# Fusing Local and Global Information for One-Step Multi-View Subspace Clustering
## 1 Introduction  
Clustering is a fundamental unsupervised learning problem that is widely used in the tasks of machine learning [1], computer vision [2], and data mining [3]. It attempts to help to understand the structure of unlabeled data by dividing the entire unlabeled samples into clusters, where the samples in the same cluster are not similar to samples in the other clusters [4; 5; 6]. With the continuous development of information technology, different features of the object can be easily acquired by different feature extractors, data sources or sensors. For example, an image can be depicted by the color, texture, and edge features. A news report is usually composed of text descriptions and pictures. In the field of autonomous driving, an obstacle can be captured by different types of sensors. These different features can be viewed as multi-view data. Since each view commonly contains view-specific information about the object, using only one view for clustering may yield poor results [7]. Therefore, it is reasonable and appropriate to fuse different views for clustering. It is known that multiple views come from the same object. Hence, multi-view data contain not only the consistency but also the diversity across views. How to reasonably utilize the consistency and diversity to find the underlying clustering structure of multi-view data has become an important research topic. To deal with the multi-view data, a natural idea is to concatenate these different feature vectors into a new vector and then adopt some existing single-view clustering methods to group the multi-view data. Although this idea is intuitive and simple to deal with multi-view data, it ignores the consistency and complementary information across these views. To address this problem, lots of multi-view clustering methods have been developed to obtain the good clustering performance. For background reading, the reader can refer to the surveys on multi-view clustering [8; 9; 10]. In this paper, we mainly focus on the multi-view subspace clustering, which has received extensive attention due to its advanced clustering performance and good mathematical interpretability. Multi-view subspace clustering attempts to construct an ideal subspace representation to describe the multiple linear subspace structure, and the clustering results are then obtained by utilizing the spectral clustering for this obtained subspace representation. The mechanism for computing the subspace representation is based on the self-expressive reconstruction model, where each sample is reconstructed by entire samples. Hence, subspace representation yielded by the self-expressive reconstruction model can exploit the global information but may ignore the local information of multi-view data. Nevertheless, exploring the local structure has been confirmed to improve the learning performance [11]. Moreover, most multi-view subspace clustering methods divide the learning subspace representation and clustering into two individual procedures, which ignores their communications. To address the above-mentioned issues, in this paper, we propose a novel subspace clustering method fusing local and global information for one-step multi-view subspace clustering (LGOMSC). The proposed method combines the procedures of constructing subspace representation, multi-view information fusion, and clustering into a unified optimization framework. In this framework, as shown in Figure 1, to exploit the local and global information of multi-view data, we integrate graph learning into the self-expressive reconstruction model by adaptively exploring the local structure information for the construction of subspace representation. To capture latent consistency information across views, the proposed method adopts a multi-view information fusion to learn the common subspace representation from these specific subspace representations of different views.