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In a linear multi-secret sharing scheme with non-threshold structures, several secret values are shared among n participants, and every secret value has a specified access structure. The efficiency of a multi-secret sharing scheme is measured by means of the complexity σ and the randomness τ. Informally, the complexity σ is the ratio between the maximum of information received by each participant and the minimum of information corresponding to every key. The randomness τ is the ratio between the amount of information distributed to the set of users U = {1, ⋯, n} and the minimum of information corresponding to every key. In this paper, we discuss σ and τ of any linear multi-secret sharing schemes realized by linear codes with non-threshold structures, and provide two algorithms to make σ and τ to be the minimum, respectively. That is, they are optimal.

Generalization of large margin classification methods from the binary classification setting to the more general multicategory setting is often found to be non-trivial. In this paper, we study large margin classification methods that can be seamlessly applied to both settings, with the binary setting simply as a special case. In particular, we explore the Fisher consistency properties of multicategory majorization losses and present a construction framework of majorization losses of the 0-1 loss. Under this framework, we conduct an in-depth analysis about three widely used multicategory hinge losses. Corresponding to the three hinge losses, we propose three multicategory majorization losses based on a coherence function. The limits of the three coherence losses as the temperature approaches zero are the corresponding hinge losses, and the limits of the minimizers of their expected errors are the minimizers of the expected errors of the corresponding hinge losses. Finally, we develop multicategory large margin classification methods by using a so-called multiclass C-loss.

Light shape detection of headlamps is an important project of yearly check. In the aspect of lowbeam detection, it is necessary to not only accurately calculate the boundary between brightness and shade, but also optical axis intersection point. By the principle that the second derivative indicates the concavity and convexity of functions, a polynomial fitting is used to calculate the columns grayscale profile of a lowbeam figure, and then get the cut-off point through second derivative of a polynomial. The boundary between brightness and shade is consisted of these cut-off points. The optical axis intersection point is obtained by second order difference of the boundary. While fully extracting graphic features, the method precisely locates positions of the boundary and the intersection.

A novel method of measuring gap and surface differential was proposed to detect headlights contour in this paper. The method is based on the line structured laser sensor and robot system, and spline curve fitting was used to obtain the contour of the headlights and mold. After the fitting, the contour was resampled to get the shortest distance vector between the headlight contour curves and the mold contour curves, and through the decomposition of the vectors, the perpendicular and parallel components were obtained, and then the gap and surface differential measurement was completed.

In this paper, we propose a general regularization framework for multiclass classification based on discriminant functions. Since the objective function in the primal optimization problem of this framework is always not differentiable, the optimal solution cannot be obtained directly. With the aid of the deterministic annealing approach, a differentiable objective function is derived subject to a constraint on the randomness of the solution. The problem can be approximated by solving a sequence of differentiable optimization problems, and such approximation converges to the original problem asymptotically. Based on this approach, class-conditional posterior probabilities can be calculated directly without assuming the underlying probabilistic model. We also notice that there is a connection between our approach and some existing statistical models, such as Fisher discriminant analysis and logistic regression.

In recent years, metric learning in the semisupervised setting has aroused a lot of research interest. One type of semisupervised metric learning utilizes supervisory information in the form of pairwise similarity or dissimilarity constraints. However, most methods proposed so far are either limited to linear metric learning or unable to scale well with the data set size. In this letter, we propose a nonlinear metric learning method based on the kernel approach. By applying low-rank approximation to the kernel matrix, our method can handle significantly larger data sets. Moreover, our low-rank approximation scheme can naturally lead to out-of-sample generalization. Experiments performed on both artificial and real-world data show very promising results.

The advantage of a kernel method often depends critically on a proper choice of the kernel function. A promising approach is to learn the kernel from data automatically. In this paper, we propose a novel method for learning the kernel matrix based on maximizing a class separability criterion that is similar to those used by linear discriminant analysis (LDA) and kernel Fisher discriminant (KFD). It is interesting to note that optimizing this criterion function does not require inverting the possibly singular within-class scatter matrix which is a computational problem encountered by many LDA and KFD methods. We have conducted experiments on both synthetic data and real-world data from UCI and FERET, showing that our method consistently outperforms some previous kernel learning methods.

