Abstract
In semisupervised fuzzy clustering, this article extends the traditional pairwise constraint (i.e., must-link or cannot-link) to fuzzy pairwise constraint. The fuzzy pairwise constraint allows a supervisor to provide the grade of similarity or dissimilarity between the implicit fuzzy vectors of a pair of samples. This constraint can represent more complicated relationship between the pair of samples and avoid eliminating the fuzzy characteristics. Then, we propose a semisupervised fuzzy clustering with fuzzy pairwise constraints (SSFPC). The nonconvex optimization problem in our SSFPC is solved by a modified expectation-maximization algorithm, involving to solve several indefinite quadratic programming problems (IQPPs). Further, a diagonal block coordinate decent (DBCD) algorithm is proposed for these IQPPs, whose stationary points are guaranteed, and the global solutions can be obtained under certain conditions. To suit for different applications, the SSFPC is extended into various metric spaces, e.g., the reproducing kernel Hilbert space. Experimental results on several benchmark datasets and a facial expression database demonstrate the outperformance of our SSFPC compared with some state-of-the-art clustering models
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