Multi-view clustering using a flexible and optimal multi-graph fusion method

Recently, many multi-view clustering (MVC) methods based on graphs have been proposed to address prevalent multi-view data. For these methods, the multi-graph fusion step, aim of which is to obtain a consensus graph is vital for obtaining good clustering performance. However, these methods still have two problems. First, the column sum of the consensus graph is restricted to one, which is not flexible enough for practical applications. Affected by the sum-to-one constraint, the similarity between some noisy points may be large, which may cause these abnormal points to be grouped into a separate cluster. Second, the cluster structure of the consensus graph is often not considered. To address these problems, in this paper, we propose a novel multi-view clustering using a flexible and optimal multi-graph fusion method (MVC/FOMF). Specifically, we first obtain the similarity graph of each view by using red the self-expressive method. Second, we fuse these graphs into a consensus graph whose column sum is constrained to s(0 < s <= 1), and we can adjust s to look for the best clustering performance. Third, we impose a rank constraint on the Laplacian matrix of the consensus graph to learn the best clustering structure. Finally, all these steps are unified into a framework and the corresponding optimization procedure, which is based on the alternating multiplier method, is also designed. More importantly, the complexity of our algorithm is also lower than those of many representative algorithms. Compared with that of the state-of-the-art algorithms, our algorithm shows very encouraging performance on some datasets. The code can be found at https://github.com/wulala2233/MVCFOMF.