eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

silhouette analysis for human action recognition based on supervised temporal t sne and incremental learning this paper develops a human action recognition method for human silhouette sequences based on supervised temporal t stochastic neighbor embedding st tsne and incremental learning inspired by the sne and its variants st tsne is proposed to learn the underlying relationship between action frames in a manifold where the class label information and temporal information are introduced to well represent those frames from the same action class as to the incremental learning an important step for action recognition we introduce three methods to perform the low dimensional embedding of new data two of them are motivated by local methods locally linear embedding and locality preserving projection those two techniques are proposed to learn explicit linear representations following the local neighbor relationship and their effectiveness is investigated for preserving the intrinsic action structure the rest one is based on manifold oriented stochastic neighbor projection to find a linear projection from high dimensional to low dimensional space capturing the underlying pattern manifold extensive experimental results and comparisons with the state of the art methods demonstrate the effectiveness and robustness of the proposed st tsne and incremental learning methods in the human action silhouette analysis

a new twist two step iterative shrinkage thresholding algorithms for image restoration iterative shrinkage thresholding 1st algorithms have been recently proposed to handle a class of convex unconstrained optimization problems arising in image restoration and other linear inverse problems this class of problems results from combining a linear observation model with a nonquadratic regularizer e g total variation or wavelet based regularization it happens that the convergence rate of these 1st algorithms depends heavily on the linear observation operator becoming very slow when this operator is ill conditioned or ill posed in this paper we introduce two step 1st twist algorithms exhibiting much faster convergence rate than 1st for ill conditioned problems for a vast class of nonquadratic convex regularizers lscrp norms some besov norms and total variation we show that twist converges to a minimizer of the objective function for a given range of values of its parameters for noninvertible observation operators we introduce a monotonic version of twist mtwist although the convergence proof does not apply to this scenario we give experimental evidence that mtwist exhibits similar speed gains over ist the effectiveness of the new methods are experimentally confirmed on problems of image deconvolution and of restoration with missing samples

maximum correntropy criterion for robust face recognition in this paper we present a sparse correntropy framework for computing robust sparse representations of face images for recognition compared with the state of the art l1norm based sparse representation classifier src which assumes that noise also has a sparse representation our sparse algorithm is developed based on the maximum correntropy criterion which is much more insensitive to outliers in order to develop a more tractable and practical approach we in particular impose nonnegativity constraint on the variables in the maximum correntropy criterion and develop a half quadratic optimization technique to approximately maximize the objective function in an alternating way so that the complex optimization problem is reduced to learning a sparse representation through a weighted linear least squares problem with nonnegativity constraint at each iteration our extensive experiments demonstrate that the proposed method is more robust and efficient in dealing with the occlusion and corruption problems in face recognition as compared to the related state of the art methods in particular it shows that the proposed method can improve both recognition accuracy and receiver operator characteristic roc curves while the computational cost is much lower than the src algorithms

general tensor discriminant analysis and gabor features for gait recognition traditional image representations are not suited to conventional classification methods such as the linear discriminant analysis lda because of the undersample problem usp the dimensionality of the feature space is much higher than the number of training samples motivated by the successes of the two dimensional lda 2dlda for face recognition we develop a general tensor discriminant analysis gtda as a preprocessing step for lda the benefits of gtda compared with existing preprocessing methods such as the principal components analysis pca and 2dlda include the following 1 the usp is reduced in subsequent classification by for example lda 2 the discriminative information in the training tensors is preserved and 3 gtda provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of gtda converges whereas that of 2dlda does not we use human gait recognition to validate the proposed gtda the averaged gait images are utilized for gait representation given the popularity of gabor function based image decompositions for image understanding and object recognition we develop three different gabor function based image representations 1 gabord is the sum of gabor filter responses over directions 2 gabors is the sum of gabor filter responses over scales and 3 gaborsd is the sum of gabor filter responses over scales and directions the gabord gabors and gaborsd representations are applied to the problem of recognizing people from their averaged gait images a large number of experiments were carried out to evaluate the effectiveness recognition rate of gait recognition based on first obtaining a gabor gabord gabors or gaborsd image representation then using gdta to extract features and finally using lda for classification the proposed methods achieved good performance for gait recognition based on image sequences from the university of south florida usf humanid database experimental comparisons are made with nine state of the art classification methods in gait recognition

c algebras of toeplitz type associated with algebraic number fields we associate with the ring r of algebraic integers in a number field a c algebra mathfrak t r it is an extension of the ring c algebra mathfrak a r studied previously by the first named author in collaboration with x li in contrast to mathfrak a r it is functorial under homomorphisms of rings it can also be defined using the left regular representation of the ax b semigroup r rtimes r times on ell 2 r rtimes r times the algebra mathfrak t r carries a natural one parameter automorphism group sigma t t in mathbb r we determine its kms structure the technical difficulties that we encounter are due to the presence of the class group in the case where r is not a principal ideal domain in that case for a fixed large inverse temperature the simplex of kms states splits over the class group the partition functions are partial dedekind zeta functions we prove a result characterizing the asymptotic behavior of quotients of such partial zeta functions which we then use to show uniqueness of the beta kms state for each inverse temperature beta in 1 2

weighted banzhaf power and interaction indexes through weighted approximations of games the banzhaf power index was introduced in cooperative game theory to measure the real power of players in a game the banzhaf interaction index was then proposed to measure the interaction degree inside coalitions of players it was shown that the power and interaction indexes can be obtained as solutions of a standard least squares approximation problem for pseudo boolean functions considering certain weighted versions of this approximation problem we define a class of weighted interaction indexes that generalize the banzhaf interaction index we show that these indexes define a subclass of the family of probabilistic interaction indexes and study their most important properties finally we give an interpretation of the banzhaf and shapley interaction indexes as centers of mass of this subclass of interaction indexes

actions as space time shapes human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion we regard human actions as three dimensional shapes induced by the silhouettes in the space time volume we adopt a recent approach 14 for analyzing 2d shapes and generalize it to deal with volumetric space time action shapes our method utilizes properties of the solution to the poisson equation to extract space time features such as local space time saliency action dynamics shape structure and orientation we show that these features are useful for action recognition detection and clustering the method is fast does not require video alignment and is applicable in but not limited to many scenarios where the background is known moreover we demonstrate the robustness of our method to partial occlusions nonrigid deformations significant changes in scale and viewpoint high irregularities in the performance of an action and low quality video

