is zero at some point in the parameter space the parameter has two parts a finite dimensional component and a general function evaluated at a subset of the conditioning variables an example is a regression function that is additive in parametric and nonparametric component as arises in sample selection models copyright 1992 by the econometric society

some studies on the p q type sequences in this paper we have introduced the p q type sequences their arithmetic and analytic properties are studied and their relations with finite automata are established the results obtained extend those of classical paperfolding sequences and some new informations are obtained

a grassmann framework for 4d facial shape analysis in this paper we investigate the contribution of dynamic evolution of 3d faces to identity recognition to this end we adopt a subspace representation of the flow of curvature maps computed on 3d facial frames of a sequence after normalizing their pose such representation allows us to embody the shape as well as its temporal evolution within the same subspace representation dictionary learning and sparse coding over the space of fixed dimensional subspaces called grassmann manifold have been used to perform face recognition we have conducted extensive experiments on the bu 4dfe dataset the obtained results of the proposed approach provide promising results highlightsrole of facial shape dynamics in identity recognition effective representation of 3d faces and their dynamics on grassmann manifolds sparse coding and dictionary learning for 4d faces classification

analytic pca construction for theoretical analysis of lighting variability in images of a lambertian object we analyze theoretically the subspace best approximating images of a convex lambertian object taken from the same viewpoint but under different distant illumination conditions we analytically construct the principal component analysis for images of a convex lambertian object explicitly taking attached shadows into account and find the principal eigenmodes and eigenvalues with respect to lighting variability our analysis makes use of an analytic formula for the irradiance in terms of spherical harmonic coefficients of the illumination and shows under appropriate assumptions that the principal components or eigenvectors are identical to the spherical harmonic basis functions evaluated at the surface normal vectors our main contribution is in extending these results to the single viewpoint case showing how the principal eigenmodes and eigenvalues are affected when only a limited subset the upper hemisphere of normals is available and the spherical harmonics are no longer orthonormal over the restricted domain our results are very close both qualitatively and quantitatively to previous empirical observations and represent the first essentially complete theoretical explanation of these observations