Feature extraction is among the most important problems in face recognition systems. In this paper, we propose an enhanced kernel discriminant analysis (KDA) algorithm called kernel fractional-step discriminant analysis (KFDA) for nonlinear feature extraction and dimensionality reduction. Not only can this new algorithm, like other kernel methods, deal with nonlinearity required for many face recognition tasks, it can also outperform traditional KDA algorithms in resisting the adverse effects due to outlier classes. Moreover, to further strengthen the overall performance of KDA algorithms for face recognition, we propose two new kernel functions: cosine fractional-power polynomial kernel and non-normal Gaussian RBF kernel. We perform extensive comparative studies based on the YaleB and FERET face databases. Experimental results show that our KFDA algorithm outperforms traditional kernel principal component analysis (KPCA) and KDA algorithms. Moreover, further improvement can be obtained when the two new kernel functions are used.

In this paper we propose a matrix-variate Dirichlet process (MATDP) for modeling the joint prior of a set of random matrices. Our approach is able to share statistical strength among regression coefficient matrices due to the clustering property of the Dirichlet process. Moreover, since the base probability measure is defined as a matrix-variate distribution, the dependence among the elements of each random matrix is described via the matrix-variate distribution. We apply MATDP to multivariate supervised learning problems. In particular, we devise a nonparametric discriminative model and a nonparametric latent factor model. The interest is in considering correlations both across response variables (or covariates) and across response vectors. We derive Markov chain Monte Carlo algorithms for posterior inference and prediction, and illustrate the application of the models to multivariate regression, multi-class classification and multi-label prediction problems.

Dictionary learning is a challenging theme in computer vision. The basic goal is to learn a sparse representation from an overcomplete basis set. Most existing approaches employ a convex relaxation scheme to tackle this challenge due to the strong ability of convexity in computation and theoretical analysis. In this paper we propose a non-convex online approach for dictionary learning. To achieve the sparseness, our approach treats a so-called minimax concave (MC) penalty as a nonconvex relaxation of the l 0 penalty. This treatment expects to obtain a more robust and sparse representation than existing convex approaches. In addition, we employ an online algorithm to adaptively learn the dictionary, which makes the non-convex formulation computationally feasible. Experimental results on the sparseness comparison and the applications in image denoising and image inpainting demonstrate that our approach is more effective and flexible.

Fisher linear discriminant analysis (LDA) and its kernel extension--kernel discriminant analysis (KDA)--are well known methods that consider dimensionality reduction and classification jointly. While widely deployed in practical problems, there are still unresolved issues surrounding their efficient implementation and their relationship with least mean squared error procedures. In this paper we address these issues within the framework of regularized estimation. Our approach leads to a flexible and efficient implementation of LDA as well as KDA. We also uncover a general relationship between regularized discriminant analysis and ridge regression. This relationship yields variations on conventional LDA based on the pseudoinverse and a direct equivalence to an ordinary least squares estimator. Experimental results on a collection of benchmark data sets demonstrate the effectiveness of our approach.

Existing semi-supervised learning methods are mostly based on either the cluster assumption or the manifold assumption. In this paper, we propose an integrated regularization framework for semi-supervised kernel machines by incorporating both the cluster assumption and the manifold assumption. Moreover, it supports kernel learning in the form of kernel selection. The optimization problem involves joint optimization over all the labeled and unlabeled data points, a convex set of basic kernels, and a discrete space of unknown labels for the unlabeled data. When the manifold assumption is incorporated, graph Laplacian kernels are used as the basic kernels for learning an optimal convex combination of graph Laplacian kernels. Comparison with related methods on the USPS data set shows very promising results.

We present a subspace learning method, called local discriminant embedding with tensor representation (LDET), that addresses simultaneously the generalization and data representation problems in subspace learning. LDET learns multiple interrelated subspaces for obtaining a lower-dimensional embedding by incorporating both class label information and neighborhood information. By encoding each object as a second- or higher-order tensor, LDET can capture higher-order structures in the data without requiring a large sample size. Extensive empirical studies have been performed to compare LDET with a second- or third-order tensor representation and the original LDE on their face recognition performance. Not only does LDET have a lower computational complexity than LDE, but LDET is also superior to LDE in terms of its recognition accuracy.

