semi supervised metric learning via topology preserving multiple semi supervised assumptions learning an appropriate distance metric is a critical problem in pattern recognition this paper addresses the problem of semi supervised metric learning we propose a new regularized semi supervised metric learning rssml method using local topology and triplet constraints our regularizer is designed and developed based on local topology which is represented by local neighbors from the local smoothness cluster low density and manifold information point of view the regularizer is then combined with the large margin hinge loss on the triplet constraints in other words we keep a large margin between different labeled samples and in the meanwhile we use the unlabeled samples to regularize it then the semi supervised metric learning method is developed we have performed experiments on classification using publicly available databases to evaluate the proposed method to our best knowledge this is the only method satisfying all the three semi supervised assumptions namely smoothness cluster low density and manifold experimental results have shown that the proposed method outperforms state of the art semi supervised distance metric learning algorithms

bayesian sensitivity analysis for unmeasured confounding in observational studies we consider bayesian sensitivity analysis for unmeasured confounding in observational studies where the association between a binary exposure binary response measured confounders and a single binary unmeasured confounder can be formulated using logistic regression models a model for unmeasured confounding is presented along with a family of prior distributions that model beliefs about a possible unknown unmeasured confounder simulation from the posterior distribution is accomplished using markov chain monte carlo because the model for unmeasured confounding is not identifiable standard large sample theory for bayesian analysis is not applicable consequently the impact of different choices of prior distributions on the coverage probability of credible intervals is unknown using simulations we investigate the coverage probability when averaged with respect to various distributions over the parameter space the results indicate that credible intervals will have approximately nominal coverage probability on average when the prior distribution used for sensitivity analysis approximates the sampling distribution of model parameters in a hypothetical sequence of observational studies we motivate the method in a study of the effectiveness of beta blocker therapy for treatment of heart failure

worst case linear discriminant analysis as scalable semidefinite feasibility problems in this paper we propose an efficient semidefinite programming sdp approach to worst case linear discriminant analysis wlda compared with the traditional lda wlda considers the dimensionality reduction problem from the worst case viewpoint which is in general more robust for classification however the original problem of wlda is non convex and difficult to optimize in this paper we reformulate the optimization problem of wlda into a sequence of semidefinite feasibility problems to efficiently solve the semidefinite feasibility problems we design a new scalable optimization method with a quasi newton method and eigen decomposition being the core components the proposed method is orders of magnitude faster than standard interior point sdp solvers experiments on a variety of classification problems demonstrate that our approach achieves better performance than standard lda our method is also much faster and more scalable than standard interior point sdp solvers based wlda the computational complexity for an sdp with m constraints and matrices of size d by d is roughly reduced from mathcal o m 3 md 3 m 2 d 2 to mathcal o d 3 m d in our case

active reranking for web image search image search reranking methods usually fail to capture the user s intention when the query term is ambiguous therefore reranking with user interactions or active reranking is highly demanded to effectively improve the search performance the essential problem in active reranking is how to target the user s intention to complete this goal this paper presents a structural information based sample selection strategy to reduce the user s labeling efforts furthermore to localize the user s intention in the visual feature space a novel local global discriminative dimension reduction algorithm is proposed in this algorithm a submanifold is learned by transferring the local geometry and the discriminative information from the labelled images to the whole global image database experiments on both synthetic datasets and a real web image search dataset demonstrate the effectiveness of the proposed active reranking scheme including both the structural information based active sample selection strategy and the local global discriminative dimension reduction algorithm

between and within cluster covariate effects in the analysis of clustered data standard methods for the regression analysis of clustered data postulate models relating covariates to the response without regard to between and within cluster covariate effects implicit in these analyses is the assumption that these effects are identical example data show that this is frequently not the case and that analyses that ignore differential between and within cluster covariate effects can be misleading consideration of between and within cluster effects also helps to explain observed and theoretical differences between mixture model analyses and those based on conditional likelihood methods in particular we show that conditional likelihood methods estimate purely within cluster covariate effects whereas mixture model approaches estimate a weighted average of between and within cluster covariate effects

random fixed points of random multivalued operators on polish spaces random coincidence point theorems and random fixed point theorems are stochastic generalizations of classical coincidence point theorems and classical fixed point theorems random fixed point theorems for contraction mappings in polish spaces were proved by spacek l and hans 2 31 for a complete survey we refer to bharucha reid 4 itoh 5 proved several random fixed point theorems and gave their applications to random differential equations in banach spaces recently sehgal and singh 7 papageorgiou 8 and lin 9 have proved different stochastic versions of the well known schauder s fixed point theorem the aim of this paper is to prove various stochastic versions of banach type fixed point theorems for multivalued operators section 2 is aimed at clarifying the terminology to be used and recalling basic definitions and facts section 3 deals with random coincidence point theorems for a pair of compatible random multivalued operators the structure of common random fixed points of these operators is also studied in section 4 the existence of a common random fixed point of two random multivalued operators satisfying the meir keeler type condition in polish spaces is proved section 5 contains a random fixed point theorem for a pair of locally contractive random multivalued operators in s chainable polish spaces as an application a theorem on random approximation is also obtained

manifold preserving an intrinsic approach for semisupervised distance metric learning in this paper we address the semisupervised distance metric learning problem and its applications in classification and image retrieval first we formulate a semisupervised distance metric learning model by considering the metric information of inner classes and interclasses in this model an adaptive parameter is designed to balance the inner metrics and intermetrics by using data structure second we convert the model to a minimization problem whose variable is symmetric positive definite matrix third in implementation we deduce an intrinsic steepest descent method which assures that the metric matrix is strictly symmetric positive definite at each iteration with the manifold structure of the symmetric positive definite matrix manifold finally we test the proposed algorithm on conventional data sets and compare it with other four representative methods the numerical results validate that the proposed method significantly improves the classification with the same computational efficiency

