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In the nearest-convex-model type classifiers, each class in the training set is approximated with a convex class model, and a test sample is assigned to a class based on the shortest distance from the test sample to these class models. In this paper, we propose new methods for approximating the distances from test samples to the convex regions spanned by training samples of classes. To this end, we approximate each class region with a polyhedral convex conic region by utilizing polyhedral conic functions (PCFs) and its extension, extended PCFs. Then, we derive the necessary formulations for computing the distances from test samples to these new models. We tested the proposed methods on different high-dimensional classification tasks including face, digit, and generic object classification as well as on some lower-dimensional classification problems. The experimental results on different datasets show that the proposed classifiers achieve either the best or comparable results on high-dimensional classification problems compared to other nearest-convex-model classifiers, which shows the superiority of the proposed methods. [ABSTRACT FROM AUTHOR]

• Adopting a block partitioning strategy to extract the local information. • Modeling both global and local information as affine hull. • Mapping the image sets into a RKHS to make them linear separable. In image set classification, dual linear regression classification (DLRC) has shown the excellent performance on face image data without the interference of the complex background. However, DLRC could not well identify the data set with the complex background. The complex background means that the background is cluttered and the viewpoint is unusual or the object is partially occluded. This paper proposes a new model, kernelized dual regression (KDR), based on DLRC and the kernel trick which is a useful technique in image classification. Different from DLRC, KDR adopts a block partitioning strategy to extract the local information, which is able to conquer the shortcoming of DLRC. To capture the nonlinear relationship between the training set and test set, KDR tactfully maps these image sets into a high-dimensional feature space by adopting the nonlinear mapping associated with the Gaussian kernel function. In the reproducing kernel Hilbert space (RKHS), KDR can find the joint coefficients by minimizing the distance between training set and test set, and has a closed-form solution. Extensive experiments on four datasets show that KDR could achieve better classification performance than that of DLRC and other existing methods. [ABSTRACT FROM AUTHOR]

Abstract In computer vision, we generally solve a classification problem by a single image. With the video cameras being widely used in our real life, it is a nature choice to solve a classification problem by image sets. Compared with the single image based methods, the image set classification deals with severe changes of appearance and makes decisions by comparing the query set with gallery sets. So the image set classification offers more promises and has therefore attracted significant research attention in recent years. In this paper, we provide a review on image set classification. Our review begins with an overview of the direction of image set classification. Then we detail some classic algorithms. Experimental analyses are provided in corresponding subsection to compare classification performance of various methods and draw some meaningful conclusions. Finally, several promising directions and tasks are provided as guidelines for future work. [ABSTRACT FROM AUTHOR]

In face of the feature extraction of face recognition, this paper proposed a new method of local neighborhood based multi-manifold metric learning for face recognition.For small sample size problem in face recognition, it pre-processed the face image by using the feature face and used the Euclidean distance to select the nearest neighbors of each data point in the pre-processed face data set. It obtained the local weight matrix by this and the error distance between the reconstructed data points and calculated the original data points.At the same time,using the image set modeling manifold, it used the affine hull to represent the dataset information of manifolds and calculated the distance metric matrix among manifolds.By maximizing the distance between the manifolds and minimizing the distance between the data points and the reconstructed data points to find the dimension matrix. A large number of comparative experiments on the face data set show that the method is accurate and effective. [ABSTRACT FROM AUTHOR]

Handling appearance variations is a challenging issue in visual tracking. Existing appearance models are usually built upon a linear combination of templates. With such kind of representation, accurate visual tracking is not desirable when heavy appearance variations are in presence. Under the framework of particle filtering, we propose a novel target representation for tracking. Namely, the target candidates are represented by affine combinations of a template set, which leads to better capability in describing unseen target appearances. Additionally, in order to adapt this representation to dynamic contexts across a video sequence, a novel template update scheme is presented. Different from conventional approaches, the scheme considers both the importance of one template to a target candidate in the current frame and the recentness of the template that is kept in the template set. Comprehensive experiments show that the proposed algorithm achieves superior performances in comparison with state-of-the-art works. [ABSTRACT FROM AUTHOR]

Based on defining a flexible convex hull, a maximum margin classification based on flexible convex hulls (MMC-FCH) is presented in this work. The flexible convex hull defined in our work is a class region approximation looser than a convex hull but tighter than an affine hull. MMC-FCH approximates each class region with a flexible convex hull of its training samples, and then finds a linear separating hyperplane that maximizes the margin between flexible convex hulls by solving a closest pair of points problem. The method can be extended to nonlinear case by using the kernel trick, and multi-class classification problems are dealt with by constructing binary pairwise classifiers as in support vector machine (SVM). The experiments on several databases show that the proposed method compares favorably to the maximum margin classification based on convex hulls (MMC-CH) or affine hulls (MMC-AH). [ABSTRACT FROM AUTHOR]

Highlights: [•] A feature extraction scheme using two-dimensional random projection, called 2DCS, is proposed. [•] A new classifier, called NCSC (including it fast version NCSC-II), is proposed. [•] Classifiers of NN, NFL and NS are the special cases of NCSC. [•] With tuned parameter, NCSC/NCSC-II outperforms NN, NFL, NS and the Orthonormal ℓ2-norm method. [Copyright &y& Elsevier]

Given an integral polyhedron P ⊆ ℝn and a rational polyhedron Q ⊆ ℝn containing the same integer points as P, we investigate how many iterations of the Chvatal--Gomory closure operator have to be performed on Q to obtain a polyhedron contained in the affine hull of P. We show that if P contains an integer point in its relative interior, then such a number of iterations can be bounded by a function depending only on n. On the other hand, we prove that if P is not full-dimensional and does not contain any integer point in its relative interior, then no finite bound on the number of iterations exists. [ABSTRACT FROM AUTHOR]

Abstract: This paper introduces a geometrically inspired large margin classifier that can be a better alternative to the support vector machines (SVMs) for the classification problems with limited number of training samples. In contrast to the SVM classifier, we approximate classes with affine hulls of their class samples rather than convex hulls. For any pair of classes approximated with affine hulls, we introduce two solutions to find the best separating hyperplane between them. In the first proposed formulation, we compute the closest points on the affine hulls of classes and connect these two points with a line segment. The optimal separating hyperplane between the two classes is chosen to be the hyperplane that is orthogonal to the line segment and bisects the line. The second formulation is derived by modifying the formulation. Both formulations are extended to the nonlinear case by using the kernel trick. Based on our findings, we also develop a geometric interpretation of the least squares SVM classifier and show that it is a special case of the proposed method. Multi-class classification problems are dealt with constructing and combining several binary classifiers as in SVM. The experiments on several databases show that the proposed methods work as good as the SVM classifier if not any better. [ABSTRACT FROM AUTHOR]