In this article, we study a challenging problem in contrastive learning when just a portion of data is aligned in multi-view dataset due to temporal, spatial, or spatio-temporal asynchronism across views. It is important to study partially view-aligned data since this type of data is common in real-world application and easily leads to data inconsistency among different views. Such a Partially View-aligned Problem (PVP) in contrastive learning has been relatively less touched so far, especially in downstream tasks, i.e., classification and clustering. In order to solve this problem, we introduce a flexible margin and propose margin-aware noise-robust contrastive learning to simultaneously identify the within-category counterparts from the other view of one data point based on the established cross-view correspondence and learn a shared representation. To be specific, the proposed learning framework is built on a novel margin-aware noise-robust contrastive loss. Since data pairs are used as input for the proposed margin-aware noise-robust contrastive learning, we build positive pairs according to the known correspondences and negative pairs in the manner of random sampling. Our margin-aware noise-robust contrastive learning framework is able to effectively reduce or remove the impacts caused by the possible existing noise for the constructed pairs in a margin-aware manner, i.e., false negative pairs led by random sampling in PVP. We relax the proposed margin-aware noise-robust contrastive loss and then give a detailed mathematical analysis for the effectiveness of our loss. As an instantiation, we construct an example under the proposed margin-aware noise-robust contrastive learning framework for validation in this work. To the best of our knowledge, this is the first attempt of extending contrastive learning to a margin-aware noise-robust version for dealing with PVP. We also enrich the learning paradigm when there is noise in the data. Extensive experiments on different datasets demonstrate the promising performance of the proposed method in the classification and clustering tasks.

Multi-view clustering has become an important research topic in machine learning and computer vision communities, which aims at achieving a consensus partition of data points across different views. However, the existing multi-view clustering methods fail to simultaneously consider the pairwise and high-order correlations among different views in the process of obtaining the final results. In this paper, we propose the Elastic multi-view Subspace Clustering with pairwise and high-order Correlations (ESCC) to solve this problem. ESCC simultaneously explores the pairwise and high-order correlations among different views, resulting in a more comprehensive shared representation. ESCC formulates these two kinds of correlations into a unified objective framework, which are able to be jointly optimized to refine each other. As an instantiation, we construct an example of ESCC (e-ESCC) in this work. To be specific, e-ESCC uses the multi-layer neural networks to study the pairwise correlation from multiple views with the guidance of the latent representation. It is also able to help obtain the nonlinear subspaces of the multi-view data. e-ESCC collects multi-view similarity matrices into a tensor and utilizes the low-rank tensor norm to exploit the high-order correlation among different views. The augmented Lagrangian multiplier is adopted to solve the formulated problem of e-ESCC. Experiments on seven data sets validate the superiority of our method over 13 state-of-the-art multi-view clustering methods under six metrics.

Multi-view clustering has gained great progress recently, which employs the representations from different views for improving the final performance. In this paper, we focus on the problem of multi-view clustering based on the Markov chain by considering low-rank constraints. Since most existing methods fail to simultaneously characterize the relations among different entries in a tensor from the global perspective and describe local structures of similarity matrices of a tensor, we propose a novel Flexible Tensor Learning for Multi-view Clustering with the Markov chain (FTLMCM) to solve this problem. We also construct transition probability matrices based on the Markov chain to fully utilize the connection between the Markov chain and spectral clustering. Specifically, the low-rank constraints of the tensor, the frontal slices and the lateral slices of the tensor are imposed on the objective function of the proposed method to achieve these goals. Besides, these three constraints can be optimized jointly to achieve mutual refinement. FTLMCM also uses the tensor rotation to better explore the relationships among different views. We formulate FTLMCM as a problem of low-rank tensor recovery and solve it with the augmented Lagrangian multiplier. Experiments on six different benchmark data sets under six metrics demonstrate that the proposed method is able to achieve better clustering performance.