distribution based dimensionality reduction applied to articulated motion recognition some articulated motion representations rely on frame wise abstractions of the statistical distribution of low level features such as orientation color or relational distributions as configuration among parts changes with articulated motion the distribution changes tracing a trajectory in the latent space of distributions which we call the configuration space these trajectories can then be used for recognition using standard techniques such as dynamic time warping the core theory in this paper concerns embedding the frame wise distributions which can be looked upon as probability functions into a low dimensional space so that we can estimate various meaningful probabilistic distances such as the chernoff bhattacharya matusita kullback leibler kl or symmetric kl distances based on dot products between points in this space apart from computational advantages this representation also affords speed normalized matching of motion signatures speed normalized representations can be formed by interpolating the configuration trajectories along their arc lengths without using any knowledge of the temporal scale variations between the sequences we experiment with five different probabilistic distance measures and show the usefulness of the representation in three different contexts sign recognition with large number of possible classes gesture recognition with person variations and classification of human human interaction sequences with segmentation problems we find the importance of using the right distance measure for each situation the low dimensional embedding makes matching two to three times faster while achieving recognition accuracies that are close to those obtained without using a low dimensional embedding we also empirically establish the robustness of the representation with respect to low level parameters embedding parameters and temporal scale parameters

principal components and orthogonal regression based on robust scales both principal components analysis pca and orthogonal regression deal with finding a p dimensional linear manifold minimizing a scale of the orthogonal distances of the m dimensional data points to the manifold the main conceptual difference is that in pca p is estimated from the data to attain a small proportion of unexplained variability whereas in orthogonal regression p equals m 1 the two main approaches to robust pca are using the eigenvectors of a robust covariance matrix and searching for the projections that maximize or minimize a robust univariate dispersion measure this article is more akin to second approach but rather than finding the components one by one we directly undertake the problem of finding for a given p a p dimensional linear manifold minimizing a robust scale of the orthogonal distances of the data points to the manifold the scale may be either a smooth m scale or a trimmed scale an iterative algorithm is developed that is shown to converge to a local minimum a

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

correntropy properties and applications in non gaussian signal processing the optimality of second order statistics depends heavily on the assumption of gaussianity in this paper we elucidate further the probabilistic and geometric meaning of the recently defined correntropy function as a localized similarity measure a close relationship between correntropy and m estimation is established connections and differences between correntropy and kernel methods are presented as such correntropy has vastly different properties compared with second order statistics that can be very useful in non gaussian signal processing especially in the impulsive noise environment examples are presented to illustrate the technique

decision theoretic foundations of qualitative possibility theory abstract this paper presents a justification of two qualitative counterparts of the expected utility criterion for decision under uncertainty which only require bounded linearly ordered valuation sets for expressing uncertainty and preferences this is carried out in the style of savage starting with a set of acts equipped with a complete preordering relation conditions on acts are given that imply a possibilistic representation of the decision maker uncertainty in this framework pessimistic i e uncertainty averse as well as optimistic attitudes can be explicitly captured the approach thus proposes an operationally testable description of possibility theory

semigroup c algebras and amenability of semigroups we construct reduced and full semigroup c algebras for left cancellative semigroups our new construction covers particular cases already considered by a nica and also toeplitz algebras attached to rings of integers in number fields due to j cuntz moreover we show how left amenability of semigroups can be expressed in terms of these semigroup c algebras in analogy to the group case

harmonic functions on topological groups and symmetric spaces let g be a metric group not necessarily locally compact acting on a metric space x for instance a right coset space of g we introduce and develop a basic structure theory for harmonic functions on x which is applicable to infinite dimensional riemannian symmetric spaces

computing power indices multilinear extensions and new characterizations abstract johnston johnston r j 1978 on the measurement of power some reactions to laver environment and planning a 10 907 914 deegan and packel deegan j packel e w 1979 a new index of power for simple n person games international journal of game theory 7 113 123 and holler holler m j 1982 forming coalitions and measuring voting power political studies 30 262 271 proposed three power indices for simple games johnston index deegan packel index and the public good index in this paper methods to compute these indices by means of the multilinear extension of the game are presented furthermore a new characterization of the public good index is given our methods are applied to two real world examples taken from the political field

on the extension of pseudo boolean functions for the aggregation of interacting criteria abstract the paper presents an analysis on the use of integrals defined for non additive measures or capacities as the choquet and the sipos integral and the multilinear model all seen as extensions of pseudo boolean functions and used as a means to model interaction between criteria in a multicriteria decision making problem the emphasis is put on the use besides classical comparative information of information about difference of attractiveness between acts and on the existence for each point of view of a neutral level allowing to introduce the absolute notion of attractive or repulsive act it is shown that in this case the sipos integral is a suitable solution although not unique properties of the sipos integral as a new way of aggregating criteria are shown with emphasis on the interaction among criteria

region level motion based background modeling and subtraction using mrfs this paper presents a new approach to automatic segmentation of foreground objects from an image sequence by integrating techniques of background subtraction and motion based foreground segmentation first a region based motion segmentation algorithm is proposed to obtain a set of motion coherence regions and the correspondence among regions at different time instants next we formulate the classification problem as a graph labeling over a region adjacency graph based on markov random fields mrfs statistical framework a background model representing the background scene is built and then is used to model a likelihood energy besides the background model a temporal coherence is also maintained by modeling it as the prior energy on the other hand color distributions of two neighboring regions are taken into consideration to impose spatial coherence then the a priori energy of mrfs takes both spatial and temporal coherence into account to maintain the continuity of our segmentation finally a labeling is obtained by maximizing the a posteriori energy of the mrfs under such formulation we integrate two different kinds of techniques in an elegant way to make the foreground detection more accurate experimental results for several video sequences are provided to demonstrate the effectiveness of the proposed approach

sensitivity analysis with finite changes an application to modified eoq models abstract in this work we introduce a new method for the sensitivity analysis of model output in the presence of finite changes in one or more of the exogenous variables we define sensitivity measures that do not rest on differentiability we relate the sensitivity measures to classical differential and comparative statics indicators we prove a result that allows us to obtain the sensitivity measures at the same cost of one variable at a time methods thus making their estimation feasible also for computationally intensive models we discuss in detail the derivation of managerial insights formulating a procedure based on the concept of settings the method is applied to the sensitivity analysis of a discrete change in optimal order quantity following a jump in the exogenous variables of a non linear programming inventory model