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

low dimensional representation of fisher vectors for microscopy image classification microscopy image classification is important in various biomedical applications such as cancer subtype identification and protein localization for high content screening to achieve automated and effective microscopy image classification the representative and discriminative capability of image feature descriptors is essential to this end in this paper we propose a new feature representation algorithm to facilitate automated microscopy image classification in particular we incorporate fisher vector fv encoding with multiple types of local features that are handcrafted or learned and we design a separation guided dimension reduction method to reduce the descriptor dimension while increasing its discriminative capability our method is evaluated on four publicly available microscopy image data sets of different imaging types and applications including the ucsb breast cancer data set miccai 2015 cbtc challenge data set and iicbu malignant lymphoma and rnai data sets our experimental results demonstrate the advantage of the proposed low dimensional fv representation showing consistent performance improvement over the existing state of the art and the commonly used dimension reduction techniques

contextual object localization with multiple kernel nearest neighbor recently many object localization models have shown that incorporating contextual cues can greatly improve accuracy over using appearance features alone therefore many of these models have explored different types of contextual sources but only considering one level of contextual interaction at the time thus what context could truly contribute to object localization through integrating cues from all levels simultaneously remains an open question moreover the relative importance of the different contextual levels and appearance features across different object classes remains to be explored here we introduce a novel framework for multiple class object localization that incorporates different levels of contextual interactions we study contextual interactions at the pixel region and object level based upon three different sources of context semantic boundary support and contextual neighborhoods our framework learns a single similarity metric from multiple kernels combining pixel and region interactions with appearance features and then applies a conditional random field to incorporate object level interactions to effectively integrate different types of feature descriptions we extend the large margin nearest neighbor to a novel algorithm that supports multiple kernels we perform experiments on three challenging image databases graz 02 msrc and pascal voc 2007 experimental results show that our model outperforms current state of the art contextual frameworks and reveals individual contributions for each contextual interaction level as well as appearance features indicating their relative importance for object localization

convergence of conditional expectations and strong laws of large numbers for multivalued random variables on etablit des lemmes de fatou et des theoremes de convergence de lebesgue pour des esperances conditionnelles multivaluees de variables aleatoires a valeurs dans des sous ensembles fermes d un espace de banach separable

ordinal margin metric learning and its extension for cross distribution image data propose a novel ordinal margin metric learning ormml by separating the data with large margins and making them distributed in order extend ormml to cope with cross distribution application scenarios named cd ormml extensively demonstrate the superiority of the proposed metric learning methods to related state of the art methods in machine learning and computer vision fields a wide range of applications such as human age estimation and head pose recognition are related to ordinal data in which there exists an order relationship to perform such ordinal estimations in a desired metric space in this paper we first propose a novel ordinal margin metric learning ormml method by separating the data classes with a sequence of margins which makes the classes distribute orderly in the learned metric space then to cope with more realistic scenarios where the data are sampled with each class across multiple distributions we present a cross distribution variant of ormml coined as cd ormml by maximizing the correlation between distributions within each class when conducting metric learning finally extensive experiments on synthetic and publicly available image datasets demonstrate the superiority of the proposed methods in performance to the state of the art methods

on the convergence in distribution of measurable multifunctions random sets normal integrands stochastic processes and stochastic infima the concept of the distribution function of a closed valued measurable multifunction is introduced and used to study the convergence in distribution of sequences of multifunctions and the epi convergence in distribution of normal integrands and stochastic processes in particular various compactness criteria are exhibited the connections with the classical convergence theory for stochastic processes are analyzed and for purposes of illustration we apply the theory to sketch out a modified derivation of donsker s theorem brownian motion as a limit of normalized random walks we also suggest the potential application of the theory to the study of the convergence of stochastic infima

hubs in space popular nearest neighbors in high dimensional data different aspects of the curse of dimensionality are known to present serious challenges to various machine learning methods and tasks this paper explores a new aspect of the dimensionality curse referred to as hubness that affects the distribution of k occurrences the number of times a point appears among the k nearest neighbors of other points in a data set through theoretical and empirical analysis involving synthetic and real data sets we show that under commonly used assumptions this distribution becomes considerably skewed as dimensionality increases causing the emergence of hubs that is points with very high k occurrences which effectively represent popular nearest neighbors we examine the origins of this phenomenon showing that it is an inherent property of data distributions in high dimensional vector space discuss its interaction with dimensionality reduction and explore its influence on a wide range of machine learning tasks directly or indirectly based on measuring distances belonging to supervised semi supervised and unsupervised learning families

distance metric learning by minimal distance maximization classic linear dimensionality reduction ldr methods such as principal component analysis pca and linear discriminant analysis lda are known not to be robust against outliers following a systematic analysis of the multi class ldr problem in a unified framework we propose a new algorithm called minimal distance maximization mdm to address the non robustness issue the principle behind mdm is to maximize the minimal between class distance in the output space mdm is formulated as a semi definite program sdp and its dual problem reveals a close connection to weighted ldr methods a soft version of mdm in which lda is subsumed as a special case is also developed to deal with overlapping centroids finally we drop the homoscedastic gaussian assumption made in mdm by extending it in a non parametric way along with a gradient based convex approximation algorithm to significantly reduce the complexity of the original sdp the effectiveness of our proposed methods are validated on two uci datasets and two face datasets

measurability and integrability of the weak upper limit of a sequence of multifunctions we provide several properties of the weak upper limit of a sequence of subsets of a separable banach space such as a criterion of non vacuity of closedness etc we also examine the measurability of the multifunction defined as the weak upper limit of a sequence of multifunctions at last applications to the existence of a measurable and bochner integrable selector for this multifunction are presented

