Incomplete multi-view clustering has become one of the important research problems due to the extensive missing multi-view data in the real world. Although the existing methods have made great progress, there are still some problems: 1) most methods cannot effectively mine the information hidden in the missing data; 2) most methods typically divide representation learning and clustering into two separate stages, but this may affect the clustering performance as the clustering results directly depend on the learned representation. To address these problems, we propose a novel incomplete multi-view clustering method with hierarchical information transfer. Firstly, we design the view-specific Graph Convolutional Networks (GCN) to obtain the representation encoding the graph structure, which is then fused into the consensus representation. Secondly, considering that one layer of GCN transfers one-order neighbor node information, the global graph propagation with the consensus representation is proposed to handle the missing data and learn deep representation. Finally, we design a weight-sharing pseudo-classifier with contrastive learning to obtain an end-to-end framework that combines view-specific representation learning, global graph propagation with hierarchical information transfer, and contrastive clustering for joint optimization. Extensive experiments conducted on several commonly-used datasets demonstrate the effectiveness and superiority of our method in comparison with other state-of-the-art approaches.

Multiview unsupervised feature selection is an emerging direction in the machine learning community because of its ability to identify informative patterns and reduce the dimensionality of multiview data. Although numerous methods have been proposed and shown to be effective, they have some limitations: 1) most existing algorithms fail to improve the model performance along the view dimension; 2) they rarely incorporate more discriminative partition information; and 3) the negative effects of marginal samples are not considered. To solve these problems, we propose a novel method termed as partition-level tensor learning-based multiview unsupervised feature selection (PTFS). The proposed method optimizes a low-rank constrained tensor assembled by the inner product of base partition matrices. By doing so, PTFS simultaneously leverages the high-order view correlation and indirectly integrates discriminative partition information. Besides, a statistic-based adaptive self-paced strategy is introduced to ensure that confident samples are prioritized for training the model. Moreover, an effective alternating optimization method is designed to solve the resulting optimization problem. Extensive experiments on ten datasets demonstrate the effectiveness and efficiency of the proposed method compared to the state-of-the-art methods. The code is available at https://github.com/HdTgon/2023-TNNLS-PTFS.

Achieving practical full projector compensation requires the projection display to adapt quickly to textured projection surfaces and unexpected movements without interrupting the display procedure. A possible solution to achieve this involves using a projector and an RGB camera and correcting both color and geometry by directly capturing and analyzing the projected natural image content, without the need for additional patterns. In this study, we approach full projector compensation as a numerical optimization problem and present a physics-based framework that can handle both geometric calibration and radiometric compensation for a Projector-camera system (Procams), using only a few sampling natural images. Within the framework, we decouple and estimate the Procams' factors, such as the response function of the projector, the correspondence between the projector and camera, and the reflectance of projection surfaces. This approach provides an interpretable and flexible solution to adapt to the changes in geometry and reflectance caused by movements. Benefitting from the physics-based scheme, our method guarantees both accurate color calculation and efficient movement and reflectance estimation. Our experimental results demonstrate that our method surpasses other state-of-the-art end-to-end full projector compensation methods, with superior image quality, reduced computational time, lower memory consumption, greater geometric accuracy, and a more compact network architecture.

Multi-view learning (MVL) is an active direction in machine learning that aims at exploiting the consensus and complementarity information among multiple distinct feature sets to boost the generalization performance of the counterpart algorithm. So far, two classical SVM-based MVL methods are SVM-2K and multi-view twin support vector machine (MvTSVM). They are designed only for two-view classification and cannot tackle the general multi-view classification problem. They also cannot effectively leverage the complementarity information among different feature views. In this paper, we propose two novel multi-view support vector machines with the consensus and complementarity information for MVL that not only can deal with the two-view classification problem but also the general multi-view classification problem by jointly learning multiple different views in a non-pairwise way. The disagreement among different views is regarded as a constraint or a regularization term in the objective function which plays an important role in exploring the consensus information. Combination weights for the reconstruction of each view in regularization terms are learned to explore complementarity information among different views. Finally, an efficient iteration algorithm with the classical convex quadratic programming is developed for optimization. Experimental results validate the effectiveness of our proposed methods.

