Kernel fuzzy c-means with automatic variable weighting

This paper presents variable-wise kernel fuzzy c-means clustering methods in which dissimilarity measures are obtained as sums of Euclidean distances between patterns and centroids computed individually for each variable by means of kernel functions. The advantage of the proposed approach over the conventional kernel clustering methods is that it allows us to use adaptive distances which change at each algorithm iteration and can either be the same for all clusters or different from one cluster to another. This kind of dissimilarity measure is suitable to learn the weights of the variables during the clustering process, improving the performance of the algorithms. Another advantage of this approach is that it allows the introduction of various fuzzy partition and cluster interpretation tools. Experiments with synthetic and benchmark datasets show the usefulness of the proposed algorithms and the merit of the fuzzy partition and cluster interpretation tools.