Semi-supervised possibilistic c-means clustering algorithm based on feature weights for imbalanced data

The possibilistic c-means clustering (PCM) algorithm improves the robustness of fuzzy c-means clustering (FCM) to noise and outliers by releasing the probabilistic constraint of memberships. The semi-supervised possibilistic cmeans clustering (SSPCM) algorithm improves the clustering effect on datasets with imbalanced sizes by introducing a small amount of label information. However, the traditional semi-supervised algorithm still faces the problem of low utilization of supervision information for datasets with large differences in sample sizes. Moreover, the Euclidean distance, which treats features equally, cannot handle feature-imbalanced data. Therefore, this paper proposes a semi-supervised possibilistic c-means clustering algorithm based on feature weights (FW-SSPCM) by introducing the ideas of supervised centers. First, the algorithm introduces the supervised center into the objective function of the SSPCM to improve the utilization rate of supervision information and thus guide the center iteration of small clusters. Second, the feature weighting strategy is introduced in the objective function to adaptively assign feature weights according to the importance of different features in different clusters, thus improving the adaptability of the algorithm to feature-imbalanced datasets. In addition, to improve the robustness of the antinoise effect and retain additional image details, a new image segmentation algorithm based on FW-SSPCM and local information (LFW-SSPCM) is proposed by introducing local spatial information obtained by bilateral filtering. Finally, through clustering experiments on synthetic data, UCI datasets and on color images characteristic of multiple features, including imbalanced sizes, imbalanced features and strong noise injection, the clustering performances of the proposed FW-SSPCM and LFW-SSPCM proposed in this paper are significantly better than those of several related clustering algorithms.