graph embedding and extensions a general framework for dimensionality reduction a large family of algorithms supervised or unsupervised stemming from statistics or geometry theory has been designed to provide different solutions to the problem of dimensionality reduction despite the different motivations of these algorithms we present in this paper a general formulation known as graph embedding to unify them within a common framework in graph embedding each algorithm can be considered as the direct graph embedding or its linear kernel tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided furthermore the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms by utilizing this framework as a tool we propose a new supervised dimensionality reduction algorithm called marginal fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class while the penalty graph connects the marginal points and characterizes the interclass separability we show that mfa effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions real face recognition experiments show the superiority of our proposed mfa in comparison to lda also for corresponding kernel and tensor extensions

a measure of top down correlation many situations exist in which n objects are ranked by two or more independent sources where interest centers primarily on agreement in the top rankings and disagreements on items at the bottom of the rankings are of little or no importance a problem with spearman s rho or kendall s coefftcient of concordance in this setting is that they are equally influenced by disagreement on the assignment of rankings at all levels in this article a concordance measure is provided that is more sensitive to agreement on the top rankings the statistics used in this setting are functions of the ordinary correlation coericient computed on savage 1956 scores the asymptotic distributions of these statistics are presented and a summary of the quantiles of the exact distribution for the two sample case are provided for n 3 1 14 the statistic for the two sample case is shown to provide a locally most powerful rank test for a model given by hajek and sidak 1967

unsupervised learning of finite mixture models this paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data the adjective unsupervised is justified by two properties of the algorithm 1 it is capable of selecting the number of components and 2 unlike the standard expectation maximization em algorithm it does not require careful initialization the proposed method also avoids another drawback of em for mixture fitting the possibility of convergence toward a singular estimate at the boundary of the parameter space the novelty of our approach is that we do not use a model selection criterion to choose one among a set of preestimated candidate models instead we seamlessly integrate estimation and model selection in a single algorithm our technique can be applied to any type of parametric mixture model for which it is possible to write an em algorithm in this paper we illustrate it with experiments involving gaussian mixtures these experiments testify for the good performance of our approach

nuclearity of semigroup c algebras and the connection to amenability abstract we study c algebras associated with subsemigroups of groups for a large class of such semigroups including positive cones in quasi lattice ordered groups and left ore semigroups we describe the corresponding semigroup c algebras as c algebras of inverse semigroups groupoid c algebras and full corners in associated group crossed products these descriptions allow us to characterize nuclearity of semigroup c algebras in terms of faithfulness of left regular representations and amenability of group actions moreover we also determine when boundary quotients of semigroup c algebras are uct kirchberg algebras this leads to a unified approach to cuntz algebras and ring c algebras

action categorization with modified hidden conditional random field in this paper we present a method for action categorization with a modified hidden conditional random field hcrf specifically effective silhouette based action features are extracted using motion moments and spectrum of chain code we formulate a modified hcrf mhcrf to have a guaranteed global optimum in the modelling of the temporal action dependencies after the hmm pathing stage experimental results on action categorization using this model are compared favorably against several existing model based methods including gmm svm logistic regression hmm crf and hcrf

morphable models for the analysis and synthesis of complex motion patterns the linear combination of prototypical views provides a powerful approach for the recognition and the synthesis of images of stationary three dimensional objects in this article we present initial results that demonstrate that similar ideas can be developed for the recognition and synthesis of complex motion patterns we present a technique that permits to represent complex motion or action patterns by linear combinations of a small number of prototypical image sequences we demonstrate the applicability of this new approach for the synthesis and analysis of biological motion using simulated and real video data from different locomotion patterns our results show that complex motion patterns are embedded in pattern spaces with a defined topological structure which can be uncovered with our methods the underlying pattern space seems to have locally but not globally the properties of a linear vector space we show how the knowledge about the topology of the pattern space can be exploited during pattern recognition our method may provide a new interesting approach for the analysis and synthesis of video sequences and complex movements

robust recovery of corrupted low rankmatrix by implicit regularizers low rank matrix recovery algorithms aim to recover a corrupted low rank matrix with sparse errors however corrupted errors may not be sparse in real world problems and the relationship between l1 regularizer on noise and robust m estimators is still unknown this paper proposes a general robust framework for low rank matrix recovery via implicit regularizers of robust m estimators which are derived from convex conjugacy and can be used to model arbitrarily corrupted errors based on the additive form of half quadratic optimization proximity operators of implicit regularizers are developed such that both low rank structure and corrupted errors can be alternately recovered in particular the dual relationship between the absolute function in l1 regularizer and huber m estimator is studied which establishes a connection between robust low rank matrix recovery methods and m estimators based robust principal component analysis methods extensive experiments on synthetic and real world data sets corroborate our claims and verify the robustness of the proposed framework

a discriminative model of motion and cross ratio for view invariant action recognition action recognition is very important for many applications such as video surveillance human computer interaction and so on view invariant action recognition is hot and difficult as well in this field in this paper a new discriminative model is proposed for video based view invariant action recognition in the discriminative model motion pattern and view invariants are perfectly fused together to make a better combination of invariance and distinctiveness we address a series of issues including interest point detection in image sequence motion feature extraction and description and view invariant calculation first motion detection is used to extract motion information from videos which is much more efficient than traditional background modeling and tracking based methods second as for feature representation we exact variety of statistical information from motion and view invariant feature based on cross ratio last in the action modeling we apply a discriminative probabilistic model hidden conditional random field to model motion patterns and view invariants by which we could fuse the statistics of motion and projective invariability of cross ratio in one framework experimental results demonstrate that our method can improve the ability to distinguish different categories of actions with high robustness to view change in real circumstances

action recognition using linear dynamic systems in this paper we propose a novel approach based on linear dynamic systems ldss for action recognition our main contributions are two fold first we introduce ldss to action recognition ldss describe the dynamic texture which exhibits certain stationarity properties in time they are adopted to model the spatiotemporal patches which are extracted from the video sequence because the spatiotemporal patch is more analogous to a linear time invariant system than the video sequence notably ldss do not live in the euclidean space so we adopt the kernel principal angle to measure the similarity between ldss and then the multiclass spectral clustering is used to generate the codebook for the bag of features representation second we propose a supervised codebook pruning method to preserve the discriminative visual words and suppress the noise in each action class the visual words which maximize the inter class distance and minimize the intra class distance are selected for classification our approach yields the state of the art performance on three benchmark datasets especially the experiments on the challenging ucf sports and feature films datasets demonstrate the effectiveness of the proposed approach in realistic complex scenarios

