Local-Global Fuzzy Clustering With Anchor Graph

Recently, anchor-based strategy is getting a lot of attention, which extends spectral clustering to reveal the dual relation between samples and features. However, the acquisition of clustering results follows the relaxed-discrete procedure, which might lead to serious information loss. Given that, local-global fuzzy clustering with anchor graph is proposed in this article, which jointly completes subspace learning and clustering. With the construction of anchor graph, we first impose the fuzzy constraint on the indicator matrix, which is beneficial for revealing the ambiguity and uncertainty in clustering tasks. Thereafter, we introduce the graph divergence regularization term for maximizing the variance of fuzzy indicator matrix, which not only avoids the trivial solutions in local graph learning, but also enhances the separability of data for explicit global structure. In this way, the local graph loss and global divergence regularization term are able to jointly capture the critical clustering structure. Finally, we can obtain the clustering results in accordance with the optimal fuzzy indicator matrix, which is updated alternately by the presented coordinate descent method in optimization process. Therefore, the desirable discrete labels come out automatically under the fuzzy strategy without extra discretization operations, which conforms to reality. The effectiveness of our method will be demonstrated through comprehensive experimental results.