Generalized eigenvalue proximal support vector machines (GEPSVMs) are a simple and effective binary classification method in which each hyperplane is closest to one of the two classes and as far as possible from the other class. They solve a pair of generalized eigenvalue problems to obtain two nonparallel hyperplanes. Multiview learning considers learning with multiple feature sets to improve the learning performance. In this paper, we propose multiview GEPSVMs (MvGSVMs) which effectively combine two views by introducing a multiview co-regularization term to maximize the consensus on distinct views, and skillfully transform a complicated optimization problem to a simple generalized eigenvalue problem. We also propose multiview improved GEPSVMs (MvIGSVMs), which use the minus instead of ratio in MvGSVMs to measure the differences of the distances between the two classes and the hyperplane and lead to a simpler eigenvalue problem. Linear MvGSVMs and MvIGSVMs are generalized to the nonlinear case by the kernel trick. Experimental results on multiple data sets show the effectiveness of our proposed approaches.

Multiview learning is more robust than single-view learning in many real applications. Canonical correlation analysis (CCA) is a popular technique to utilize information stemming from multiple feature sets. However, it does not exploit label information effectively. Later multiview linear discriminant analysis (MLDA) was proposed through combining CCA and linear discriminant analysis (LDA). Due to the successful application of uncorrelated LDA (ULDA), which seeks optimal discriminant features with minimum redundancy, we propose a new supervised learning method called multiview ULDA (MULDA) in this paper. This method combines the theory of ULDA with CCA. Then we adapt discriminant CCA (DCCA) instead of the CCA in MLDA and MULDA, and discuss about the effect of this modification. Furthermore, we generalize these methods to the nonlinear case by kernel-based learning techniques. The new method is called kernel multiview uncorrelated discriminant analysis (KMUDA). Then we modify kernel multiview discriminant analysis and KMUDA by replacing Kernel CCA with Kernel DCCA. Our methods are tested on different real datasets and compared with other state-of-the-art methods. Experimental results validate the effectiveness of our methods.

Semisupervised learning has been an active research topic in machine learning and data mining. One main reason is that labeling examples is expensive and time-consuming, while there are large numbers of unlabeled examples available in many practical problems. So far, Laplacian regularization has been widely used in semisupervised learning. In this paper, we propose a new regularization method called tangent space intrinsic manifold regularization. It is intrinsic to data manifold and favors linear functions on the manifold. Fundamental elements involved in the formulation of the regularization are local tangent space representations, which are estimated by local principal component analysis, and the connections that relate adjacent tangent spaces. Simultaneously, we explore its application to semisupervised classification and propose two new learning algorithms called tangent space intrinsic manifold regularized support vector machines (TiSVMs) and tangent space intrinsic manifold regularized twin SVMs (TiTSVMs). They effectively integrate the tangent space intrinsic manifold regularization consideration. The optimization of TiSVMs can be solved by a standard quadratic programming, while the optimization of TiTSVMs can be solved by a pair of standard quadratic programmings. The experimental results of semisupervised classification problems show the effectiveness of the proposed semisupervised learning algorithms.

Twin support vector machines are a powerful learning method for binary classification. Compared to standard support vector machines, they learn two hyperplanes rather than one as in standard support vector machines, and work faster and sometimes perform better than support vector machines. However, relatively little is known about their theoretical performance. As recent tightest bounds for practical applications, PAC-Bayes bounds are based on a prior and posterior over the distribution of classifiers. In this paper, we study twin support vector machines from a theoretical perspective and use the PAC-Bayes bound to measure the generalization error bound of twin support vector machines. Experimental results on real-world datasets show better predictive capabilities of the PAC-Bayes bound for twin support vector machines compared to the PAC-Bayes bound for support vector machines.

Twin support vector machines are a recently proposed learning method for binary classification. They learn two hyperplanes rather than one as in conventional support vector machines and often bring performance improvements. Multi-view learning is concerned about learning from multiple distinct f eature sets, which aims to exploit distinct views to improve generalization performance. In this paper, we propose multi-view twin support vector machines by solving a pair of quadratic programming problems. This paper gives a detailed derivation of the Lagrange dual optimization formulation. The linear multi-view twin support vector machines are further generalized to the nonlinear case by the kernel trick. Experimental results demonstrate that our proposed methods are effective.