Example of tree structures obtained over one iteration of the proposed feature selection algorithm. Possible generalized Dirichlet tree structures that could be obtained from the initialization step and one iteration of the proposed feature selection algorithm, for a composition Y with five components. Figure (a) shows a possible tree structure that could be obtained from the initalization step, where component Y1 is added first, followed by Y2. In the subsequent figures, one possible outcome of an iteration over the GDFS algorithm is depicted. Component Y3 is added in Figure (b), component Y2 is removed in Figure (c). Figure (d) shows the final step for this iteration, where the current grouping model Y(c)=(Y1,Y3) is permuted to Y(c)=(Y3,Y1). This would occur if the BIC of the fitted generalized Dirichlet model for (Y3,Y1) gave a higher BIC than that for the model fitted to (Y1,Y3).