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We present Batch Self Organizing Map (BSOM) algorithms for data de-scribed by distributions. As unsupervised classification algorithms, BSOM depend on a suitable choice of a distance measure. Using the L2 Wasserstein distance for distributional data and its decomposition, we show how adaptive distances can be exploited in the learning process for describing the structure of the data. Adaptive distances induce a set of relevance weights on the descriptors of the data acting, then, as feature selection method. We present different types of adaptive distances based on different constraints and, using real data, we show the results of the pro-posed method.