distributional properties of correspondences on loeb spaces abstract we present some regularity properties for the set of distributions induced by the measurable selections of a correspondence over a loeb space which include closedness convexity compactness purification and semicontinuity we also note that all the properties reported in the main theorems are not satisfied by some correspondences on the unit lebesgue interval

assessing the sensitivity of regression results to unmeasured confounders in observational studies this paper presents a general approach for assessing the sensitivity of the point and interval estimates of the primary exposure effect in an observational study to the residual confounding effects of unmeasured variable after adjusting for measured covariates the proposed method assumes that the true exposure effect can be represented in a regression model that includes the exposure indicator as well as the measured and unmeasured confounders one can use the corresponding reduced model that omits the unmeasured confounder to make statistical inferences about the true exposure effect by specifying the distributions of the unmeasured confounder in the exposed and unexposed groups along with the effects of the unmeasured confounder on the outcome variable under certain conditions there exists a simple algebraic relationship between the true exposure effect in the full model and the apparent exposure effect in the reduced model one can then estimate the true exposure effect by making a simple adjustment to the point and interval estimates of the apparent exposure effect obtained from standard software or published reports the proposed method handles both binary response and censored survival time data accommodates any study design and allows the unmeasured confounder to be discrete or normally distributed we describe applications on two major medical studies

deep transfer metric learning conventional metric learning methods usually assume that the training and test samples are captured in similar scenarios so that their distributions are assumed to be the same this assumption does not hold in many real visual recognition applications especially when samples are captured across different data sets in this paper we propose a new deep transfer metric learning dtml method to learn a set of hierarchical nonlinear transformations for cross domain visual recognition by transferring discriminative knowledge from the labeled source domain to the unlabeled target domain specifically our dtml learns a deep metric network by maximizing the inter class variations and minimizing the intra class variations and minimizing the distribution divergence between the source domain and the target domain at the top layer of the network to better exploit the discriminative information from the source domain we further develop a deeply supervised transfer metric learning dstml method by including an additional objective on dtml where the output of both the hidden layers and the top layer are optimized jointly to preserve the local manifold of input data points in the metric space we present two new methods dtml with autoencoder regularization and dstml with autoencoder regularization experimental results on face verification person re identification and handwritten digit recognition validate the effectiveness of the proposed methods

generalized iterative relief for supervised distance metric learning the relief algorithm is a popular approach for feature weighting many extensions of the relief algorithm are developed and i relief is one of the famous extensions in this paper i relief is generalized for supervised distance metric learning to yield a mahananobis distance function the proposed approach is justified by showing that the objective function of the generalized i relief is closely related to the expected leave one out nearest neighbor classification rate in addition the relationships among the generalized i relief the neighbourhood components analysis and graph embedding are also pointed out experimental results on various data sets all demonstrate the superiority of the proposed approach

a stochastic approach to stability in stochastic programming abstract a random optimization problem p 0 min x 0 0 x is approximated by a sequence of random surrogate problems p n n n with p n min x n n x p a given probability space we investigate the convergence almost surely and in probability of the optimal values and the solution sets the results can be regarded as random versions of well known stability statements of parametric programming semicontinuous convergence almost surely in probability of sequences of random functions is a crucial assumption in this framework and will be investigated in more detail

convergence of best approximations from unbounded sets given a metric space whose bounded sets are relatively compact i e have compact closures we show that a nearest point selection from a sequence of kuratowski converging sets converges to the nearest point in the limit set whenever the latter point is unique the result is extended to kuratowski limits of linear varieties in infinite dimensional hilbert spaces where this nearest point relative to the origin is necessarily unique finally we show that the kuratowski limit of hyperplanes must itself be a hyperplane and that a necessary and sufficient condition for the associated nearest points to the origin to converge as above is that the canonial points parametrizing the hyperplanes converge

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

learning spectral descriptors for deformable shape correspondence informative and discriminative feature descriptors play a fundamental role in deformable shape analysis for example they have been successfully employed in correspondence registration and retrieval tasks in recent years significant attention has been devoted to descriptors obtained from the spectral decomposition of the laplace beltrami operator associated with the shape notable examples in this family are the heat kernel signature hks and the recently introduced wave kernel signature wks the laplacian based descriptors achieve state of the art performance in numerous shape analysis tasks they are computationally efficient isometry invariant by construction and can gracefully cope with a variety of transformations in this paper we formulate a generic family of parametric spectral descriptors we argue that to be optimized for a specific task the descriptor should take into account the statistics of the corpus of shapes to which it is applied the signal and those of the class of transformations to which it is made insensitive the noise while such statistics are hard to model axiomatically they can be learned from examples following the spirit of the wiener filter in signal processing we show a learning scheme for the construction of optimized spectral descriptors and relate it to mahalanobis metric learning the superiority of the proposed approach in generating correspondences is demonstrated on synthetic and scanned human figures we also show that the learned descriptors are robust enough to be learned on synthetic data and transferred successfully to scanned shapes

on abstract conditional expectations i if c is a sub a field of 2 f o f o p a e and there is a nonnegative real valued function 40 e l q s t i f o 1 then lim ezf w e o this is just the lebesgue dominated convergence theorem for abstract conditional expectations see s ii if zm z are sub a fields of 2 v c z or fi i 2 c andfel q 1 pc co then ezn l e j furthermore if p 1 then eznf o ezf w p a e these are known as martingale convergence theorems see s and 14 theorem 51 together with the general theory of martingales have an increasingly important impact in banach space theory see 5 chap vi

on a paper by khan and majumdar abstract in this paper we generalize two results of khan and majumdar on the weak sequential convergence of functions in the lebesgue bochner space l x 1 and on a fatou like convergence theorem

