| Summary: | With the rapid increase in the number of collected data samples, semi-supervised clustering (SSC) has become a useful mining tool to find an intrinsic data structure with the help of prior knowledge. The common used prior knowledge includes pair-wise constraints and cluster labels. In the past decades, many relevant methods are proposed to improve clustering performance of SSC by mining prior knowledge. In general, the prior knowledge is assumed to be beneficial to yielding desirable results. However, one can gather inappropriate prior knowledge in some scenarios, such as wrong cluster labels. In this case, prior knowledge can result in degenerating clustering performance. Therefore, how to raise safe semi-supervised clustering (S3C) should be investigated. A main goal of S3C is that the corresponding result is never inferior to that of the corresponding unsupervised clustering part. To achieve the goal, we propose safe semi-supervised Fuzzy c -Means clustering (S<sup>3</sup>FCM) which is extended from traditional semi-supervised FCM (SSFCM). In our algorithm, wrongly labeled samples are carefully explored by constraining the corresponding predictions to be those yielded by unsupervised clustering. Meanwhile, the predictions of the other labeled samples should approach to the given labels. Therefore the labeled samples are expected to be safely explored through a balance between unsupervised clustering and SSC. From the reported clustering results on different datasets, we can find that S<sup>3</sup>FCM can yield comparable, if not the best, performance among different unsupervised clustering and SSC methods even if the wrong ratio achieves 20%.
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