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

convex half quadratic criteria and interacting auxiliary variables for image restoration this paper deals with convex half quadratic criteria and associated minimization algorithms for the purpose of image restoration it brings a number of original elements within a unified mathematical presentation based on convex duality firstly the geman and yang 1995 and geman and reynolds 1992 constructions are revisited with a view to establishing the convexity properties of the resulting half quadratic augmented criteria when the original nonquadratic criterion is already convex secondly a family of convex gibbsian energies that incorporate interacting auxiliary variables is revealed as a potentially fruitful extension of the geman and reynolds construction

statistical shape analysis clustering learning and testing using a differential geometric treatment of planar shapes we present tools for 1 hierarchical clustering of imaged objects according to the shapes of their boundaries 2 learning of probability models for clusters of shapes and 3 testing of newly observed shapes under competing probability models clustering at any level of hierarchy is performed using a minimum variance type criterion and a markov process statistical means of clusters provide shapes to be clustered at the next higher level thus building a hierarchy of shapes using finite dimensional approximations of spaces tangent to the shape space at sample means we implicitly impose probability models on the shape space and results are illustrated via random sampling and classification hypothesis testing together hierarchical clustering and hypothesis testing provide an efficient framework for shape retrieval examples are presented using shapes and images from eth surrey and amcom databases

a unified framework for subspace face recognition pca lda and bayesian analysis are the three most representative subspace face recognition approaches in this paper we show that they can be unified under the same framework we first model face difference with three components intrinsic difference transformation difference and noise a unified framework is then constructed by using this face difference model and a detailed subspace analysis on the three components we explain the inherent relationship among different subspace methods and their unique contributions to the extraction of discriminating information from the face difference based on the framework a unified subspace analysis method is developed using pca bayes and lda as three steps a 3d parameter space is constructed using the three subspace dimensions as axes searching through this parameter space we achieve better recognition performance than standard subspace methods

transformation invariant subspace clustering subspace clustering has achieved great success in many computer vision applications however most subspace clustering algorithms require well aligned data samples which is often not straightforward to achieve this paper proposes a transformation invariant subspace clustering framework by jointly aligning data samples and learning subspace representation by alignment the transformed data samples become highly correlated and a better affinity matrix can be obtained the joint problem can be reduced to a sequence of least squares regression problems which can be efficiently solved we verify the effectiveness of the proposed method with extensive experiments on unaligned real data demonstrating its higher clustering accuracy than the state of the art subspace clustering and transformation invariant clustering algorithms highlightsa transformation invariant subspace clustering algorithm is proposed alignment and subspace clustering are mutually dependent state of the art clustering results on the unconstrained face dataset

texture segmentation using 2 d gabor elementary functions many texture segmentation schemes use an elaborate bank of filters to decompose a textured image into a joint space spatial frequency representation although these schemes show promise and although some analytical work has been done the relationship between texture differences and the filter configurations required to distinguish them remain largely unknown this paper examines the issue of designing individual filters using a 2 d texture model we show analytically that applying a properly configured bandpass filter to a textured image produces distinct output discontinuities at texture boundaries the analysis is based on gabor elementary functions but it is the bandpass nature of the filter that is essential depending on the type of texture difference these discontinuities form one of four characteristic signatures a step ridge valley or a step change in average local output variation accompanying experimental evidence indicates that these signatures are useful for segmenting an image the analysis indicates those texture characteristics that are responsible for each signature type detailed criteria are provided for designing filters that can produce quality output signatures we also illustrate occasions when asymmetric filters are beneficial an issue not previously addressed

composite multilinearity epistemic uncertainty and risk achievement worth abstract risk achievement worth is one of the most widely utilized importance measures raw is defined as the ratio of the risk metric value attained when a component has failed over the base case value of the risk metric traditionally both the numerator and denominator are point estimates relevant literature has shown that inclusion of epistemic uncertainty i induces notable variability in the point estimate ranking and ii causes the expected value of the risk metric to differ from its nominal value we investigate the conditions under which the equality of the nominal and expected values of a reliability risk metric holds we then study how the presence of epistemic uncertainty affects raw and the associated ranking we propose an extension of raw called eraw which allows one to obtain a ranking robust to epistemic uncertainty we discuss the properties of eraw and the conditions under which it coincides with raw we apply our findings to a probabilistic risk assessment model developed for the safety analysis of nasa lunar space missions

investment decisions and sensitivity analysis npv consistency of rates of return abstract investment decisions may be evaluated via several different metrics criteria which are functions of a vector of value drivers the economic significance and the reliability of a metric depend on its compatibility with the net present value npv traditionally a metric is said to be npv consistent if it is coherent with npv in signaling value creation this paper makes use of sensitivity analysis sa for measuring coherence between rates of return and npv in particular it introduces a new stronger definition of npv consistency that takes into account the influence of value drivers on the metric output a metric is strongly npv consistent if it signals value creation and the ranking of the value drivers in terms of impact on the output is the same as that provided by the npv the degree of in coherence is calculated with spearman 1904 correlation coefficient and iman and conover 1987 top down coefficient we focus on the class of airrs magni 2010 2013 and show that the average return on investment roi enjoys strong npv consistency under several possibly all methods of sensitivity analysis

the reliability importance of components and prime implicants in coherent and non coherent systems including total order interactions abstract in the management of complex systems knowledge of how components contribute to system performance is essential to the correct allocation of resources recent works have renewed interest in the properties of the joint j and differential d reliability importance measures however a common background for these importance measures has not been developed yet in this work we build a unified framework for the utilization of j and d in both coherent and non coherent systems we show that the reliability function of any system is multilinear and its taylor expansion is exact at an order t we then introduce a total order importance measure d t that coincides with the exact portion of the change in system reliability associated with any finite or infinitesimal change in component reliabilities we show that d t synthesizes the birnbaum joint and differential importance of all orders in one unique indicator we propose an algorithm that enables the numerical estimation of d t by varying one probability at a time making it suitable in the analysis of complex systems findings demonstrate that the simultaneous utilization of d t and j provides reliability analysts with a complete dissection of system performance

