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Description
Currently, the way we define the contribution of non-aligned nodes to the cost function is as a middle point between a "perfect alignment" and the worst possible alignment. This implies that a wrong alignment is more penalized than a non-alignment. That is, given two vectors a=(0,1,0) and b=(1,0,1), muritz will avoid the alignment (a,b) and instead favour the alignment (a, NULL) and (NULL,b).
Although defining the cost function of non-aligned nodes as a middle point between the worst and the best alignments produces a perfect alignment of a network to itself, this definition is arbitrary and not necessarily the best option. We think that we should discuss whether or not favouring a bad alignment instead would be a better option. In addition, we think that the contribution of non-aligned nodes to the overall cost function could be a tool for identifying substructures that are highly conserved across environments. That is, given two different networks, studying the transition between favouring or penalizing non-alignment may reveal a global kernel between both networks.