Clustering Structure-Induced Robust Multi-View Graph Recovery

Graph based classification methods have been widely applied in the fields of computer vision and machine learning. The quality of the graph highly affects the performance of these methods. The same object is commonly represented by different features, i.e., multi-view features, which leads to multiple graphs corresponding to different features in multi-view learning. However, what kind of graph is important for the task is unknown in advance. Moreover, existing multi-view learning methods become weak in dealing with noisy graphs when the data is corrupted by the noise. In this paper, we address this problem by observing that the noise of each graph has specific structure. Then, based on this observation we propose a robust multi-view graph recovery (RMGR) method in which the specific structure is used to clean the multiple input noisy graphs and these cleaned graphs are simultaneously aggregated into a consensus graph by adaptively assigning great weighted coefficients for important graphs. To make the consensus graph suit classification, the clustering structure is introduced to restrain the rank of Laplacian matrix of the consensus graph such that the number of its connected components is equal to that of clustering. In doing so, the graph is adaptively adjusted during optimization to more accurately partition data. The optimization problem is solved by proposed the iterative update algorithm. Extensive experiments on synthetic and several benchmark data sets show the effectiveness of the proposed method.