large margin cost sensitive learning of conditional random fields we tackle the structured output classification problem using the conditional random fields crfs unlike the standard 0 1 loss case we consider a cost sensitive learning setting where we are given a non 0 1 misclassification cost matrix at the individual output level although the task of cost sensitive classification has many interesting practical applications that retain domain specific scales in the output space e g hierarchical or ordinal scale most crf learning algorithms are unable to effectively deal with the cost sensitive scenarios as they merely assume a nominal scale hence 0 1 loss in the output space in this paper we incorporate the cost sensitive loss into the large margin learning framework by large margin learning the proposed algorithm inherits most benefits from the svm like margin based classifiers such as the provable generalization error bounds moreover the soft max approximation employed in our approach yields a convex optimization similar to the standard crf learning with only slight modification in the potential functions we also provide the theoretical cost sensitive generalization error bound we demonstrate the improved prediction performance of the proposed method over the existing approaches in a diverse set of sequence image structured prediction problems that often arise in pattern recognition and computer vision domains

kernel risk sensitive loss definition properties and application to robust adaptive filtering nonlinear similarity measures defined in kernel space such as correntropy can extract higher order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non gaussian signal processing and machine learning in this paper we propose a new similarity measure in kernel space called the kernel risk sensitive loss krsl and provide some important properties we apply the krsl to adaptive filtering and investigate the robustness and then develop the mkrsl algorithm and analyze the mean square convergence performance compared with correntropy the krsl can offer a more efficient performance surface thereby enabling a gradient based method to achieve faster convergence speed and higher accuracy while still maintaining the robustness to outliers theoretical analysis results and superior performance of the new algorithm are confirmed by simulation

occlusion aware motion layer extraction under large interframe motions extracting motion layers from videos is an important task for video representation analysis and compression for videos with large interframe motions motion layer extraction is challenging in two respects the estimation of large disparity motions and the awareness of large occluded regions in this paper we propose an effective method for motion layer extraction under large disparity motions to robustly estimate large displacement motions we have developed an efficient voting based method that estimates planar homographies from sparse feature matches to handle occlusions we first integrate color and motion consistency into a markov random field framework to achieve per pixel assignment with occlusion detection then we perform motion color segmentation and an earth mover s distance based comparison to determine motion labels for occluded pixels experimental results show that our proposed method achieves good performance in automatically extracting multiple moving objects under large disparity motions while maintaining a low computational cost

human action recognition based on graph embedded spatio temporal subspace human action recognition is an important issue in the pattern recognition field with applications ranging from remote surveillance to the indexing of commercial video content however human actions are characterized by non linear dynamics and are therefore not easily learned and recognized accordingly this study proposes a silhouette based human action recognition system in which a three step procedure is used to construct an efficient discriminant spatio temporal subspace for k nn classification purposes in the first step an adaptive locality preserving projection alpp method is proposed to obtain a low dimensional spatial subspace in which the linearity in the local data structure is preserved to resolve the problem of overlaps in the spatial subspace resulting from the ambiguity of the human body shape among different action classes temporal data are extracted using a non base central difference action vector ncdav method finally the large margin nearest neighbor lmnn metric learning method is applied to construct an efficient spatio temporal subspace for classification purposes the experimental results show that the proposed system accurately recognizes a variety of human actions in real time and outperforms most existing methods in addition a robustness test with noisy data indicates that our system is remarkably robust toward noise in the input images

robust recovery of subspace structures by low rank representation in this paper we address the subspace clustering problem given a set of data samples vectors approximately drawn from a union of multiple subspaces our goal is to cluster the samples into their respective subspaces and remove possible outliers as well to this end we propose a novel objective function named low rank representation lrr which seeks the lowest rank representation among all the candidates that can represent the data samples as linear combinations of the bases in a given dictionary it is shown that the convex program associated with lrr solves the subspace clustering problem in the following sense when the data is clean we prove that lrr exactly recovers the true subspace structures when the data are contaminated by outliers we prove that under certain conditions lrr can exactly recover the row space of the original data and detect the outlier as well for data corrupted by arbitrary sparse errors lrr can also approximately recover the row space with theoretical guarantees since the subspace membership is provably determined by the row space these further imply that lrr can perform robust subspace clustering and error correction in an efficient and effective way

robust matrix decomposition with sparse corruptions suppose a given observation matrix can be decomposed as the sum of a low rank matrix and a sparse matrix and the goal is to recover these individual components from the observed sum such additive decompositions have applications in a variety of numerical problems including system identification latent variable graphical modeling and principal components analysis we study conditions under which recovering such a decomposition is possible via a combination of l1 norm and trace norm minimization we are specifically interested in the question of how many sparse corruptions are allowed so that convex programming can still achieve accurate recovery and we obtain stronger recovery guarantees than previous studies moreover we do not assume that the spatial pattern of corruptions is random which stands in contrast to related analyses under such assumptions via matrix completion

robust pca via ell _ 0 ell _ 1 regularization we study the problem of low rank and sparse decomposition from possibly noisy observations known as robust pca where the sparse component can be seen as outliers we first propose a modified objective function where the nuclear norm captures the low rank term ell 0 norm addresses the sparse outlier term and an ell 1 norm to deal with the additive noise term the associated algorithm termed sparsity regularized principal component pursuit srpcp is shown to converge under certain model and algorithm parameter settings it is shown that srpcp can recover the low rank component and sparse component exactly in the noiseless case in the noisy case we first prove that the widely used principal component pursuit pcp method which was designed for the noiseless case is actually stable to dense noise then we show that srpcp has smaller estimation error bound and can identify outlier entries without any false alarm another important byproduct of our analysis is the result that pcp with missing entries is also stable to dense noise we further propose another objective function which replaces the above nuclear norm by the log determinant the proposed algorithm termed iterative reweighted sparsity regularized principal component pursuit is also shown to converge in each iteration it solves a weighted nuclear norm regularized robust matrix completion problem we propose an alternating direction method of multipliers algorithm to solve this nonconvex subproblem which also converges empirical studies demonstrate the efficacy of the proposed ell 0 ell 1 regularization framework to deal with the outliers as well as its advantage over the existing state of the art methods

