Fuzzy clustering of distribution-valued data using an adaptive L2 Wasserstein distance

In this paper, a fuzzy c-means algorithm based on an adaptive L
₂
-Wasserstein distance for histogram-valued data is proposed. The adaptive distance induces a set of weights associated with the components of histogram-valued data and thus of the variables. The minimization of the criterion in the fuzzy c-means algorithm is performed according three steps such that the representation, the allocation and the weights associated to the components of the variables are alternately computed until a the convergence of the solution to a local optimum. The effectiveness of the proposed algorithm is demonstrated through experiments with synthetic and real-world datasets.