Joint Adaptive Neighbours and Metric Learning for Multi-view Subspace Clustering

Due to the existence of various views or representations in many real-world data, multi-view learning has drawn much attention recently. Multi-view spectral clustering methods based on similarity matrixes or graphs are pretty popular. Generally, these algorithms learn informative graphs by directly utilizing original data. However, in the real-world applications, original data often contain noises and outliers that lead to unreliable graphs. In addition, different views may have different contributions to data clustering. In this paper, a novel Multiview Subspace Clustering method unifying Adaptive neighbours and Metric learning (MSCAM), is proposed to address the above problems. In this method, we use the subspace representations of different views to adaptively learn a consensus similarity matrix, uncovering the subspace structure and avoiding noisy nature of original data. For all views, we also learn different Mahalanobis matrixes that parameterize the squared distances and consider the contributions of different views. Further, we constrain the graph constructed by the similarity matrix to have exact c (c is the number of clusters) connected components. An iterative algorithm is developed to solve this optimization problem. Moreover, experiments on a synthetic dataset and different real-world datasets demonstrate the effectiveness of MSCAM.