generating the discrete efficient frontier to the capital budgeting problem in this paper we characterize the capital budgeting problem by two objective functions one is maximizing the present value of accepted projects and the other is minimizing their risk as we assume that the weights assigned to these objectives are unspecified we utilize a discrete efficient frontier def approach to represent all the efficient combinations we found an optimality range for each efficient combination covering the entire possible range of weights zero to one furthermore we present different properties and characteristics of the def and develop two algorithms for constructing the def the first one is a simple heuristic and the second one is an optimal algorithm we conducted experiments measuring the effectiveness of the heuristic algorithm and the effect of terminating the optimal algorithm before its completion we have shown that the heuristic algorithm which is the first phase of the branch and bound algorithm has an average error of about 2 furthermore we have shown that this average error can be reduced by applying only part of the optimal algorithm and terminating it before its actual completion

multivariate image segmentation using semantic region growing with adaptive edge penalty multivariate image segmentation is a challenging task influenced by large intraclass variation that reduces class distinguishability as well as increased feature space sparseness and solution space complexity that impose computational cost and degrade algorithmic robustness to deal with these problems a markov random field mrf based multivariate segmentation algorithm called multivariate iterative region growing using semantics mirgs is presented in mirgs the impact of intraclass variation and computational cost are reduced using the mrf spatial context model incorporated with adaptive edge penalty and applied to regions semantic region growing starting from watershed over segmentation and performed alternatively with segmentation gradually reduces the solution space size which improves segmentation effectiveness as a multivariate iterative algorithm mirgs is highly sensitive to initial conditions to suppress initialization sensitivity it employs a region level k means rkm based initialization method which consistently provides accurate initial conditions at low computational cost experiments show the superiority of rkm relative to two commonly used initialization methods segmentation tests on a variety of synthetic and natural multivariate images demonstrate that mirgs consistently outperforms three other published algorithms

from differential to difference importance measures for markov reliability models this paper presents the development of the differential importance measures dim proposed recently for the use in risk informed decision making in the context of markov reliability models the proposed dim are essentially based on directional derivatives they can be used to quantify the relative contribution of a component or a group of components a state or a group of states of the system on the total variation of system performance provoked by the changes in system parameters values the estimation of dim at steady state using only a single sample path of a markov process is also investigated a numerical example of a dynamic system is finally introduced to illustrate the use of dim as well as the advantages of proposed evaluation approaches

efficient methods for overlapping group lasso the group lasso is an extension of the lasso for feature selection on predefined nonoverlapping groups of features the nonoverlapping group structure limits its applicability in practice there have been several recent attempts to study a more general formulation where groups of features are given potentially with overlaps between the groups the resulting optimization is however much more challenging to solve due to the group overlaps in this paper we consider the efficient optimization of the overlapping group lasso penalized problem we reveal several key properties of the proximal operator associated with the overlapping group lasso and compute the proximal operator by solving the smooth and convex dual problem which allows the use of the gradient descent type of algorithms for the optimization our methods and theoretical results are then generalized to tackle the general overlapping group lasso formulation based on the eq norm we further extend our algorithm to solve a nonconvex overlapping group lasso formulation based on the capped norm regularization which reduces the estimation bias introduced by the convex penalty we have performed empirical evaluations using both a synthetic and the breast cancer gene expression dataset which consists of 8 141 genes organized into overlapping gene sets experimental results show that the proposed algorithm is more efficient than existing state of the art algorithms results also demonstrate the effectiveness of the nonconvex formulation for overlapping group lasso

matching shape sequences in video with applications in human movement analysis we present an approach for comparing two sequences of deforming shapes using both parametric models and nonparametric methods in our approach kendall s definition of shape is used for feature extraction since the shape feature rests on a non euclidean manifold we propose parametric models like the autoregressive model and autoregressive moving average model on the tangent space and demonstrate the ability of these models to capture the nature of shape deformations using experiments on gait based human recognition the nonparametric model is based on dynamic time warping we suggest a modification of the dynamic time warping algorithm to include the nature of the non euclidean space in which the shape deformations take place we also show the efficacy of this algorithm by its application to gait based human recognition we exploit the shape deformations of a person s silhouette as a discriminating feature and provide recognition results using the nonparametric model our analysis leads to some interesting observations on the role of shape and kinematics in automated gait based person authentication

motion segmentation by multistage affine classification we present a multistage affine motion segmentation method that combines the benefits of the dominant motion and block based affine modeling approaches in particular we propose two key modifications to a recent motion segmentation algorithm developed by wang and adelson 1994 1 the adaptive k means clustering step is replaced by a merging step whereby the affine parameters of a block which has the smallest representation error rather than the respective cluster center is used to represent each layer and 2 we implement it in multiple stages where pixels belonging to a single motion model are labeled at each stage performance improvement due to the proposed modifications is demonstrated on real video frames

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

silhouette based gait recognition using procrustes shape analysis and elliptic fourier descriptors this paper presents a gait recognition method which combines spatio temporal motion characteristics statistical and physical parameters referred to as stm spp of a human subject for its classification by analysing shape of the subject s silhouette contours using procrustes shape analysis psa and elliptic fourier descriptors efds stm spp uses spatio temporal gait characteristics and physical parameters of human body to resolve similar dissimilarity scores between probe and gallery sequences obtained by psa a part based shape analysis using efds is also introduced to achieve robustness against carrying conditions the classification results by psa and efds are combined resolving tie in ranking using contour matching based on hu moments experimental results show stm spp outperforms several silhouette based gait recognition methods

a new lda based face recognition system which can solve the small sample size problem a new lda based face recognition system is presented in this paper linear discriminant analysis lda is one of the most popular linear projection techniques for feature extraction the major drawback of applying lda is that it may encounter the small sample size problem in this paper we propose a new lda based technique which can solve the small sample size problem we also prove that the most expressive vectors derived in the null space of the within class scatter matrix using principal component analysis pca are equal to the optimal discriminant vectors derived in the original space using lda the experimental results show that the new lda process improves the performance of a face recognition system signi cantly 2000 pattern recognition society published by elsevier science ltd all rights reserved

support vector machines for histogram based image classification traditional classification approaches generalize poorly on image classification tasks because of the high dimensionality of the feature space this paper shows that support vector machines svm can generalize well on difficult image classification problems where the only features are high dimensional histograms heavy tailed rbf kernels of the form k x y e sup spl rho spl sigma sub i sup xia yia b with a spl les 1 and b spl les 2 are evaluated on the classification of images extracted from the corel stock photo collection and shown to far outperform traditional polynomial or gaussian radial basis function rbf kernels moreover we observed that a simple remapping of the input x sub i spl rarr x sub i sup a improves the performance of linear svm to such an extend that it makes them for this problem a valid alternative to rbf kernels

on the euclidean distance of images we present a new euclidean distance for images which we call image euclidean distance imed unlike the traditional euclidean distance imed takes into account the spatial relationships of pixels therefore it is robust to small perturbation of images we argue that imed is the only intuitively reasonable euclidean distance for images imed is then applied to image recognition the key advantage of this distance measure is that it can be embedded in most image classification techniques such as svm lda and pca the embedding is rather efficient by involving a transformation referred to as standardizing transform st we show that st is a transform domain smoothing using the face recognition technology feret database and two state of the art face identification algorithms we demonstrate a consistent performance improvement of the algorithms embedded with the new metric over their original versions