The kernel fractional-stop nonlinear discriminant analysis (KF-NDA) method not only extends the fractional-step linear discriminant analysis (F-LDA) method to a nonlinear version, but also further improves the generalization ability of traditional kernel nonlinear discriminant analysis (K-NDA). On the other hand, the Gabor transformed face images exhibit strong characteristics of spatial locality, scale and orientation selectivity, similar to those displayed by Gabor wavelets. Such characteristics produce salient local features that are most suitable for face recognition (FR). Hence, the augmented Gabor feature vector (AGFV) derived from a set of downsampled Gabor wavelet representations of face images is robust to the various of face images and simultaneously exhibits the more discriminatory information. Based on the AGFV and the KF-NDA, a robust feature extraction framework, i.e., the Gabor KF-NDA (GKF-NDA), is proposed for FR. In this framework, the KF-NDA method is directly applied to extract the robust nonlinear feature from the AGFV. Experimental results tested on the popular databases show that the GKF-NDA is more effective than oilier existing FR approaches.

Linear discriminant analysis (LDA) is a very effective tool used for dimensionality reduction and feature extraction in pattern recognition. However, the LDA is inadequate to describe complex and nonlinear patterns. To solve this problem, kernel nonlinear discriminant analysis (K-NDA) has been proposed. Although successful in many cases, classic K-NDA also suffers from the small sample size problem (SSSP) and loses some significant discriminatory information as same as classic LDA. In this paper, a novel K-NDA, i.e., the kernel generalized nonlinear discriminant analysis (KG-NDA) algorithm is introduced to effectively overcome these problems and it also views the optimal discriminant vectors as a global transform in the feature space to some extent. It not only deals with the nonlinear problem, but also effectively solves the SSSP. The KG-NDA is applied to the experiments on face recognition and the results tested on two popular databases demonstrate that this method is very effective.

We study the use of kernel subspace methods that learn low-dimensional subspace representations for classification tasks. In particular, we propose a new method called kernel weighted nonlinear discriminant analysis (KWNDA) which possesses several appealing properties. First, like all kernel methods, it handles nonlinearity in a disciplined manner that is also computationally attractive. Second, by introducing weighting functions into the discriminant criterion, it outperforms existing kernel discriminant analysis methods in terms of the classification accuracy. Moreover, it also effectively deals with the small sample size problem. We empirically compare different subspace methods with respect to their classification performance of facial images based on the simple nearest neighbor rule. Experimental results show that KWNDA substantially outperforms competing linear as well as nonlinear subspace methods.

On the one hand, the support vector machine (SVM) has the high performance in tackling small sample size and high-dimensional data, and has the good generalization ability too. On the other hand, Gabor wavelet exhibits strong characteristics of spatial locality, scale, and orientation selectivity, and the Gabor representations of face images can produce salient local features that are most suitable for face recognition. This paper proposes a new face recognition method based on independent Gabor features (IGF) and SVM. The proposed method has four steps as follows: 1) an augmented Gabor feature vector (AGFV) is derived from a set of downsampled Gabor wavelet representations of face images; 2) an IGF is obtained by applying the independent component analysis (ICA) to the AGFV; 3) To decrease the computational complexity and improve the recognition rate, Genetic Algorithms (GA) is used to select the optimal IGF set for classification; 4) the SVM is used to classify the optimal IGF. The experiments tested on the Yale database show that this method is very effective.

This paper introduces a novel Gabor direct generalized optimal discriminant vectors (GDG-ODV) method for face recognition (FR). This method can apply directly the generalized optimal discriminant vectors (G-ODV) method that views the optimal set of discriminant vectors as a global transform to the high-dimensional augmented Gabor feature vectors (AGFV) derived from the Gabor wavelet representation of face images. This method has three novelties: 1) it is robust to the facial variations; 2) it can efficiently solve the small sample size problem (SSSP), which widely exists in FR tasks; 3) it can consider the separability of optimal discriminant vectors (ODV) from a global viewpoint. The GDG-ODV method is compared, in terms of classification accuracy, to other common methods on the ORL database. The results indicate that this method is overall superior to those various FR methods.

This paper introduces a novel Gabor Generalized Foley-Sammon Transform (GGFST) method for face recognition (FR). The GGFST method can directly apply the generalized Foley-Sammon transform (GFST) method that has the best separable ability in a global sense to the high-dimensional augmented Gabor feature vectors derived from the Gabor wavelet representation of face images. This method has three novelties: 1) the GGFST method is robust to facial variations; 2) the GGFST method can overcome the limitations of traditional FR approaches by incorporating some middle methods as the preprocessing steps for dimension reduction so as to discard some significant discriminatory information; and 3) the GGFST method has the best separable ability in a global sense. The comparative experiments on the ORL database show that the GGFST method is more effective than the previous methods.