Adaptive Fuzzy C-Means with Graph Embedding
This work addresses a long-standing challenge in fuzzy clustering for researchers and practitioners, though it is incremental as it builds upon existing FCM and mixture model methods.
The paper tackles the problem of automatically selecting membership degree hyper-parameters in Fuzzy C-Means clustering and handling non-Gaussian data, achieving effective results as demonstrated through experiments on synthetic and real-world datasets.
Fuzzy clustering algorithms can be roughly categorized into two main groups: Fuzzy C-Means (FCM) based methods and mixture model based methods. However, for almost all existing FCM based methods, how to automatically selecting proper membership degree hyper-parameter values remains a challenging and unsolved problem. Mixture model based methods, while circumventing the difficulty of manually adjusting membership degree hyper-parameters inherent in FCM based methods, often have a preference for specific distributions, such as the Gaussian distribution. In this paper, we propose a novel FCM based clustering model that is capable of automatically learning an appropriate membership degree hyper-parameter value and handling data with non-Gaussian clusters. Moreover, by removing the graph embedding regularization, the proposed FCM model can degenerate into the simplified generalized Gaussian mixture model. Therefore, the proposed FCM model can be also seen as the generalized Gaussian mixture model with graph embedding. Extensive experiments are conducted on both synthetic and real-world datasets to demonstrate the effectiveness of the proposed model.