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

a differential semantics for jointree algorithms a new approach to inference in belief networks has been recently proposed which is based on an algebraic representation of belief networks using multi linear functions according to this approach belief network inference reduces to a simple process of evaluating and differentiating multilinear functions we show here that mainstream inference algorithms based on jointrees are a special case of the approach based on multi linear functions in a very precise sense we use this result to prove new properties of jointree algorithms we also discuss some practical and theoretical implications of this new finding

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

amenability reiter s condition and liouville property abstract we show that the liouville property and reiter s condition are equivalent for semigroupoids this result applies to semigroups as well as semigroup actions in the special case of measured groupoids and locally compact groupoids our result proves kaimanovich s conjecture of the equivalence of amenability and the liouville property

recognizing gaits across views through correlated motion co clustering human gait is an important biometric feature which can be used to identify a person remotely however view change can cause significant difficulties for gait recognition because it will alter available visual features for matching substantially moreover it is observed that different parts of gait will be affected differently by view change by exploring relations between two gaits from two different views it is also observed that a part of gait in one view is more related to a typical part than any other parts of gait in another view a new method proposed in this paper considers such variance of correlations between gaits across views that is not explicitly analyzed in the other existing methods in our method a novel motion co clustering is carried out to partition the most related parts of gaits from different views into the same group in this way relationships between gaits from different views will be more precisely described based on multiple groups of the motion co clustering instead of a single correlation descriptor inside each group a linear correlation between gait information across views is further maximized through canonical correlation analysis cca consequently gait information in one view can be projected onto another view through a linear approximation under the trained cca subspaces in the end a similarity between gaits originally recorded from different views can be measured under the approximately same view comprehensive experiments based on widely adopted gait databases have shown that our method outperforms the state of the art

highlights and critical points in the theory and application of the analytic hierarchy process abstract this paper provides a detailed discussion with references on the fundamentals of the analytic hierarchy process and in particular of relative measurement the points discussed are grouped under the following categories structure in the ahp hierarchies and networks scales of measurement judgments consistency and the eigenvector synthesis and normative vs descriptive the paper also includes a discussion of rank and a number of citations of rank reversals attributed to a variety of factors ranging from intransitivity to procedure invariance that are thought to be unexplained by utility theory with its underlying principle to always preserve rank it is shown that when there is synergy due to the number of elements the ahp can be used to both preserve rank when it is desired to preserve it and allow it to reverse when it should reverse

acquiring linear subspaces for face recognition under variable lighting previous work has demonstrated that the image variation of many objects human faces in particular under variable lighting can be effectively modeled by low dimensional linear spaces even when there are multiple light sources and shadowing basis images spanning this space are usually obtained in one of three ways a large set of images of the object under different lighting conditions is acquired and principal component analysis pca is used to estimate a subspace alternatively synthetic images are rendered from a 3d model perhaps reconstructed from images under point sources and again pca is used to estimate a subspace finally images rendered from a 3d model under diffuse lighting based on spherical harmonics are directly used as basis images in this paper we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis vectors of a low dimensional linear space and that this subspace is close to those acquired by the other methods more specifically there exist configurations of k point light source directions with k typically ranging from 5 to 9 such that by taking k images of an object under these single sources the resulting subspace is an effective representation for recognition under a wide range of lighting conditions since the subspace is generated directly from real images potentially complex and or brittle intermediate steps such as 3d reconstruction can be completely avoided nor is it necessary to acquire large numbers of training images or to physically construct complex diffuse harmonic light fields we validate the use of subspaces constructed in this fashion within the context of face recognition

reconstruction of structurally incomplete matrices with reweighted low rank and sparsity priors most matrix reconstruction methods assume that missing entries randomly distribute in the incomplete matrix and the low rank prior or its variants are used to well pose the problem however in practical applications missing entries are structurally rather than randomly distributed and cannot be handled by the rank minimization prior individually to remedy this this paper introduces new matrix reconstruction models using double priors on the latent matrix named reweighted low rank and sparsity priors relasp in the proposed relasp models the matrix is regularized by a low rank prior to exploit the inter column and inter row correlations and its columns rows are regularized by a sparsity prior under a dictionary to exploit intra column row correlations both the low rank and sparse priors are reweighted on the fly to promote low rankness and sparsity respectively numerical algorithms to solve our relasp models are derived via the alternating direction method under the augmented lagrangian multiplier framework results on synthetic data image restoration tasks and seismic data interpolation show that the proposed relasp models are quite effective in recovering matrices degraded by highly structural missing and various types of noise complementing the classic matrix reconstruction models that handle random missing only

3d periodic human motion reconstruction from 2d motion sequences we present and evaluate a method of reconstructing three dimensional 3d periodic human motion from two dimensional 2d motion sequences using fourier decomposition we construct a compact representation for periodic human motion a low dimensional linear motion model is learned from a training set of 3d fourier representations by means of principal components analysis two dimensional test data are projected onto this model with two approaches least square minimization and calculation of a maximum a posteriori probability using the bayes rule we present two different experiments in which both approaches are applied to 2d data obtained from 3d walking sequences projected onto a plane in the first experiment we assume the viewpoint is known in the second experiment the horizontal viewpoint is unknown and is recovered from the 2d motion data the results demonstrate that by using the linear model not only can missing motion data be reconstructed but unknown view angles for 2d test data can also be retrieved

transformations and invariance in the sensitivity analysis of computer experiments summary monotonic transformations are widely employed in statistics and data analysis in computer experiments they are often used to gain accuracy in the estimation of global sensitivity statistics however one faces the question of interpreting results that are obtained on the transformed data back on the original data the situation is even more complex in computer experiments because transformations alter the model input output mapping and distort the estimators this work demonstrates that the problem can be solved by utilizing statistics which are monotonic transformation invariant to do so we offer an investigation into the families of metrics either based on densities or on cumulative distribution functions that are monotonic transformation invariant and we introduce a new generalized family of metrics numerical experiments show that transformations allow numerical convergence in the estimates of global sensitivity statistics both invariant and not in cases in which it would otherwise be impossible to obtain convergence however one fully exploits the increased numerical accuracy if the global sensitivity statistic is monotonic transformation invariant conversely estimators of measures that do not have this invariance property might lead to misleading deductions

