Gaussian kernel fuzzy c-means with width parameter computation and regularization

• The paper provides fuzzy c-means algorithms based on Gaussian kernel functions. • The first algorithm computes the width parameters though suitable constraints. • The second algorithm computes the width parameters though entropy regularization . • Experiments with benchmark data sets shows the usefulness of the algorithms. The conventional Gaussian kernel fuzzy c-means clustering algorithms require selecting the width hyper-parameter, which is data-dependent and fixed for the entire execution. Not only that, but these parameters are the same for every dataset variable. Therefore, the variables have the same importance in the clustering task , including irrelevant variables. This paper proposes a Gaussian kernel fuzzy c-means with kernelization of the metric and automated computation of width parameters. These width parameters change at each iteration of the algorithm and vary from each variable and from each cluster. Thus, this algorithm can re-scale the variables differently, thus highlighting those that are relevant to the clustering task. Fuzzy clustering algorithms with regularization have become popular due to their high performance in large-scale data clustering , robustness for initialization, and low computational complexity . Because the width parameters of the variables can also be controlled by entropy, this paper also proposes Gaussian kernel fuzzy c-means algorithms with kernelization of the metric and automated computation of width parameters through entropy regularization. To demonstrate their usefulness, the proposed algorithms are compared with the conventional KFCM-K algorithm and previous algorithms that automatically compute the width parameter of the Gaussian kernel .