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In many applications of C-means clustering, the given data set often contains noisy points. These noisy points will affect the resulting clusters, especially if they are far away from the data points. In this paper, we develop a pruning approach for robust C-means clustering. This approach identifies and prunes the outliers based on the sizes and shapes of the clusters so that the resulting clusters are least affected by the outliers. The pruning approach is general, and it can improve the robustness of many existing C-means clustering methods. In particular, we apply the pruning approach to improve the robustness of hard C-means clustering, fuzzy C-means clustering, and deterministic-annealing C-means clustering. As a result, we obtain three clustering algorithms that are the robust versions of the existing ones. In addition, we integrate the pruning approach with the fuzzy approach and the possibilistic approach to design two new algorithms for robust C-means clustering. The numerical results demonstrate that the pruning approach can achieve good robustness.