learning and matching of dynamic shape manifolds for human action recognition in this paper we learn explicit representations for dynamic shape manifolds of moving humans for the task of action recognition we exploit locality preserving projections lpp for dimensionality reduction leading to a low dimensional embedding of human movements given a sequence of moving silhouettes associated to an action video by lpp we project them into a low dimensional space to characterize the spatiotemporal property of the action as well as to preserve much of the geometric structure to match the embedded action trajectories the median hausdorff distance or normalized spatiotemporal correlation is used for similarity measures action classification is then achieved in a nearest neighbor framework to evaluate the proposed method extensive experiments have been carried out on a recent dataset including ten actions performed by nine different subjects the experimental results show that the proposed method is able to not only recognize human actions effectively but also considerably tolerate some challenging conditions e g partial occlusion low quality videos changes in viewpoints scales and clothes within class variations caused by different subjects with different physical build styles of motion etc

silhouette analysis based gait recognition for human identification human identification at a distance has recently gained growing interest from computer vision researchers gait recognition aims essentially to address this problem by identifying people based on the way they walk in this paper a simple but efficient gait recognition algorithm using spatial temporal silhouette analysis is proposed for each image sequence a background subtraction algorithm and a simple correspondence procedure are first used to segment and track the moving silhouettes of a walking figure then eigenspace transformation based on principal component analysis pca is applied to time varying distance signals derived from a sequence of silhouette images to reduce the dimensionality of the input feature space supervised pattern classification techniques are finally performed in the lower dimensional eigenspace for recognition this method implicitly captures the structural and transitional characteristics of gait extensive experimental results on outdoor image sequences demonstrate that the proposed algorithm has an encouraging recognition performance with relatively low computational cost

principal manifolds and nonlinear dimensionality reduction via tangent space alignment we present a new algorithm for manifold learning and nonlinear dimensionality reduction based on a set of unorganized data points sampled with noise from a parameterized manifold the local geometry of the manifold is learned by constructing an approximation for the tangent space at each data point and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold we also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases we illustrate our algorithm using curves and surfaces both in two dimensional three dimensional 2d 3d euclidean spaces and in higher dimensional euclidean spaces we also address several theoretical and algorithmic issues for further research and improvements

gabor feature based classification using the enhanced fisher linear discriminant model for face recognition this paper introduces a novel gabor fisher 1936 classifier gfc for face recognition the gfc method which is robust to changes in illumination and facial expression applies the enhanced fisher linear discriminant model efm to an augmented gabor feature vector derived from the gabor wavelet representation of face images the novelty of this paper comes from 1 the derivation of an augmented gabor feature vector whose dimensionality is further reduced using the efm by considering both data compression and recognition generalization performance 2 the development of a gabor fisher classifier for multi class problems and 3 extensive performance evaluation studies in particular we performed comparative studies of different similarity measures applied to various classifiers we also performed comparative experimental studies of various face recognition schemes including our novel gfc method the gabor wavelet method the eigenfaces method the fisherfaces method the efm method the combination of gabor and the eigenfaces method and the combination of gabor and the fisherfaces method the feasibility of the new gfc method has been successfully tested on face recognition using 600 feret frontal face images corresponding to 200 subjects which were acquired under variable illumination and facial expressions the novel gfc method achieves 100 accuracy on face recognition using only 62 features

image representation using 2d gabor wavelets this paper extends to two dimensions the frame criterion developed by daubechies for one dimensional wavelets and it computes the frame bounds for the particular case of 2d gabor wavelets completeness criteria for 2d gabor image representations are important because of their increasing role in many computer vision applications and also in modeling biological vision since recent neurophysiological evidence from the visual cortex of mammalian brains suggests that the filter response profiles of the main class of linearly responding cortical neurons called simple cells are best modeled as a family of self similar 2d gabor wavelets we therefore derive the conditions under which a set of continuous 2d gabor wavelets will provide a complete representation of any image and we also find self similar wavelet parametrization which allow stable reconstruction by summation as though the wavelets formed an orthonormal basis approximating a tight frame generates redundancy which allows low resolution neural responses to represent high resolution images

robust principal component analysis based on maximum correntropy criterion principal component analysis pca minimizes the mean square error mse and is sensitive to outliers in this paper we present a new rotational invariant pca based on maximum correntropy criterion mcc a half quadratic optimization algorithm is adopted to compute the correntropy objective at each iteration the complex optimization problem is reduced to a quadratic problem that can be efficiently solved by a standard optimization method the proposed method exhibits the following benefits 1 it is robust to outliers through the mechanism of mcc which can be more theoretically solid than a heuristic rule based on mse 2 it requires no assumption about the zero mean of data for processing and can estimate data mean during optimization and 3 its optimal solution consists of principal eigenvectors of a robust covariance matrix corresponding to the largest eigenvalues in addition kernel techniques are further introduced in the proposed method to deal with nonlinearly distributed data numerical results demonstrate that the proposed method can outperform robust rotational invariant pcas based on l1 norm when outliers occur

mpca multilinear principal component analysis of tensor objects this paper introduces a multilinear principal component analysis mpca framework for tensor object feature extraction objects of interest in many computer vision and pattern recognition applications such as 2d 3d images and video sequences are naturally described as tensors or multilinear arrays the proposed framework performs feature extraction by determining a multilinear projection that captures most of the original tensorial input variation the solution is iterative in nature and it proceeds by decomposing the original problem to a series of multiple projection subproblems as part of this work methods for subspace dimensionality determination are proposed and analyzed it is shown that the mpca framework discussed in this work supplants existing heterogeneous solutions such as the classical principal component analysis pca and its 2d variant 2d pca finally a tensor object recognition system is proposed with the introduction of a discriminative tensor feature selection mechanism and a novel classification strategy and applied to the problem of gait recognition results presented here indicate mpca s utility as a feature extraction tool it is shown that even without a fully optimized design an mpca based gait recognition module achieves highly competitive performance and compares favorably to the state of the art gait recognizers