Sparsity Fuzzy C-Means Clustering with Principal Component Analysis Embedding

The clustering method has been widely used in data mining, pattern recognition, and image identification. Fuzzy c-means (FCM) is a soft clustering method that introduces the concept of membership. In this method, the fuzzy membership matrix is obtained by calculating the distance between data points in the original space. However, these methods may yield suboptimal results owing to the influence of redundant features. Moreover, FCM is always sensitive to noise points and heavily subject to outliers. In this article, we propose a method called sparsity FCM clustering with principal component analysis embedding (P-SFCM). We simultaneously conduct principal component analysis and membership learning, and then add an additional weighting factor for each data point. The goal of this operation is to identify the noise or outliers. Overall, the benefit of our framework is that it retains most of the information in the subspace while improving the robustness of the noise. In this article, we employ an iterative optimization algorithm to efficiently solve our model. To verify the reliability of the proposed method, we conduct a convergence analysis, noise robustness analysis, and multicluster experiments. Furthermore, comparative experiments are conducted on both synthetic and real benchmark datasets. The experimental results show that the P-SFCM is competitive with comparable methods.