learning a mahalanobis distance metric for data clustering and classification distance metric is a key issue in many machine learning algorithms this paper considers a general problem of learning from pairwise constraints in the form of must links and cannot links as one kind of side information a must link indicates the pair of the two data points must be in a same class while a cannot link indicates that the two data points must be in two different classes given must link and cannot link information our goal is to learn a mahalanobis distance metric under this metric we hope the distances of point pairs in must links are as small as possible and those of point pairs in cannot links are as large as possible this task is formulated as a constrained optimization problem in which the global optimum can be obtained effectively and efficiently finally some applications in data clustering interactive natural image segmentation and face pose estimation are given in this paper experimental results illustrate the effectiveness of our algorithm

estimation in generalized linear models with random effects summary a conceptually very simple but general algorithm for the estimation of the fixed effects random effects and components of dispersion in generalized linear models with random effects is proposed conditions are described under which the algorithm yields approximate maximum likelihood or quasi maximum likelihood estimates of the fixed effects and dispersion components and approximate empirical bayes estimates of the random effects the algorithm is applied to two data sets to illustrate the estimation of components of dispersion and the modelling of overdispersion

iterative procedures for solutions of random operator equations in banach spaces we construct random iterative processes for weakly contractive and asymptotically nonexpansive random operators and study necessary conditions for the convergence of these processes it is shown that they converge to the random fixed points of these operators in the setting of banach spaces we also proved that an implicit random iterative process converges to the common random fixed point of a finite family of asymptotically quasi nonexpansive random operators in uniformly convex banach spaces

fusing mathcal r r features and local features with context aware kernels for action recognition the performance of action recognition in video sequences depends significantly on the representation of actions and the similarity measurement between the representations in this paper we combine two kinds of features extracted from the spatio temporal interest points with context aware kernels for action recognition for the action representation local cuboid features extracted around interest points are very popular using a bag of visual words bovw model such representations however ignore potentially valuable information about the global spatio temporal distribution of interest points we propose a new global feature to capture the detailed geometrical distribution of interest points it is calculated by using the 3d mathcal r r transform which is defined as an extended 3d discrete radon transform followed by the application of a two directional two dimensional principal component analysis for the similarity measurement we model a video set as an optimized probabilistic hypergraph and propose a context aware kernel to measure high order relationships among videos the context aware kernel is more robust to the noise and outliers in the data than the traditional context free kernel which just considers the pairwise relationships between videos the hyperedges of the hypergraph are constructed based on a learnt mahalanobis distance metric any disturbing information from other classes is excluded from each hyperedge finally a multiple kernel learning algorithm is designed by integrating the l 2 l2 norm regularization into a linear svm classifier to fuse the mathcal r r feature and the bovw representation for action recognition experimental results on several datasets demonstrate the effectiveness of the proposed approach for action recognition

semi supervised learning via regularized boosting working on multiple semi supervised assumptions semi supervised learning concerns the problem of learning in the presence of labeled and unlabeled data several boosting algorithms have been extended to semi supervised learning with various strategies to our knowledge however none of them takes all three semi supervised assumptions i e smoothness cluster and manifold assumptions together into account during boosting learning in this paper we propose a novel cost functional consisting of the margin cost on labeled data and the regularization penalty on unlabeled data based on three fundamental semi supervised assumptions thus minimizing our proposed cost functional with a greedy yet stagewise functional optimization procedure leads to a generic boosting framework for semi supervised learning extensive experiments demonstrate that our algorithm yields favorite results for benchmark and real world classification tasks in comparison to state of the art semi supervised learning algorithms including newly developed boosting algorithms finally we discuss relevant issues and relate our algorithm to the previous work

quasi uniformization of hyperspaces and convergence of nets of semicontinuous multifunctions abstract we introduce several quasi uniformities on the hyperspace of a topological space in order to study convergence of nets of semicontinuous multifunctions the interplay between conjugate quasi uniformities yields results on both the topological structure of hyperspaces and the convergence of semicontinuous multifunctions

person re identification by dual regularized kiss metric learning person re identification aims to match the images of pedestrians across different camera views from different locations this is a challenging intelligent video surveillance problem that remains an active area of research due to the need for performance improvement person re identification involves two main steps feature representation and metric learning although the keep it simple and straightforward kiss metric learning method for discriminative distance metric learning has been shown to be effective for the person re identification the estimation of the inverse of a covariance matrix is unstable and indeed may not exist when the training set is small resulting in poor performance here we present dual regularized kiss dr kiss metric learning by regularizing the two covariance matrices dr kiss improves on kiss by reducing overestimation of large eigenvalues of the two estimated covariance matrices and in doing so guarantees that the covariance matrix is irreversible furthermore we provide theoretical analyses for supporting the motivations specifically we first prove why the regularization is necessary then we prove that the proposed method is robust for generalization we conduct extensive experiments on three challenging person re identification datasets viper grid and cuhk 01 and show that dr kiss achieves new state of the art performance

convergence of multivalued mappings via approximable measurable selectors we investigate the convergence of measurable selectors for the limit of measurable multivalued maps the relationship between the convergence of measurable selectors and lower and upper limits of measurable multivalued mappings with closed images is also derived

