Semi-supervised clustering, utilizing the supervision information to guide the clustering process, could improve the clustering effect of the models. Most of existing semi-supervised clustering models only consider pairwise constraints or pointwise constraints. In this paper, the semi-supervised method is applied to the fuzzy clustering algorithm, and a robust semi-supervised fuzzy clustering algorithm is proposed. Firstly, fully considering prior knowledge, our models integrate pointwise constraints and pairwise constraints into a unified framework to improve the clustering performance of the fuzzy clustering algorithm. Secondly, in order to alleviate the impact of outliers, the robust performance of the models is considered by introducing an adaptive loss function into the models. Thirdly, our models can capture the global structures and the local manifold structures of data sets. Finally, a simple and efficient algorithm is proposed to solve the models, which ensures that the obtained solution is sparse and satisfies the constraint conditions in our models. Compared with five representative methods, experimental results on public datasets, such as text dataset (dbworld), voice dataset (Isolet), image datasets (YALE, Umist), chemical dataset (wine) and biological datasets (colon, TOX-171), show the effectiveness of the proposed models.

In this paper, we present an approach to fit some clustering fuzzy linear regression models based on the fuzzy response variables and fuzzy parameters. In this approach, we first introduce a method for clustering crisp/fuzzy data based on fuzzy c-means clustering, and then, we fit some clustering fuzzy regression models based on the geometric mean. The optimal clustering fuzzy regression models are evaluated under two indices of goodness of fit. The applications of the proposed approach are studied in modeling some real data sets.

In this paper, we convert the fuzzy clustering ensemble consensus function problem into an optimization problem based on the reliability-based co-association matrix that minimize distance between co-association matrix of final clustering and co-association matrix of base-clusterings in the ensemble. The optimization problem is a constrained nonlinear objective function and we solve it by sparse sequential quadratic programming (SSQP).