Consistency Meets Inconsistency: A Unified Graph Learning Framework for Multiview Clustering Graph Learning has emerged as a promising technique for multiview clustering, and has recently attracted lots of attention due to its capability of adaptively learning a unified and probably better graph from multiple views. However, the existing multiview graph learning methods mostly focus on the multiview consistency, but neglect the potential multiview inconsistency (which may be incurred by noise, corruptions, or viewspecific characteristics). To address this, this paper presents a new graph learningbased multiview clustering approach, which for the first time, to our knowledge, simultaneously and explicitly formulates the multiview consistency and the multiview inconsistency in a unified optimization model. To solve this model, a new alternating optimization scheme is designed, where the consistent and inconsistent parts of each singleview graph as well as the unified graph that fuses the consistent parts of all views can be iteratively learned. It is noteworthy that our multiview graph learning model is applicable to both similarity graphs and dissimilarity graphs, leading to two graph fusionbased variants, namely, distance (dissimilarity) graph fusion and similarity graph fusion. Experiments on various multiview datasets demonstrate the superiority of our approach. The MATLAB source code is available at https:github.comyouweiliangConsistentGraphLearning.

Consensus Graph Weighting via Trace Ratio Criterion for Multiview Unsupervised Feature Selection The problem of multiview unsupervised feature selection receive more attention in recent years. Most of existing works explore the shared information across multiviews. Several embedded algorithms have been developed. All these methods use additional hyperparameter for regularization, which makes these algorithms are less attractive in practical applications, where it is not easy to select the proper model among potential large candidate parameter spaces. In this paper, we aim at consider a Twolevel Weighted Graph Matching for Unsupervised Multiview Feature Selection. We construct viewspecific graphs to capture the local structure of each view. We also compute the featurelevel graphs to obtain the local structure of data characterized by single feature. Thus, we learn the optimal unknown graph from both the viewspecific graphs and the featurelevel graphs. The approximation between the consensus graph and the feature level graphs is achieved by the twolevel weighted linear combination measured by the squared loss function. The consensus between the final graph and viewspecific graphs are captured by the integrated pairwise alignment among sample pairs. Moreover, these two criteria are integrated into a unified learning procedure under the traceratio framework.