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

discriminant adaptive nearest neighbor classification nearest neighbour classification expects the class conditional probabilities to be locally constant and suffers from bias in high dimensions we propose a locally adaptive form of nearest neighbour classification to try to ameliorate this curse of dimensionality we use a local linear discriminant analysis to estimate an effective metric for computing neighbourhoods we determine the local decision boundaries from centroid information and then shrink neighbourhoods in directions orthogonal to these local decision boundaries and elongate them parallel to the boundaries thereafter any neighbourhood based classifier can be employed using the modified neighbourhoods the posterior probabilities tend to be more homogeneous in the modified neighbourhoods we also propose a method for global dimension reduction that combines local dimension information in a number of examples the methods demonstrate the potential for substantial improvements over nearest neighbour classification

adaptive relevance matrices in learning vector quantization we propose a new matrix learning scheme to extend relevance learning vector quantization rlvq an efficient prototype based classification algorithm toward a general adaptive metric by introducing a full matrix of relevance factors in the distance measure correlations between different features and their importance for the classification scheme can be taken into account and automated and general metric adaptation takes place during training in comparison to the weighted euclidean metric used in rlvq and its variations a full matrix is more powerful to represent the internal structure of the data appropriately large margin generalization bounds can be transferred to this case leading to bounds that are independent of the input dimensionality this also holds for local metrics attached to each prototype which corresponds to piecewise quadratic decision boundaries the algorithm is tested in comparison to alternative learning vector quantization schemes using an artificial data set a benchmark multiclass problem from the vci repository and a problem from bioinformatics the recognition of splice sites for c elegans

convergence of ishikawa iterates of quasi nonexpansive mappings abstract this paper deals with a necessary and sufficient condition for the convergence of ishikawa iterates of quasi nonexpansive mapping in a banach space the convergence of ishikawa iterates for nonexpansive mappings in a uniformly convex banach space is also discussed

a stability result for differential inclusions in banach spaces on etablit un resultat de stabilite pour les inclusions differentielles definies sur un espace de banach separable

kernel entropy component analysis we introduce kernel entropy component analysis kernel eca as a new method for data transformation and dimensionality reduction kernel eca reveals structure relating to the renyi entropy of the input space data set estimated via a kernel matrix using parzen windowing this is achieved by projections onto a subset of entropy preserving kernel principal component analysis kernel pca axes this subset does not need in general to correspond to the top eigenvalues of the kernel matrix in contrast to the dimensionality reduction using kernel pca we show that kernel eca may produce strikingly different transformed data sets compared to kernel pca with a distinct angle based structure a new spectral clustering algorithm utilizing this structure is developed with positive results furthermore kernel eca is shown to be an useful alternative for pattern denoising

a diagnostic test for the mixing distribution in a generalised linear mixed model summary we introduce a diagnostic test for the mixing distribution in a generalised linear mixed model the test is based on the difference between the marginal maximum likelihood and conditional maximum likelihood estimators of a subset of the fixed effects in the model we derive the asymptotic variance of this difference and propose a test statistic that has a limiting chi squared distribution under the null hypothesis that the mixing distribution is correctly specified this strategy uses an idea presented by hausman 1978 who considered analogous tests for the linear mixed model an important advantage of the methods outlined here is that the resulting diagnostic test is easily implemented in commercial software we illustrate the method by applying it to data from a clinical trial investigating the effect of hormonal contraceptives in women

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

asymptotic stochastic programs consider a stochastic program with unique solution by the notion of epi convergence in distribution in local coordinates we define the asymptotic stochastic program associated to it stochastic programs may be classified according to the type of the pertaining asymptotic program in particular three such types are studied in detail the normal shift program the wiener type program and the poisson hyperplane program conditions for the convergence to each of the three types are given

distance learning in discriminative vector quantization discriminative vector quantization schemes such as learning vector quantization lvq and extensions thereof offer efficient and intuitive classifiers based on the representation of classes by prototypes the original methods however rely on the euclidean distance corresponding to the assumption that the data can be represented by isotropic clusters for this reason extensions of the methods to more general metric structures have been proposed such as relevance adaptation in generalized lvq glvq and matrix learning in glvq in these approaches metric parameters are learned based on the given classification task such that a data driven distance measure is found in this letter we consider full matrix adaptation in advanced lvq schemes in particular we introduce matrix learning to a recent statistical formalization of lvq robust soft lvq and we compare the results on several artificial and real life data sets to matrix learning in glvq a derivation of lvq like learning based on a heuristic cost function in all cases matrix adaptation allows a significant improvement of the classification accuracy interestingly however the principled behavior of the models with respect to prototype locations and extracted matrix dimensions shows several characteristic differences depending on the data sets

random fixed points of set valued maps some random fixed point theorems for set valued random operators under very mild conditions are established some recent results of o regan proc amer math soc 126 1998 3045 3053 and computers math applic 35 1998 27 34 are improved significantly the discussion in this paper underlines in addition to generality the unifying aspects of our result

adjusting for unmeasured confounding due to either of two crossed factors with a logistic regression model motivated by an investigation of the effect of surface water temperature on the presence of vibrio cholerae in water samples collected from different fixed surface water monitoring sites in haiti in different months we investigated methods to adjust for unmeasured confounding due to either of the two crossed factors site and month in the process we extended previous methods that adjust for unmeasured confounding due to one nesting factor such as site which nests the water samples from different months to the case of two crossed factors first we developed a conditional pseudolikelihood estimator that eliminates fixed effects for the levels of each of the crossed factors from the estimating equation using the theory of u statistics for independent but non identically distributed vectors we show that our estimator is consistent and asymptotically normal but that its variance depends on the nuisance parameters and thus cannot be easily estimated consequently we apply our estimator in conjunction with a permutation test and we investigate use of the pigeonhole bootstrap and the jackknife for constructing confidence intervals we also incorporate our estimator into a diagnostic test for a logistic mixed model with crossed random effects and no unmeasured confounding for comparison we investigate between within models extended to two crossed factors these generalized linear mixed models include covariate means for each level of each factor in order to adjust for the unmeasured confounding we conduct simulation studies and we apply the methods to the haitian data copyright 2016 john wiley sons ltd

