  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.
