Pairwise constraints-based semi-supervised fuzzy clustering with multi-manifold regularization.

Introducing a handful of pairwise constraints into fuzzy clustering models to revise memberships has been proven beneficial to boosting clustering performance. However, current pairwise constraints-based semi-supervised fuzzy clustering methods suffer from common deficiencies, i.e., the insufficient and imprecise revisions of memberships, by which the further improvement of clustering performance may be encumbered. To yield more pleasurable results, this paper proposes a new pairwise constraints-based semi-supervised fuzzy clustering method with multi -manifold regularization (MMRFCM), which can overcome the above deficiencies simultaneously. Firstly, data are regarded as located in various manifolds, and the multi-manifold regularization is delicately designed to sufficiently revise memberships for all data objects to guarantee good overall clustering performance. Secondly, local structural information is incorporated into designed multi-manifold regularization to ensure the precision and stability of the revisions on memberships. Thirdly, the approximated non-linear similarities evolving from ensemble &Laplacian are applied to discover implicit local structures more thoroughly to further strengthen the effect of the multi-manifold regularization. Based on these strategies, MMRFCM efficiently exploits pairwise constraints to sufficiently and precisely modify memberships during the clustering process and thus achieves excellent results. Like most fuzzy clustering methods, MMRFCM is solved by alternative updates and the solutions are locally optimal. In the comprehensive experiments conducted on different types of datasets, MMRFCM successfully outperforms several classical and state-of-the-art fuzzy clustering methods in terms of clustering accuracy (CA), normalized mutual information (NMI), and adjusted rand index (ARI). The excellent results demonstrate the superiority, stability, and reliability of the proposed method.