non linear metric learning using pairwise similarity and dissimilarity constraints and the geometrical structure of data the problem of clustering with side information has received much recent attention and metric learning has been considered as a powerful approach to this problem until now various metric learning methods have been proposed for semi supervised clustering although some of the existing methods can use both positive must link and negative cannot link constraints they are usually limited to learning a linear transformation i e finding a global mahalanobis metric in this paper we propose a framework for learning linear and non linear transformations efficiently we use both positive and negative constraints and also the intrinsic topological structure of data we formulate our metric learning method as an appropriate optimization problem and find the global optimum of this problem the proposed non linear method can be considered as an efficient kernel learning method that yields an explicit non linear transformation and thus shows out of sample generalization ability experimental results on synthetic and real world data sets show the effectiveness of our metric learning method for semi supervised clustering tasks

metric and kernel learning using a linear transformation metric and kernel learning arise in several machine learning applications however most existing metric learning algorithms are limited to learning metrics over low dimensional data while existing kernel learning algorithms are often limited to the transductive setting and do not generalize to new data points in this paper we study the connections between metric learning and kernel learning that arise when studying metric learning as a linear transformation learning problem in particular we propose a general optimization framework for learning metrics via linear transformations and analyze in detail a special case of our framework that of minimizing the logdet divergence subject to linear constraints we then propose a general regularized framework for learning a kernel matrix and show it to be equivalent to our metric learning framework our theoretical connections between metric and kernel learning have two main consequences 1 the learned kernel matrix parameterizes a linear transformation kernel function and can be applied inductively to new data points 2 our result yields a constructive method for kernelizing most existing mahalanobis metric learning formulations we demonstrate our learning approach by applying it to large scale real world problems in computer vision text mining and semi supervised kernel dimensionality reduction

on the algorithmic implementation of multiclass kernel based vector machines in this paper we describe the algorithmic implementation of multiclass kernel based vector machines our starting point is a generalized notion of the margin to multiclass problems using this notion we cast multiclass categorization problems as a constrained optimization problem with a quadratic objective function unlike most of previous approaches which typically decompose a multiclass problem into multiple independent binary classification tasks our notion of margin yields a direct method for training multiclass predictors by using the dual of the optimization problem we are able to incorporate kernels with a compact set of constraints and decompose the dual problem into multiple optimization problems of reduced size we describe an efficient fixed point algorithm for solving the reduced optimization problems and prove its convergence we then discuss technical details that yield significant running time improvements for large datasets finally we describe various experiments with our approach comparing it to previously studied kernel based methods our experiments indicate that for multiclass problems we attain state of the art accuracy

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

asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems we study the asymptotic behavior of the statistical estimators that maximize a not necessarily dieren tiable criterion function possibly subject to side constraints equalities and inequalities the consistency results generalize those of wald and huber conditions are also given under which one is still able to obtain asymptotic normality the analysis brings to the fore the relationship between the problem of nding statistical estimators and that of nding the optimal solutions of stochastic optimization problems with partial information the last section is devoted to the properties of the saddle points of the associated lagrangians

sharable and individual multi view metric learning this paper presents a sharable and individual multi view metric learning mvml approach for visual recognition unlike conventional metric leaning methods which learn a distance metric on either a single type of feature representation or a concatenated representation of multiple types of features the proposed mvml jointly learns an optimal combination of multiple distance metrics on multi view representations where not only it learns an individual distance metric for each view to retain its specific property but also a shared representation for different views in a unified latent subspace to preserve the common properties the objective function of the mvml is formulated in the large margin learning framework via pairwise constraints under which the distance of each similar pair is smaller than that of each dissimilar pair by a margin moreover to exploit the nonlinear structure of data points we extend mvml to a sharable and individual multi view deep metric learning mvdml method by utilizing the neural network architecture to seek multiple nonlinear transformations experimental results on face verification kinship verification and person re identification show the effectiveness of the proposed sharable and individual multi view metric learning methods

dimensionality reduction of multimodal labeled data by local fisher discriminant analysis reducing the dimensionality of data without losing intrinsic information is an important preprocessing step in high dimensional data analysis fisher discriminant analysis fda is a traditional technique for supervised dimensionality reduction but it tends to give undesired results if samples in a class are multimodal an unsupervised dimensionality reduction method called locality preserving projection lpp can work well with multimodal data due to its locality preserving property however since lpp does not take the label information into account it is not necessarily useful in supervised learning scenarios in this paper we propose a new linear supervised dimensionality reduction method called local fisher discriminant analysis lfda which effectively combines the ideas of fda and lpp lfda has an analytic form of the embedding transformation and the solution can be easily computed just by solving a generalized eigenvalue problem we demonstrate the practical usefulness and high scalability of the lfda method in data visualization and classification tasks through extensive simulation studies we also show that lfda can be extended to non linear dimensionality reduction scenarios by applying the kernel trick

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

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

distance metric learning for large margin nearest neighbor classification the accuracy of k nearest neighbor knn classification depends significantly on the metric used to compute distances between different examples in this paper we show how to learn a mahalanobis distance metric for knn classification from labeled examples the mahalanobis metric can equivalently be viewed as a global linear transformation of the input space that precedes knn classification using euclidean distances in our approach the metric is trained with the goal that the k nearest neighbors always belong to the same class while examples from different classes are separated by a large margin as in support vector machines svms the margin criterion leads to a convex optimization based on the hinge loss unlike learning in svms however our approach requires no modification or extension for problems in multiway as opposed to binary classification in our framework the mahalanobis distance metric is obtained as the solution to a semidefinite program on several data sets of varying size and difficulty we find that metrics trained in this way lead to significant improvements in knn classification sometimes these results can be further improved by clustering the training examples and learning an individual metric within each cluster we show how to learn and combine these local metrics in a globally integrated manner

convergence of set valued sub and supermartingales in the kuratowski mosco sense the purpose of this paper is to prove some convergence theorems of closed and convex set valued sub and supermartingales in the kuratowski mosco sense to get submartingale convergence theorems we give sufficient conditions for the kudo aumann integral and hiai umegaki conditional expectation to be closed both for compact convex set valued random variables and for closed convex set valued random variables we also give an example of a bounded closed convex set valued random variable whose kudo aumann integral is not closed

