Batch self organizing maps for interval and histogram data

"An extension of Batch Self Organizing Map (BSOM) is here proposed for interval. and histogram data in the context of Symbolic Data Analysis. The BSOM cost function is then. based on two distance functions: the Euclidean distance, for interval data, and the Wasserstein. distance, for both interval and histogram data. This last distance has been widely proposed in. several techniques of analysis (clustering, regression) when input data are expressed by distributions. (empirical by histograms or theoretical by probability distributions). The peculiarity of. such distance is to be an Euclidean distance between quantile functions so that all the properties. proved for L2 distances are veri\fed again. An adaptive versions of BSOM is also introduced. considering an automatic system of weights in the cost function in order to take into account. the dierent eect of the several variables in the Self-Organizing Map grid. Applications on real. data sets are proposed to corroborate the procedures."