approximation solvability of nonlinear random a η resolvent operator equations with random relaxed cocoercive operators in this paper we introduce and study a new class of nonlinear random a h resolvent operator equations with random relaxed cocoercive operators in hilbert spaces by using chang s lemma theorem 3 1 of liu and li and the resolvent operator technique for a h monotone operators due to lan we also prove the existence theorems of the solutions and convergence theorems of the new generalized random iterative procedures with errors for this nonlinear random a h resolvent operator equations involving non monotone random set valued operators in hilbert spaces the results presented in this paper improve and generalize some known corresponding results in the literature

on the conditional expectation and convergence properties of random sets in this paper we study random sets with values in a separable banach space first we establish several useful properties of the set valued conditional expectation and then prove some convergence theorems for set valued amarts and uniform amarts using the weak kuratowski mosco and hausdorff modes of set convergence

daml domain adaptation metric learning the state of the art metric learning algorithms cannot perform well for domain adaptation settings such as cross domain face recognition image annotation etc because labeled data in the source domain and unlabeled ones in the target domain are drawn from different but related distributions in this paper we propose the domain adaptation metric learning daml by introducing a data dependent regularization to the conventional metric learning in the reproducing kernel hilbert space rkhs this data dependent regularization resolves the distribution difference by minimizing the empirical maximum mean discrepancy between source and target domain data in rkhs theoretically by using the empirical rademacher complexity we prove risk bounds for the nearest neighbor classifier that uses the metric learned by daml practically learning the metric in rkhs does not scale up well fortunately we can prove that learning daml in rkhs is equivalent to learning daml in the space spanned by principal components of the kernel principle component analysis kpca thus we can apply kpca to select most important principal components to significantly reduce the time cost of daml we perform extensive experiments over four well known face recognition datasets and a large scale web image annotation dataset for the cross domain face recognition and image annotation tasks under various settings and the results demonstrate the effectiveness of daml

logdet divergence based metric learning with triplet constraints and its applications how to select and weigh features has always been a difficult problem in many image processing and pattern recognition applications a data dependent distance measure can address this problem to a certain extent and therefore an accurate and efficient metric learning becomes necessary in this paper we propose a logdet divergence based metric learning with triplet constraints ldmlt approach which can learn mahalanobis distance metric accurately and efficiently first of all we demonstrate the good properties of triplet constraints and apply it in logdet divergence based metric learning model then to deal with high dimensional data we apply a compressed representation method to learn store and evaluate mahalanobis matrix efficiently besides a dynamic triplets building strategy is proposed to build a feedback from the obtained mahalanobis matrix to the triplet constraints which can further improve the ldmlt algorithm furthermore the proposed method is applied to various applications including pattern recognition facial expression recognition and image retrieval the results demonstrate the improved performance of the proposed approach

robust transfer metric learning for image classification metric learning has attracted increasing attention due to its critical role in image analysis and classification conventional metric learning always assumes that the training and test data are sampled from the same or similar distribution however to build an effective distance metric we need abundant supervised knowledge i e side label information which is generally inaccessible in practice because of the expensive labeling cost in this paper we develop a robust transfer metric learning rtml framework to effectively assist the unlabeled target learning by transferring the knowledge from the well labeled source domain specifically rtml exploits knowledge transfer to mitigate the domain shift in two directions i e sample space and feature space in the sample space domain wise and class wise adaption schemes are adopted to bridge the gap of marginal and conditional distribution disparities across two domains in the feature space our metric is built in a marginalized denoising fashion and low rank constraint which make it more robust to tackle noisy data in reality furthermore we design an explicit rank constraint regularizer to replace the rank minimization np hard problem to guide the low rank metric learning experimental results on several standard benchmarks demonstrate the effectiveness of our proposed rtml by comparing it with the state of the art transfer learning and metric learning algorithms

an introduction to kernel based learning algorithms this paper provides an introduction to support vector machines kernel fisher discriminant analysis and kernel principal component analysis as examples for successful kernel based learning methods we first give a short background about vapnik chervonenkis theory and kernel feature spaces and then proceed to kernel based learning in supervised and unsupervised scenarios including practical and algorithmic considerations we illustrate the usefulness of kernel algorithms by discussing applications such as optical character recognition and dna analysis

linear dimensionality reduction survey insights and generalizations linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data due to their simple geometric interpretations and typically attractive computational properties these methods capture many data features of interest such as covariance dynamical structure correlation between data sets input output relationships and margin between data classes methods have been developed with a variety of names and motivations in many fields and perhaps as a result the connections between all these methods have not been highlighted here we survey methods from this disparate literature as optimization programs over matrix manifolds we discuss principal component analysis factor analysis linear multidimensional scaling fisher s linear discriminant analysis canonical correlations analysis maximum autocorrelation factors slow feature analysis sufficient dimensionality reduction undercomplete independent component analysis linear regression distance metric learning and more this optimization framework gives insight to some rarely discussed shortcomings of well known methods such as the suboptimality of certain eigenvector solutions modern techniques for optimization over matrix manifolds enable a generic linear dimensionality reduction solver which accepts as input data and an objective to be optimized and returns as output an optimal low dimensional projection of the data this simple optimization framework further allows straightforward generalizations and novel variants of classical methods which we demonstrate here by creating an orthogonal projection canonical correlations analysis more broadly this survey and generic solver suggest that linear dimensionality reduction can move toward becoming a blackbox objective agnostic numerical technology

existence and multiplicity of solutions of semilinear elliptic equations the existence and multiplicity results of solutions are obtained by the reduction method and the minimax methods for nonautonomous semilinear elliptic dirichlet boundary value problem some well known results are generalized

learning representations from multiple manifolds the problem we address in this paper is how to learn joint representation from data lying on multiple manifolds we are given multiple data sets and there is an underlying common manifold among the different data sets each data set is considered to be an instance of this common manifold the goal is to achieve an embedding of all the points on all the manifolds in a way that preserves the local structure of each manifold and that at the same time collapses all the different manifolds into one manifold in the embedding space while preserving the implicit correspondences between the points across different data sets we propose a framework to learn embedding of such data which can preserve the intra manifolds local geometric structure and the inter manifolds correspondence structure the proposed solution works as extensions to current state of the art spectral embedding approaches to handling multiple manifolds graphical abstractdisplay omitted highlightsa framework to learn joint embedding space from multiple manifold data is presented intra manifolds geometric structure and inter manifolds structure are preserved implicit correspondence between the points across different data sets is estimated several embedding examples in different data sets are provided current spectral embedding approaches are extended to handle multiple manifolds

supervised distance metric learning through maximization of the jeffrey divergence over the past decades distance metric learning has attracted a lot of interest in machine learning and related fields in this work we propose an optimization framework for distance metric learning via linear transformations by maximizing the jeffrey divergence between two multivariate gaussian distributions derived from local pairwise constraints in our method the distance metric is trained on positive and negative difference spaces which are built from the neighborhood of each training instance so that the local discriminative information is preserved we show how to solve this problem with a closed form solution rather than using tedious optimization procedures the solution is easy to implement and tractable for large scale problems experimental results are presented for both a linear and a kernelized version of the proposed method for k nearest neighbors classification we obtain classification accuracies superior to the state of the art distance metric learning methods in several cases while being competitive in others highlightswe propose a novel distance metric learning method dmlmj for classification dmlmj is simple to implement and it can be solved analytically we extend dmlmj into a kernelized version to tackle non linear problems experiments on several data sets show the effectiveness of the proposed method

on the convergence of closed valued measurable multifunctions in this paper we study the convergence almost everywhere and in measure of sequences of closed valued multifunctions we first give a number of criteria for the convergence of sequences of closed subsets these results are used to obtain various characterizations for the convergence of measurable multifunctions in particular we are interested in the convergence properties of measurable selections

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

on the convergence in probability of random sets measurable multifunctions it is shown that the convergence in probability of random sets introduced by salinetti and wets is consistent with the more standard definitions of convergence in probability and is metric invariant

inequalities in banach spaces with applications well known that many problems in a hilbert space h are solved by applying the following identity ilax 1 a yi12 a412 1 llyl12 a 1 mx yl12 1 1 for all x y in h and 0 5 i 5 1 therefore one natural method to solve problems in a banach space xis to establish equalities and usually inequalities in xanalogous to 1 1 this is in fact shown by some authors recent work see for example reich l poffald and reich 2 lim 3 lim et af 4 prus and smarzewski 5 smarzewski 6 and reich 21 the purpose of this paper is to continue carrying out investigations in this line more precisely in section 3 we establish some inequalities analogous to 1 l in either uniformly convex or uniformly smooth banach spaces as corollaries we obtain new characteristics of p uniform convexity and q uniform smoothness of a banach space x via the functionals i lip and ii llq respectively we give in section 4 applications of the inequalities obtained in section 3 to fixed points of uniformly lipschitzian mappings and to best approximation theory

measurability of fixed point sets of multivalued random operators let m d be a complete separable metric space a measurable space with a algebra of subsets of andt m cb m a multivalued random operator the measurability of the functionfof fixed point sets oftdefined byf x m x t x is studied in particular it is proved thatfis measurable providedtis a random contraction ormis a weakly compact convex separable subset of a banach space andtis a random multivalued nonexpansive mapping such thati t is demiclosed at 0 for every the same result is also verified for a single valued random nonexpansive mapping in a uniformly smooth banach space

quantitative stability of variational systems i the epigraphical distance this paper proposes a global measure for the distance between the elements of a variational system parametrized families of optimization problems

quadratic projection based feature extraction with its application to biometric recognition this paper presents a novel quadratic projection based feature extraction framework where a set of quadratic matrices is learned to distinguish each class from all other classes we formulate quadratic matrix learning qml as a standard semidefinite programming sdp problem however the conventional interior point sdp solvers do not scale well to the problem of qml for high dimensional data to solve the scalability of qml we develop an efficient algorithm termed dualqml based on the lagrange duality theory to extract nonlinear features to evaluate the feasibility and effectiveness of the proposed framework we conduct extensive experiments on biometric recognition experimental results on three representative biometric recognition tasks including face palmprint and ear recognition demonstrate the superiority of the dualqml based feature extraction algorithm compared to the current state of the art algorithms highlightsa novel quadratic projection based feature extraction framework is developed a set of quadratic matrices is learnt to distinguish each class from other classes quadratic matrix learning qml is formulated as an sdp problem an efficient algorithm is developed to solve qml based on lagrange duality theory experiments on biometric recognition show the effectiveness of our algorithm

convergence of set valued and fuzzy valued martingales the purpose of this paper is to prove the convergence theorems of set valued and fuzzy valued martingales in kuratowski mosco sense without assuming that their values are compact or of compact level sets

separating between and within cluster covariate effects by using conditional and partitioning methods summary we consider the situation where the random effects in a generalized linear mixed model may be correlated with one of the predictors which leads to inconsistent estimators we show that conditional maximum likelihood can eliminate this bias conditional likelihood leads naturally to the partitioning of the covariate into between and within cluster components and models that include separate terms for these components also eliminate the source of the bias another viewpoint that we develop is the idea that many violations of the assumptions including correlation between the random effects and a covariate in a generalized linear mixed model may be cast as misspecified mixing distributions we illustrate the results with two examples and simulations